Something that someone pointed out once is that the general knowledge of modern/20th century mathematics, compared to other disciplines, is *extremely* poor.
Like everybody *vaguely* knows what a proton or DNA is. I think the average person knows a shocking amount about modern theories on dinosaurs, Shakespeare, rocks and medieval history. Most people have a vague idea of what ideas of Foucault or Said.
But very few people have ever heard of a Riemann surface or Grothendieck. There's zero public expectation that even an educated person should know anything about maths beyond basic calculus (which has been around for 500 years). There's an incredibly hard British quiz TV show called "University Challenge" and I remember that one of their hardest questions was on the definition of a Hermitian matrix...
To me, this seems like a major part of the answer.
Most people outside of mathematics don't have any concept of what academic math actually is. When I tell people that I'm a mathematician, it's common for them to ask what I actually do or to assume that I do some type of hard calculus because that's what they associate with "advanced mathematics". I don't mean this in any sort of elitist way - it's just that most people aren't exposed to math beyond calculus or maybe a linear algebra and differential equations course. If someone has absolutely no exposure to the idea of a group or ring, how can you possibly tell them about cutting edge algebra research in a tweet? I have an elevator pitch about my research that I use when laypeople ask and I'd say that 90% of the time they stop really listening before I finish the second sentence.
I also think that some of the self-promotion that I see in other areas would probably be culturally seen as ... tacky in math? We do self-promote in things like research statements, but I think even there, we tend to want to be very precise about our contributions in a way that isn't very compatible with hype. Individual mathematicians vary, of course, so there are exceptions who are more into the hype. But I guess I get the impression from my colleagues/friends that most of us view that hype with mild amusement.
I’m curious if maybe it has to do with the higher needs and competitiveness for grant money in other fields. This is my own ignorant hypothesis (correct me if I’m wrong) but it doesn’t seem to me like math necessarily relies on quite as much big money funding. In my own discipline people promote themselves quite a bit because our research can’t really happen without getting grants, and so it’s useful to be well known.
This is my understanding. A lot of experimental fields (medicine and experimental physics come to mind) require large facilities, expensive equipment, and lots of people, all of which cost money.
Many mathematicians, on the other hand, can make do with pencil, paper, and a large broom closet. The others will want computers, white/blackboards, a little more room, and maybe some time on the supercomputer, but these things are still orders of magnitude cheaper than precision optics, rare chemicals, or proper double-blind medical trials.
> it's just that most people aren't exposed to math beyond calculus or maybe a linear algebra and differential equations course.
I don't think most people have ever heard of linear algebra or differential equations. They've heard of calculus: it's that advanced math that scientists use.
I remember in undergrad telling someone that Linear Algebra had Calc 2 as a prereq and they didn’t believe me because “why do you need calculus for y=mx+b” and wouldn’t accept that it was anything other than y=mx+b.
Now when I teach linear, I hate telling non-math people for the same reason
I would be just as surprised to learn that Linear Algebra needs calculus as a prerequisite. Don't you just work over arbitrary fields anyways for a pretty long time in the beginning? Then why care about calculus?
It’s also helpful to have calc 2 when you want to give a range of examples of inner products since you can use the integral to define an inner product on continuous functions
It always interests me the slight differences in how math is taught around the world. In the UK, we would always use y = mx + c not + b. I’ve also noticed the differences in the order of operations pneumonics, we would use BIDMAS (Brackets, Indices, Division, Multiplication…) whereas in the US you guys seem to use PEMDAS. Also in the UK we have a weird thing for histograms, my teacher said her husband was a French professor of mathematics and he has never heard of them before, whereas here they are taught when you are ~14 I think? They’re pretty useless imo anyway 🤷♂️
I find it pretty interesting too. Here it's y=ax+b. In high school we also didn't learn sec or csc, maybe because they seem like the least useful ones, I guess, but it's hard to say the reason.
On the other hand we learned about simple integration in high school, for some reason. The funnier thing was that we hadn't actually encountered the differentiatial operation beforehand, not entirely at least, we used the prime symbol and didn't even mention what variable was affected, it was just assumed to be X.
Naturally this created a lot of problems past the first few classes as different letters got added, some of my classmates had trouble properly understanding that the different letters were treated as constants and should be reduced to zero if not tied to an X.
>Most people outside of mathematics don't have any concept of what academic math actually is. When I tell people that I'm a mathematician, it's common for them to ask what I actually do
Folks seem to think I must be an accountant or auditor because "being good at math" equates with numbers and money for many people. Even the more technical folks mostly only think of maybe up to calculus and linear algebra for use in engineering. Practically speaking, only other mathematicians have any idea beyond.
As a previous teacher, many people just blank when they start seeing symbols, or even when they see too many numbers. It's a culturally reinforced response because everyone instinctively wants to say they are "bad at math" to not feel weird. Most of them can actually do it and if you start talking about sports they'll start quoting statistics and actually analyzing it decently well while telling you so they can't do math. So there's some cultural aspect as well as finding a personal interest in it.
People at work know I have a math degree, and so whenever someone has an arithmetic problem, they ask me. I'm terrible at arithmetic. God awful. I hated math and barely paid attention until I had a great teacher in highschool, which is when I fell in love. My coworkers can't seem to fathom that I studied math and yet can't do arithmetic well at all. It's kind of obnoxious, because I think some of them think I'm making it up.
Out of curiosity, can you give us the elevator pitch? Sometimes it's the case that people just don't pick the right words to connect with an interested person
Sorry, I don't post anything about my research on Reddit because this isn't intended to be a professional account and it's identifying due to how specialized research becomes.
It's also not exactly a canned talk. I usually start by asking the other person a little bit about their background and then I explain differently based on what ideas/vocabulary they're familiar with. I do get positive reactions sometimes, so I think that I'm probably not terrible at it. I could also probably be better, but I think the loss of interest comes more from the fact that most people aren't really that interested and just ask to be polite or because they want a one sentence answer that is not really possible for me to give. It's easier in other fields to say something like " I study cancer" or "I study black holes". If I just say the name of an object that I'm thinking about, that's not meaningful to the person asking. Often even the name of my subfield isn't meaningful.
Haha, I definitely don't start by launching into an elevator pitch. I'll usually start by saying that I work in academia and do a little bit of teaching and mostly research. If they ask about my research, I'll give the name of my subfield and a 2-3 sentence explanation of what that is, usually with an example of an application that I think they'll like (even though it's not related at all to my own research). If they ask further about *my* research, I'll tell them that it requires a little bit of set-up and then start asking about their background if they still seem interested.
I have decent enough social skills that I try to give them some polite places to opt out of hearing more. :)
>most people aren't exposed to math beyond calculus or maybe a linear algebra and differential equations course.
Would you mind adding what people don't know? What does a mathematician do?
From this post I have learned that mathematicians are very well spoken.
On that note, the other 10% stop listening just after you finish the second sentence.
>Most people outside of mathematics don't have any concept of what academic math actually is.
While it's true, I'm still quite shocked by how little many experimental people understand how theoretical fields like (pure) math work. I spoke to a group that had mostly (lab-based) Biology/Engineering students and to their credit, labs/PIs and "umbrella/direct-admit programs" also exist in Math because "it's STEM."
The other day I was watching a video about debunking Terrance Howard appearance on Joe Rogan. At some point Terrance talks about how he found a "new wave and it's conjugates". The youtuber types conjugate into Google and goes "see! This is nonsense! You can't conjugate a wave cause it's not a verb!".
>Something that someone pointed out once is that the general knowledge of modern/20th century mathematics, compared to other disciplines, is extremely poor.
The overwhelming majority of the math we teach children is many, many hundreds of years old. Even for math majors, they won’t learn things less than about 150 years old until they’re seniors. For grad students, decades old. In a lot of fields, research-level work can’t even be explained in a meaningful way until several years into a graduate program.
That’s not to say some things aren’t accessible. Some problems in number theory are readily explainable to children, even if their solution techniques are not. The public could probably wrap their heads around “a new model for controlling and managing the spread of a plant disease in orange groves” and at least believe it’s important.
But yeah, most math is barely accessible to mathematicians; forget the public.
> Even for math majors, they won’t learn things less than about 150 years old until they’re seniors.
This is a bit of an exaggeration -- replace "150 years old" by "90 years old" and it becomes correct. For example, the term "abstract algebra" was coined in the 20th century, ideals in rings were first defined by Noether in the 1920's, and the importance of structures like abstract vector spaces wasn't really understood until the 1930's. Likewise, the first textbook on graph theory was *Graph Theory* by Dénes Kőnig, which was published in 1936. Metric spaces were defined by Fréchet in 1906, and topological spaces were defined by Hausdorff in 1914.
Yes, but aside from at the strongest of departments, most undergrads are not going to see category theory, except in so far as they'll here words ending in morphism.
I think the general public could easily get a vague inkling of what some of the important objects in maths are about. Mention a "manifold" at a dinner party, and you'll face bemusement. Mention an electron, Schrodinger's equation, or general relativity, and you'll get cautious nods. But a manifold is probably easier to explain than all the above!
I don't really see why there's an objective reason why general relativity or electromagnetism is in the public consciousness, but cohomology groups are not. We shouldn't expect that the public understands these ideas on any high level at all, but an inkling would be nice.
> I don't really see why there's an objective reason why general relativity or electromagnetism is in the public consciousness, but cohomology groups are not.
I think it is completely obvious why cohomology groups are not at all in the public consciousness while GR and E&M are. People have had direct tangible experience with E&M their whole lives. Even though GR is a much more abstract thing, people have heard in passing about its unusual *physical* effects. There is nothing physical about cohomology groups. Sure, they have a role in geometry, but not in a way that would ever make them an object of popular fascination like branches of physics are. Why should the public *care* about cohomology groups?
In the popular consciousness, atoms are visualized as tiny solar systems with the nucleus as a "sun" and electrons as "planets" even though that idea of atomic structure has been obsolete for about 100 years. And it's even used in the logo of the International Atomic Energy Agency. Such simple images persist despite being in accurate, but I don't see how you would convey a simple idea of cohomology groups (even with some inaccuracies) that the public would care about.
On the other hand, the public *does* know what prime numbers are and can appreciate that they somehow play a role in cryptography, which everyone has an appreciation for, even without knowing exactly *how* primes are playing that role. So prime numbers are an example of a serious mathematical concept that is broadly well-known.
This is pretty accurate honestly. My first intro to big boi analysis was with a really young professor. He stated that he was annoyed with the fact that he had to teach things to at were nearing 100 years old, and wished he could teach the newer concepts. Unfortunately, you kind of need the “basic” concepts to even start into functional analysis, and then a few more years of refining those skills to think about really understanding cutting edge stuff.
I can’t imagine being introduced to Hilbert, Banach, C^* algebras etc. without going through the process of learning the (now) classical concepts.
But I also agree with several other comments related to telling someone you have a phd (or BS/MS) in math and getting the “wow, you must be really smart!” Or the obligatory “what’s 687 times 4523?!”
Smile and nod boys. Smile and nod. (Edit: Girls too, or just people in general, ya know!)
There’s a lot of counterexamples to your general rule there, and I didn’t even go to a particularly good school for math. Differential equations, vector calculus, abstract algebra, combinatorics, game theory, graph theory, cryptography, analysis (Hilbert), computability theory (Gödel, Turing)… Maybe that last one feels out of place, but I pity the math major who wasn’t required to take a few courses from the CS department.
Hell, even physics majors get some modern math before their senior year. You need modern math to learn modern physics…
I was going to comment on the same thing. Are we talking about the French philosopher Michel Foucault or the 19th century physicist Leon? And which Said? The only Said I know is the literary critic Edward Said. I don't know any mathematical Saids.
you can safely drop that to <1%. any time someone tries to guess what portion of the population knows x, they tend to wildly overestimate the portion that knows the same things they do.
> about maths beyond basic calculus (which has been around for 500 years).
I sometimes wonder what life would be like if the average science education stopped in the mid 1600s. Darwin is 200 years too advanced. Boyle's Law might be acceptable, but certainly nothing on combustion (1700s), or even conservation of mass. No atoms or periodic table. Certainly no mention of nuclear physics, relativity or quantum mechanics.
I think a lot of people get mixed up because their science courses do at least mention the existence of relatively recent science, and some of the products of science are large and obvious. With a typical education we at least get the gist of what happens on an airplane wing or inside a nuclear reactor. So we mentally assume that we were taught similarly recent math, when in reality math education stops centuries before science education.
That famous Carl Sagan quote about his prediction for the looming American Idiocracy sure seems relevant. I’m not gonna quote it, you know which one I’m talking about if you’re on this hellsite.
The average science education arguably has stopped in the 1600s in parts of the USA, and replaced with Bible study. No Darwin is a given.
I suppose they still get Newton’s laws, for now…
Besides, the way a real mathematician hypes himself is to wait until someone else mentions a result he’s found and reply, “I knew that,” or, “I proved that in 1976, but I didn’t think it was worth publishing.”
That's a thought-provoking comment.
That got me thinking though if it would be fair to say then that the diminishing returns of research for mathematics dimminished much faster than other fields. Like the entire modern world is built on mathemics, but all that mathematics was developed so long ago, it is still good, and most people today do not have to learn 20th/21st century mathematics to participate in the 21st century.
But then I also remembered statistics and probability, where some parts of it are relatively more recent and they lay the foundations for all the machine learning and deep learning we have today.
Not really. Number theory was useless for hundreds of years, then we developed computers and it suddenly became important. Computational algebraic geometry is becoming more important along with topological data analysis etc.
>Number theory was useless for hundreds of year
That was kind of the point I was making that the older stuff produced significantly higher returns to scoiety because they are still being used in the state-of-the-art today.
In your example of DNA, it also produced high returns to society, but was also much more recent.
>Computational algebraic geometry is becoming more important along with topological data analysis etc.
It seems like new mathematics being developed today is only intended to solve a particular niche problem.
>being developed today is only intended to solve a particular niche problem.
Well, initially, calculus was just designed for orbital mechanics. It has to start somewhere.
I think the reason that you don’t get more mathematicians hyping their work on social media is i) it often takes a lot of background to describe a problem/solution, and ii) writing for other mathematicians in your niche subfield and writing for a more general audience are distinct skills. Most mathematicians do not practice the latter, so writing for general audiences can be very time consuming. I find that you end up describing mathematical ideas to a general audience using analogy, which can introduce inaccuracies. I have a lot of respect for outlets like Quanta that specialize in finding ways to communicate mathematical thinking with reasonable fidelity to a non-mathematical audience.
> I find that you end up describing mathematical ideas to a general audience using analogy, which can introduce inaccuracies.
That's true of physics as well, but people do it anyway.
I don't think the concept of inertia requires much math to understand. Neither does the concept of forces attracting or repelling each other. If you want to actually *do* physics then sure, math. But explaining "how do moon go around earth" can be explained as far as anyone will need to understand with basically no math at all
Pop physics is physics without the math, how are we going to make math without the math? We have Numberphile and it's great, but compared to pop science it's nothing.
that's not nice. everything produces crackpots, just ask math departments who get letters about proving that pi is not irrational.
but indeed, i learned discrete math in uni, and i would LOVE to learn more about other areas of mathematics more at a level i can understand. and many other people as well. we are just not as loud and abnoxious as the crackpots
I wouldn't say "produces". It seems more likely that delusional, arrogant, and egotistical people would exist regardless. Pop science simply makes science accessible to everyone including them
Pop science mass produces crackpots but it also mass produces scientists. Pop science gets people introduced to science it's up to them what they do with that
There are some magazines (especially Quanta) that do a fantastic job in trying to appease the general public to enjoy mathematics. I do also believe that some Youtube creators (like 3B1B and Numberphile) do a great job.
Mathematics (mainly pure) is always going to be difficult to explain to the general public. The level of research is so advanced, detailed and "out of contact" with the real world (abstract) that it becomes a tremendously difficult task. Physics and biology for example are way easier because people can grasp the fundamentals. Some areas of mathematics (more on the applied side) can perhaps be more easily explained to the general public.
I think there has been an increase of content creators that take the approach of Quanta and 3B1B (focus on visualisation) which is very nice. I hope we can take this to more "mainstream" media in the future and maybe attract more people to this beautiful subject.
Advanced math exposition rarely leads to increased understanding. In fact, it's usually the opposite. People with no math background seem to always come away from exposition with loads of misconceptions.
There are too many people who genuinely believe 1+2+...=-1/12. Almost everyone thinks fractals are self-similar shapes. Even those who know these things are not true couldn't tell you why.
The average math understanding is so poor that communicating about math is like trying to explain things to someone who speaks a different language.
Its magic to 99.99% of people.
In the 1700s, Jean-Baptiste Fourier finds that periodic function can be thought of a sum of trigonometric functions, now Fourier series are the basis of the modern music industry.
In 1917, Johann Radon defines a new integral transform, it becomes the basis of CT scans.
In 1928, Paul Dirac finds 2 solutions to an equation, now PET scans are used to find cancer.
The average person knows nothing of this.
> It is weird that we live in a world where most people do not know the quantum notations
Yes and its the biggest science revolution in the past 100 years. Just mention transistors and people know its important.
This feels true; mention quantum mechanics and people thought of transistors.
Mention .jpeg / .mp4 and nobody thought of Jean-Baptiste Fourier.
I certain that there's a big problem in mathematics communication between experts and the mass of people.
The general public barely know the alphabet of math. How am I to talk to them about my multi-paragraph long research, or describe the context of a mathematical result? How does one describe the result of research into English to a person who can't spell, or even read?
By the time I've reduced math research into something that an undergrad can understand - I've already robbed my statements of meaningful truth, everything becomes obvious and trivial. Plus I've wasted a considerable amount of time producing content that will be ignored or dismissed.
For example; I study the normalization of volume forms via generalizations of mean curvature flow within the canonical tractor bundles associated to parabolic geometries. To describe why I study such things is easy for someone who understands the importance of geometric invariants and the difficulty of producing them, but to anyone else such a thing - or why I should be so specific about which geometric invariants is meaningless.
Even mathematicians only speak their own dialect. An analytical number theorist wouldn't even understand the abstract of a paper on symplectic geometry. How on earth do you expect a layman to?
A virologist and a neuroanatomist won't know the state of the art in the others' fields, but they can have a meaningful discussion about their own research with each other because the distance between their fields at least admits a common vocabulary. But if you put a biomathematician like me in a room with an algebraic geometer like you, there's going to be a lot of time in just getting basic definitions out of the way.
An Ubuntu Linux distribution for farmer-hackers who root their agricultural equipment and yearn for freedom from the tyranny of John Deere. (Seriously, [they exist](https://en.wikipedia.org/wiki/Right_to_repair#History).)
We should swap knowledge! I know about tractor bundles - but mean curvature flow is doing my head in.
Roughly: It is possible to convert an over-determined system of PDE over a manifold into vector bundle (called the prolongation) in such a way that solutions to the PDE correspond to parallel sections of the bundle. If you do this "just right" the resulting bundle has a uniqueness property that implies that it is the associated vector bundle of a Cartan connection where the representation is "nice". When this happens the bundle is called "a tractor bundle". If it is very nice then it is called the "canonical tractor bundle" associated to the prologation.
So.... mean curvature flow used to find solutions of PDE on manifolds.
Why do you study such invariants? I have heard of canonical tractor bundles appearing in Cartan geometries, but I'm not familiar with the analytical/PDE aspects that you mentioned.
Good question.
In Riemannian geometry (geometry of principle bundles with groups that "allow" a metric) we know what all the "equivarent invariants" are. Some research in the 60s and 70s figured this out.
We don't know the answer for geometries associated to groups that do not "allow" a metric. Efforts seem to be focussed on conformal geometric and the geometric of projective manifolds (of some type that I don't understand). Both of these structures fall under the heading "projective geometry". Which as you mention is roughly the geometric of Cartan geometries without the restriction that the lie algebra that the connection takes values in is associated to the lie group that gives the bundle.
Just a friendly comment (it's by no means a criticism but more of a question, I don't know anything about your field) because I am probably the type of idiot who would not get what you are talking about but can get it in a few days (i.e., generally what you do, not your papers) if I need to and refer to the definitions:
For some reason, "the normalization of volume forms via generalizations of mean curvature flow within the canonical tractor bundles associated to parabolic geometries" does not seem like the friendliest way to explain your research (I would not say that's for sure the case because I do not understand some of the terms and I need to Google it).
Usually, people start by explaining the challenges they work on, and then follow up with a high level description of the technique.
You, instead, decided that no one will get it because they don't already know the challenge, while the challenge is usually the first part of a post of presentation.
Usually, when: "why I should be so specific about which geometric invariants is meaningless.", well, in this case just don't state it in Twitter (?)...
I actually appreciate the technical definition as well though, because it can help me to learn the concepts if I need to.
It's always clarity vs rigours (well, not always, but many times... Sometimes "simple terms" are a mess).
i’m doing warped product manifolds and the heat kernel / spectrum of the laplacian on cusps induced by a warping function. doing this on S^1 X_f S^3 (warped einstein universe) has implications on thermodynamics, and i can’t explain anything about my research to people outside of math and/or physics. even with those people i’m doing something pretty niche
has smooth warping, but the warping function applied to the metric causes little “spikes” that extend to infinity but keep the manifold of finite volume. they can be thought of as singularities in the einstein universe
I think there are three main problems.
For much of modern mathematics you will need formal training to even hope to understand what a paper is about and even then you will probably have to read up on pre-requisites if the paper wasn't written in your particular field of expertise. How are you going to communicate this to a person who only vaguely remembers what a matrix is.
The next issue is making laymen care about your research. To an outsider mathematical research probably seems like a massive waste of time. They probably don't know anything about how often seemingly abstract results have been used for solutions of concrete problems years or decades after. Or how the developed machinery helps in other areas like homology was developed for studying topological invariants but then moved on to applications in other fields. In other fields than mathematics you can at least give a vague idea of how your research could be useful without going too much into details most of the time.
Last but not least, people have been conditioned to hate maths. Schools aren't exactly good at making people fall in love with maths. There are too many cases of bad maths communication which is then attempted to be compensated by inflicting pressure on students. Maths being a considerable hurdle in a successful graduation - be it high school or college - which directly impacts your chances of "making it" damaged maths reputation. I've had numerous people tell me that they hate maths immediately after me telling them I study it. With YouTube channels like 3Blue1Brown this has certainly gotten better, but it's still a niche subject not a lot of people will care about unfortunately.
One thing I love about mathematical culture is that we frown on researchers who overhype their work. Of course, some amount of hype is necessary in order to improve funding, but we’re not going to outright lie about what we’re doing. If we cared more about money than honesty, we certainly wouldn’t have become mathematicians. While I certainly think the general public and politicians *should* financially support mathematical research, it’s unethical to trick them into doing so.
>How tf the public going to fund pure mathematics if they cannot imagine what mathematicians are doing.
That's not how scientific research gets funded. Soecific branches aren't ran by the public to see which gets funding. It's done by an organ like the NSF and grant proposals are reviewed by the panel. Pure math funding in this sense depends on how much political power mathematicians have on these. Directors of the major institutes also regularly communicate with elected representatives, both formally and informally. Whether math research gets sufficient funding isn't because we don't have good enough instagram pages.
Have you seen the state of math on social media? The majority are trying to do basic algebra using fruit or simplify an arithmetic expression, and failing…
Aside from the fact that it is just part of the nature of modern math that it is VERY hard to communicate in any meaningful way to a non mathematician, as others have already said, I would add that I don’t think it would inspire funding the way you’re hoping. I think for most people, if they had a vague understanding of what mathematicians do, the response would be, “the fuck, this is what we’re paying for?” Fortunately, people see mathematicians as magicians who do the unknowable sorcery that underlies the rest of the sciences, and that’s enough to justify funding. Consider this: if the very dumbest people fully take governmental power (cough-maga-cough), then much of the sciences will be quickly defunded, but I’d say there is a chance that math won’t be, and this is because it is opaque, so it hasn’t been demonized by idiots.
>the fuck, this is what we’re paying for?”
To be honest they are not paying very much. Sure, we have nice conferences every so often; but mathematicians are badly underfunded compared to chemists or physicists. It's much easier to get funding for a postdoc or PhD in physics compared to maths. In Europe, at least, mathematics has the funding level of a humanities subject not a science.
The head of the physics department goes to the dean of the university, asking for funding to build a new cyclotron. The dean groans at the tremendous expense, and asks “why can’t you be like the mathematics department? All they need are paper, pencils and a wastebasket! Or the philosophers - they don’t even need the wastebasket!”
"Fortunately, people see mathematicians as magicians who do the unknowable sorcery that underlies the rest of the sciences"
THIS IS SO TRUE. I once encountered a problem; didn't understand the math -> blindly bow-bow-clap-clap convert the formula to programming language and somehow it is true.
I don’t think I or anyone else is suggesting lying to the public—I’m not really sure what you mean. I think the closest most mathematicians get to lying to the public is when they try to make tenuous claims about real world applications of their research in NSF grant applications. Let me clarify something though: I very much support people’s efforts to try to communicate math to general audiences, I just have doubts that it is an avenue to increased funding. And when it is, that’s probably where you would find a bit of a lie (e.g., knot theory is really cool, here are some pictures, and it’s important because DNA unknotting and stuff). And honestly I think that’s fine.
Other fields need a lot of research funding to survive. If you're a particle physicist, 10% of your job is actually doing particle physics and the other 90% is begging various organisations and government departments for a new particle accelerator. Ultimately, most pop science exists because most scientists want the public to vote to make the funding pot bigger.
Mathematicians are content with a few notepads and pens. The really boujee ones might treat themselves to some hagoromo chalk. They therefore don't need to fight for funding in the same way as other scientists - a university can pay salaries for an entire maths department for less than they'd spend on equipment/supplies for a single chemistry lab.
My parents, both chemical engineers who graduated from [my country's leading technical university](https://en.wikipedia.org/wiki/National_University_of_Engineering), which has a reputation for the brutal amount of math, physics and chemistry you need to know *just to be admitted in*, never mind to survive the first two years...
... even they struggle to understand what I do, when they ask me and I answer them. And I'm also an engineer, so I'm a bit more qualified than the typical mathematician at communicating in terms an engineer would understand.
Given this, I hold no illusions that math can be hyped in social media, or that it's worth it to even try.
There's one big reason that I'm a little surprised no one's mentioned yet, although it is something we as a field are generally hesitant to mention: 99% of pure mathematics research has no, and will probably never have any, applicability outside of pure math itself, and that's totally fine to us.
When people ask us things about how pure mathematics is "useful", we all have the same rote answers in our back pocket, like how important Fourier transforms are, or how number theory turned out to be key to the development of cryptography decades later. If we want to get into things more esoteric in the general public, we might mention how significant Lie theory has ended up being in mathematical physics, or the fundamental connections between category theory and functional programming. Then we usually cap off with "we can't know what will be useful until the future; there's always a chance that something that seems useless now will turn out to be key to something in a hundred years." This is all true, but we often leave off "but even if my own research never finds an ounce of use, I don't mind, since I just love learning more about this topic for its own sake."
Pure mathematics research simply isn't _about_ what benefit it could bring outside providing more insight into mathematics itself. It's research for the sake of learning more about mathematical structures and their properties. And I don't say this to denigrate it, because I think that's awesome, and research for research's sake _should_ be more valued than it is.
Honestly, I'd bet this is probably the case for a lot of theoretical scientific researchers too: that they research not because of how it might be useful, but for the sake of learning more about things in and of itself, with applicability as a secondary concern. It's just not as big a "problem" there because...well, the things they're studying are things that exist, not platonic ideals of mathematical structures. Things like "research for the sake of learning more about high-energy particle interactions", or "learning more about ursine genetics", or "learning more about mantle boundary conditions" are blatantly tied to the real world, and so need less justification to laypeople than "learning more about independent set enumeration in trees".
My advisor was asked (mostly as a joke) the following question at the end of his PhD defence:
"If you're stuck on a plane and were asked about the applicability of your research to the layperson, what would you say ?"
His answer ? "Can you get the door for me ?"
Jokes aside, the thing about modern maths is that, in order to even state the definitions or communicate the vague ideas, so much prerequisite knowledge and context is needed that, should you take a jab at any kind of explanation, you would have produced a PhD candidate by the end of it.
I think it’s because maths a lot less tangible than any other subject. It requires a lot of abstraction, protons, shakespeare, big bang, it doesn’t require any imagination it’s all there, compared to a riemann surface which isn’t so easy to conceptualise.
>How tf the public going to fund pure mathematics if they cannot imagine what mathematicians are doing.
It's not the public who decides, it's the NSF, which has a better idea of what research goes on.
There's Mathologer, blackpen redpen, and tons of stuff on well established math. There's like a zillion videos explaining Fourier Transforms, specifically.
As for new research, if I were a mathematician, I wouldn't show any work in progress to anybody publicly like that until I had it published. If you show stuff before that, A it could be wrong , and B someone else could publish it before you do.
The biggest problem is the level of abstraction involved in pure math that many people find alienating. A large amount of people already struggle with calculus, trigonometry, and high school/early college algebra and these subjects are very commonly used to describe the natural world. Trying to convey concepts and developments in topology, analysis, set theory, algebraic geometry, etc., to the general public would be much harder, especially in short form social media that can be found on twitter, instagram, and tik tok.
The best math communication I have found for pure math has been youtubers like numberphile and 3blue1brown (and the channels they inspired), but that is because they spend a lot of time laying the groundwork and developing an intuition for the problem at hand. Due to this, their content requires some level of time investment and interest that many people using social media do not have or want to give to math. They have done a great job at increasing interest in math (i can attest to this personally), but I do not think math will ever have quite the same appeal to the general public as the sciences which are inherently tied to understanding tangible concepts about the world we live in. I think more can be done to increase public interest but it will be an uphill battle in a world where a good amount of people’s immediate reaction to seeing math is either “math is boring/when will i ever need to use this?” or “i’m just bad at math”.
Imagine Banach and Tarski hyping their work on the internet by saying that it is possible to split a soybean into *finitely many* pieces, move them around, reassemble them to obtain a solid ball as large as the entire earth.
Well we have grant sanderson who does a great job and the SoME does exactly what you’re asking.
I can’t speak for everyone but what I’ve noticed among people my age and demographic (young black males) is math is scary(I disagree with this), you have to be genius to be successful(I double disagree), it’s boring(disagree), and there is no clear use or point to math(again disagree). When I’m more qualified, after my prospectus or something, I have hopes of being sort of like grant but for people not remotely interested in math, among other things.
Communicating with the general public is not mathematician's strong suit, and often one of the worst.
In addition, explaining to general public on high level pure math is extremely difficult to begin with, and those mathematicians are not able to tell people how their research can be useful because they do not care AND they don't known.
Applied math is a whole lot better at least you can tell people how it matters to certain real world problems
Compared to what exactly? Other sciences are heavily grounded in the applications to real world events. I.e. we filter micro plastics but none of the underlying science.
Even ML which isn't super complicated and has a lot of eyes on it is entirely framed in its applications. The number of people who think chatgpt is going to be sentient is vastly larger than those that can explain the transformer architecture and why it matters.
just because the majority of people do not understand math beyond calculus it does not mean that math is in any jeopardy. everyone knows how difficult it is and know that in some shape or form whether by intuition or belief that math is invaluable to humans and it is here to stay no matter how reclusive it may seem.
Because we abide by the statement “the pleasure of finding things out”, and further refuse to dumb down our theories for the masses the way scientists so publicly do just to get likes.
If you want to understand differential equations, we will explain it to you until you understand it, or die trying, but we will not allow you to skip the details.
If there’s a hot new physics result, there’s usually a way to literally point to either some application or something, well, physical. “We’ve detected a black hole merger” means something even if you don’t know how we detected it, what general relativity is, or even what a black hole is. Likewise, if you say we’ve made a breakthrough in fusion energy, they can form an image in their head of what that means even if it’s 99% wrong. Even if all their working definitions of the terminology is completely wrong, a lay person can think they understand a part of it, visualize it, and maybe even grasp why it’s important (like cheaper energy or a better battery).
For an important mathematical result, none of the words really mean anything for a lay person.
Also, in science, a lay person has an image of someone doing experiments or pointing a telescope at the sky. Someone might think an economist just spends their time trying to balance the government budget, but hey at least the budget is relevant to economics! If you told someone you’re a mathematician, they might unironically think that you just calculate big numbers all day or just purely teach. They have zero cultural exposure to what mathematicians actually do.
In contrast, applied mathematicians probably have a much easier job explaining what they do. “I came up with a way to do simulations more accurately” or “I sped up the computer calculations” might be crude but at least gets *a* basic point across.
It’s also CS people are more united imo. Open source projects etc etc… they need the visibility so people maintained most of the projects while other fields people are way more gatekeeping and greedy. Can’t think of any other field as cooperative as it’s CS
I would argue that the lack of "proper outreach" is an issue for math. I am at a very applied math institute, where our day-to-day work is more computational physics than actual "pure math". However, to explain our work and its importance to people outside the community still takes enormous effort, eventhough our work has direct consequences on i.e. industry applications.
The lack of outreach also has consequences on the amount of funding we can obtain. Often even small funds for projects in e.g. experimental physics have budgets of far more than a million €. Meanwhile if the entire math departement gets this much money per year, they can consider themselves lucky.
I believe for outreach in math to be effective we might need to start earlier in school and teach math more rigorously but also display the applications to motivate.
>How tf the public going to fund pure mathematics if they cannot imagine what mathematicians are doing.
I think you should read some basic political science textbook so that you'd learn that the public is not making decisions about funding anything: the public delegates the power to the government, and it is they who make such decisions. Some of these decisions may be unpopular, other may deal with arcane matters such as funding fundamental science, but it is not the case that everything should be understood by the public to get funded.
I tried and can confirm this very much:
> Mathematical research is complicated and takes a very long time to read. Hence, noone will leave any kind of response to these research if being publicized.
It even applies to r/math, or any math forums not focused precisely on the topic of research (except when the subject is sufficiently mainstream).
About funding.. well, you have to talk to the right people (especially being lucky enough for them to listen to you), I guess. These are usually professors who are paid more for their administrative work and teaching than anything else.
A bit part of it is that there’s a limit on how much math can be taught over the course of a k-12 education. By the time you reach grade 3, most students are still grasping multiplication tables and basic algorithms for larger numbers. By 5th grade you might be starting to get into some basic algebra (solve for X type of problems). Middle school is then mostly an introduction to basic trig, geometry, and more complicated algebra. Over the next four years of high school the furthest that most students will make it is to calculus.
To discuss even the concepts of any more advanced math you need to have this foundation. It’s not like chemistry where you can say “there are these things called protons, but don’t worry about how they behave.” You can grasp the concept of a proton without even having a discussion of quantum chromodynamics or the residual strong force. As far as I know, there’s nothing in pure math that can be explained as simply.
There is no clickbait stuff in mathematics.
E g. People want to hear wormholes, not the math behind it. People want to watch the AI generated stuff, but not the linear algebra, calculus and loads of other math that made it possible.
Well, the problem is, as many others have said, is that the public has an extremely ignorant view on mathematics. For example, when I say I got my bachelors in mathematics, most people who try to talk about math talk about trigonometry, adding/multiplying arbitrary large numbers, geometry, and equations. No one would understand my interests in non commutative ring theory. Not even half of the undergraduates/graduate students. Another reason relating to the previous note is that is hard to explain research mathematics to laymen. Research mathematics is also very hard for mathematicians that are not even in that field; meaning, mathematicians tend to be very specialized. Lastly, if the general public could understand mathematics, it would definitely reduce its funding. Pure mathematics, even for me, has almost no public utility. For example, nothing in model theory or category theory could be used in real life; what is the application of the Yoneda lemma in real life look like?
People simply don't care, and many mathematicians don't want to bore people. Quite simply, we find our fields exciting, most people don't, so why put them through that? As has been pointed out, general mathematical knowledge is thin. People may know what the Pythagorean theorem is, they may vaguely remember the quadratic formula, and that's generally it.
The language of math is somewhat dense and doesn't always translate well for general audiences. Physics is exciting when stripped down for general consumption, filled with nest words and intriguing possibilities. Harder to replicate that with math.
I think another aspect is that most mathematicians don’t want to do pop math. Most researchers who are interested in doing something more glitzy are typically drawn into other fields. Part of the joy many pure math professors get is that there’s no bs, they are just messing around trying to solve puzzles they find interesting, and selling people on that is not the point
In my view, it's partially because most interesting mathematical results won't fit in a Tweet (an...X?) or in a TikTok. I think part of it is also because mathematicians, even really good ones, realize that they fit into a community and don't want to hype their stuff without showing deference to mathematicians whose work provided the foundation for theirs. (This is also why even single-author papers tend to use the pronoun "we".)
I'll quote Evan Chen:
"I think that if the general public understood what mathematicians *actually* do for a career, they just *might* be a little less willing to pay us."
The reality of it is that:
• Pure mathematics is very difficult to popularize, because most of it is just playing around with rules of logic, with a specific interpretation for your symbols in mind, with no other application other than producing more results in pure mathematics.
• If you're a pure mathematician working on the cutting edge, there's usually just a handful of people in the world, who can *begin* to understand your research, without spending at least a few years studying the preliminary formalisms. And the reason these few people can understand the cutting edge research is due to them already working on the same problems, so they already took the time to master the required information.
• Working on modelling drug behaviour (one of your examples) is already in the domain of computational physics, not pure mathematics.
• When asked, most pure mathematicians cannot provide an example of where their research could be applied, because quite frankly they don't know. They don't think about it from that perspective.
But yes, all of this means thst getting funding is rather difficult in pure mathematics. There have also been quite a few attempts to get rid of pure math departments across different application-oriented universities in the past.
And yes, people blab about all kinds of science topics without knowing anything about it, and the result is the spreading of misinformation. The public is not willing to work on mathematics full time, so they could become informed, and therefore tweeting about pure research math to the general public serves no purpose.
1) Audience capacity to understand
2) It's sort of seen as gauche? Like there is plenty of ego, don't get me wrong, but there's a culture around it where the work is supposed to stand on its own. If it's significant, it will make itself apparent.
3) Assuming "pure" math - hype doesn't get you much. Other fields of research you need resources ($$$, access to equipment) to get on the cutting edge. Shiny research gets you the shiny toys. Math is cheap. The only thing you really need to fight for is time. So the ROI on self-promotion is low.
Either the result is insanely complicated and can't be understood or its insanely trivial sounding to the point where the public says "so what?" That is the problem with 40 character explanations of math research.
I think Cédric Villani's interview on numberphile (https://www.youtube.com/watch?v=xopM9BFjcNo) gives a quite interesting explanation. Math doesn't really need all that much funding (since pen and paper is infinitely cheaper than particle accelerators, fancy instruments or hard-to-produce chemicals), so the culture in academic math isn't as focused on trying to broadcast how important your work is to try and get grant money, and therefore mathematicians aren't used to trying to explain their research to a non-specialized audience. I will say, quantamag seems to be only outlet genuinely trying to present the weird and wonderful world of math to a general audience.
if i published the things i did in social media, most people will have no clue of what i’m talking about, and the rest is people i would rather tell in person.
also… i don’t know if “like other scientists” is a good comparison. i don’t really think math is a science. and sciences talk about… the real world, and things a lot of people already care about.
Exactly. My first thought when reading "Why mathematicians do not hype their research on social media..." was that the OP obviously has not heard of Ono.
For the funding part, this is usually inherent in their applications. Usually federal funds to research things of interest for the government like cryptography. What is the purpose of hyping it up at all? It's not a product to sell. The people you convince are those likeDoE or DoD not the public . We the researches go to these government departments and convince them, not the public
I work in stochastic analysis, and more recently geometric measure theory. I feel like I could explain most of my projects to a layman with some knowledge of calculus. So yeah I’m not sure why it’s not done more often.
There are a couple hype places (eg Quanta), but they tend to focus on somewhat accessible work and their pieces are pretty clearly being suggested by a small group of sources who are academic mathematicians (eg Gil Kalai).
I’d say mainly that math is easier to judge than other subjects, so the hype cycle is just less important to publication decisions. It also means math tends to have a more hierarchical journal system than other subjects, and mathematicians attach a lot of meaning to publication venue (other subjects do this too, but to a slightly lesser extent). As a young mathematician, publishing a paper in Annals, for instance, does more for your career than any publication decision which happens in computer science, for instance.
I spend a fair amount of time finding ways to make my work accessible to a general audience, although I try to be careful about not hyping the results too much. For me, that means maintaining an blog and occasionally making YouTube videos about my work. This is a time intensive process, but I do think it’s worthwhile to do outreach.
I might be wrong, but I believe this has to do with the usefulness of what's being hyped and how easy is for the non researchers to undertand it. For example, news about stuffs arriving in Mars is kinda easy for a normal person to understand what is happening and what's the importance of it, even tho they dont know "how". The same with the progress in the AI field. Now if someone solves the P X NP problem, how would a non mathematician understand the importance of it and what this even means? I guess mathematics has achieved a point where most of the new discoveries are too abstract and complex for a normal person to understand it, not only the "how" of the discoveries (like in most of the other fields), but also WHAT is being discovered
This is extremely taboo in math. Other mathematicians will hear about your work the normal way, via Arxiv and via the community. There are probably only a few dozen specialists on Earth who really understand it anyway.
If they did, it would mean nothing to anyone who isn't a mathematician or studying math in university currently. Without stripping all of what makes it exciting just so it can be accessible.
Plus, most math research is not about having some application or potentially benefitting society.
The research that gets hyped up involves stuff people either have a vague or basic understanding of, could potentially impact either them or society in some way, or it's just cool.
EX: I study active matter in the chemistry department. Many people, when I told them I studied chemistry and math during undergrad, they could appreciate the chemistry because of basic experiencing or understanding of how chemistry as a field has benefitted society.
Just look at physics. At the high level, physics is very math heavy. Yet, an average person asked at random will have more appreciation for physics than math.
Or how, relative to other fields, mathematicians don't really have to care about speaking to non-mathematians regarding their work all that much if its not applied work.
Like, in my chemistry field, I'm being trained to speak to a wide range of people and knowledge. From experts to people who only know high-school chemistry. Even though most of the work I do is theoretical and computational based. Since it's common for chemists to speak to a wide range of audiences. This idea applies to other fields, STEM or not.
Math, though, unless you do applied math research of some kind, there's no reason to train a mathematician in stuff like this really
I'm pretty sure they do, people don't find it so interesting but I keep up with plenty of math communication to the public on YouTube and Twitter.
I personally don't find the need to speak to an empty room. I'll tell my friends because my friends are also studying math tho, and I welcome any curious people. And I also just don't use social media.
And perhaps another thing is that mathematics pertains with *proof* and normal people just don't mesh with formal logic, it takes effort to to tell something informative and engaging to the public that's also *correct*
From my (non-expert) view, it seems like black holes are more comprehensible to a layperson on some basic and oversimplified level than whatever vector calculus/infinite series/whatever the mathematician found.
It's very simple actually. Math isn't science. It's best understood in this situation as a language.
Say I study elvish. I read and write it with calligraphy, I speak it, I study all of the Tolkien books, etc.
Someone comes up to me and asks "can you show me what you do?"
Naturally I start speaking elvish.
"But I don't understand, can you show me what you do, but in English?"
No, I can't do that. I can just explain that I do elvish. If you want a taste of that you need to put in the effort too.
Lots of complicated math could be made somewhat (if only roughly or vaguely) accessible to much more of the general public. I think the limiting factor is really trying to get people interested in it. It's easier to grab interest if you can make the case that it will lead to warp drives or teleportation or whatever is the current popsci hype. An important part of this is also getting mathematicians excited to share their work to the general public.
Do you understand what he's doing? That's why he's not hyping it.
It's much easier to understand "this cancer research will save lives" than it is to understand "this theoretical maths proof will advance other areas of science".
Consider computer science - it's all just applied maths.
Computers don't work without binary maths. There is, afaik and I'm sure someone will correct me if I'm wrong, basically no value in researching binary maths without other sciences existing to use it.
I remember talking to my professor about something similar. He was actively working on the same conjecture for like 30 years. Although he made an insane amount of progress, he refused to lean in any general direction of suspected outcome. His answer was essentially still, “Yeah, still I have no idea if this is true or false.” Even when pressed on a leaning, he was adamant that he genuinely didn’t know one way or the other.
This relates, because I think that math research is very “pure” compared to other fields. Where if I talked to my professors about their research in other fields, there was an obvious leaning, “We suspect this is almost certainly true (or false).” But math was always met with, “I don’t know, and I don’t care. It’s not about being right or wrong, it’s just about the pursuit of truth. I don’t care one way or the other about its truth value. I only care to prove it.”
Coming from the perspective of someone who is certainly not a mathematician or particularly gifted at math, I think it's the failure of public education. Mind you, this is VERY subjective and from a layman's experience but the feeling I get is that many people are taught the "what" and not the "why" or "how" at a young age because math is so damn complex, even though it's important to teach children. In high school there were very few times here I was taught why I was using a cerain equation or how it was discovered. It felt like I was never getting the full picture of why I was doing something which lead to frustration since it was as if I was just doing busy work. I had a long conversation with my friends about this and we all had pretty much agreed despite going to different schools. When I got to college I continued to have not interest in math until I took logic as one of my philosophy course requirements. It felt like everything I did had a reason behind it and I fully understood the steps I was taking through a problem. This was literally the first time I was excited to move into a new unit to see how what I've learned builds on predicate logic, set theory, etc. and what contemporary problems or weirdness happens in logic research. I definately appreciated math much more when I moved onto stats for my psych requirements. The irony of all this is that I, a social worker, am more interested in math than most of my firend group which consists compuer scientists and engineers. They're certainly better at math than me but I still want to learn more than them!
TL;DR I think most young people aren't being taught in a way that encourages curiosity which leads to disinterest, misunderstanding and unfortunately hatred for math, leading to low hype for mathematics research among laymen.
I try to, e.g. this was very well received: https://beta.epiplexis.xyz/logs/crystalline Granted that was about the process of doing math research, not really explaining the details, but I do that elsewhere.
Math is a kind of philosophy, but with the real universal language. I think mathicians doesn't really care about the popularity of math, they care about the true and the development of knowledge.
-discover a equation/theory in math
-ask if it was discovered before
-answer: "probably was"+no source+downvotes
when you are a nobody online people will act as such, so don't hype math on social media, take your chances with peers in real life
I don’t understand people saying you’d be lying to the public if you “hyped” mathematics. People can’t be knowledgeable on everything, so it’s very important to simplify the most complex concepts to make them understandable and also fun to learn. Ignoring the funding issue for a second, this is culturally relevant as knowledge enriches people. Also if Math is better understood and publicised, more people will become interested in math which is always a good thing.
Being technical and precise isn’t as important as conveying the intuitive aspects of a theory and conveying the sense of wonder only sciences can make people feel. You’re not lying to people, because the premise while doing science communication is that you’re simplifying the concepts (also because in a tweet or a twenty second video you can say only a limited amount of things).
Also even in University things are simplified for the sake of understanding (not much for the entertainment value though lol). I study physics, and mathematical and also physical concepts are simplified for the sake of the models I’m studying at any given time. That doesn’t mean what I study is meaningless just because it isn’t the latest model accepted by the scientific community.
Not every mathematician should talk about their work to a general public (also because Math is particularly difficult to explain) but people who do it aren’t lying and with the right compromises even very abstract concepts might be understandable by a general public.
Its just very hard to express these really abstract topics to people with no formal mathematical background. Especially if there is (as of yet) no application. We can help ground people in the understanding of certain fairly advanced topics in math by relating them to their associated applications. This is why you see LOTS of popscience media on Fourier transforms, Chaos Theory, Fractals, etc.
It’s just very hard to do. Anyone with a significantly advanced degree in math will likely go on to pursue a more lucrative career than trying to hit the lottery and develop a self sustaining career as a math communicator. Being a science communicator and a scientists are VERY different and often take distinctly different talents. I love science/math but I’m not particularly great at science communication, even though I try really hard to be.
So in short, I think most mathematicians would love for it to exist, but it’s very hard to do and not very lucrative, so the likelihood of enough people doing it to make any reasonable impact is very low.
Truthfully, and I have to be really, as I’m autistic, I think it’s largely because purely approximating, Maths, along with Philosophy probably, are seen as the most academically-challenging fields. We could argue that that’s because it’s often badly taught and therefore a very low level of Maths is taught to most people. The modal average student leaving school in my country, doesn’t even know how to confidently use the basic level of Maths, that they actually need for ordinary life skills. So how realistic is it that the average person would even think they could understand current Maths research? In my experience the average person, even the average “intelligent lay person” assumes they won’t understand anything about Maths so they don’t even try. They hear the word “Maths” and switch their brains off, deciding that the “mathsy” person is probably terribly clever and smile politely.
Let’s be honest: even within an area of Maths, there are few other Mathematicians who properly understand research of their colleagues. Say we randomly selected: 100 Mathematicians and 100 Biologists and 100 Historians and put them, each group separately, in prolonged intense socialising situations. Apart from the fact that the biologists and Historians would socialise marginally better, I believe they would also be successfully discussing their research more with each other. They would probably send each other links to papers and they would read each other’s work. It’s true that there would be the odd word or concept they would have to look up, but they would do it, because it would be largely comprehensible, so it would be worth sharing. The Mathematicians would be there, even within/adjacent fields, largely talking about many other topics because they mostly don’t read each other’s work unless it’s almost exactly their very specific area. They would be doing so very carefully and precisely, correcting tiny errors in their previous phrasings that no ordinary person would even have noticed… (This is my experience anyway, although I admit my knowledge of Biologists and Historians is vastly more limited than my experience of Mathematicians.)
The problem is that when Maths is “dumbed down”, we Mathematicians are (rightfully) irate. Sorry I haven’t finished my point, which I haven’t properly got to yet… I’ll edit this tomorrow. It’s late in the land, where Maths is the usual shortened term for Mathematics.
Frankly I think because it's a lot easier to "bullshit" stuff in other sciences.
I am not saying that the hyped research itself is BS, but often the headlines and even the articles in pop-sci media use language that is essentially BS and makes something sound awesome to the "general public".
In addition, for pop-sci you can take out most of the abstract stuff and math and just use some colorful analogy.... much harder to do with mathematics.
Quite simple actually, public and private schools don't know how to teach math to folks, make it interesting for them and explain to them what is the use of maths, hence why mathematicians don't share their research online; you need to at least understand stuff and if you do, you already check for new studies or reasearch in your given field, therefore there is no need for you to post on socials.
People in high towers stuff.
I think it’s because math is a language, and most mathematicians do not know how to talk about mathematics in any language but mathematics. They usually can’t translate their achievements or questions, or the significance of those things, into the word-based language the rest of us speak.
Tao is practically a modern-day Feynman with the way he makes state of the art research seem almost understandable to mere mortals. There’s just not that many people who have ever lived, who had that kind of mathematical ability and also the ability to explain it to more than a room full of their contemporaries.
Something like the Langlands problem, there can’t be more than a million people currently alive who could even understand the problem statement, never mind how to solve it.
Theoretical physics? Well, we all know what atoms are. There’s a tangible interest due to nuclear energy and fusion. It’s not as abstract. So there’s more interest and a greater ability to grok the basic idea.
Also, I think AI grifters are setting unrealistic expectations for what a researcher’s Twitter presence should look like…
Something that someone pointed out once is that the general knowledge of modern/20th century mathematics, compared to other disciplines, is *extremely* poor. Like everybody *vaguely* knows what a proton or DNA is. I think the average person knows a shocking amount about modern theories on dinosaurs, Shakespeare, rocks and medieval history. Most people have a vague idea of what ideas of Foucault or Said. But very few people have ever heard of a Riemann surface or Grothendieck. There's zero public expectation that even an educated person should know anything about maths beyond basic calculus (which has been around for 500 years). There's an incredibly hard British quiz TV show called "University Challenge" and I remember that one of their hardest questions was on the definition of a Hermitian matrix...
To me, this seems like a major part of the answer. Most people outside of mathematics don't have any concept of what academic math actually is. When I tell people that I'm a mathematician, it's common for them to ask what I actually do or to assume that I do some type of hard calculus because that's what they associate with "advanced mathematics". I don't mean this in any sort of elitist way - it's just that most people aren't exposed to math beyond calculus or maybe a linear algebra and differential equations course. If someone has absolutely no exposure to the idea of a group or ring, how can you possibly tell them about cutting edge algebra research in a tweet? I have an elevator pitch about my research that I use when laypeople ask and I'd say that 90% of the time they stop really listening before I finish the second sentence. I also think that some of the self-promotion that I see in other areas would probably be culturally seen as ... tacky in math? We do self-promote in things like research statements, but I think even there, we tend to want to be very precise about our contributions in a way that isn't very compatible with hype. Individual mathematicians vary, of course, so there are exceptions who are more into the hype. But I guess I get the impression from my colleagues/friends that most of us view that hype with mild amusement.
I’m curious if maybe it has to do with the higher needs and competitiveness for grant money in other fields. This is my own ignorant hypothesis (correct me if I’m wrong) but it doesn’t seem to me like math necessarily relies on quite as much big money funding. In my own discipline people promote themselves quite a bit because our research can’t really happen without getting grants, and so it’s useful to be well known.
This is my understanding. A lot of experimental fields (medicine and experimental physics come to mind) require large facilities, expensive equipment, and lots of people, all of which cost money. Many mathematicians, on the other hand, can make do with pencil, paper, and a large broom closet. The others will want computers, white/blackboards, a little more room, and maybe some time on the supercomputer, but these things are still orders of magnitude cheaper than precision optics, rare chemicals, or proper double-blind medical trials.
> it's just that most people aren't exposed to math beyond calculus or maybe a linear algebra and differential equations course. I don't think most people have ever heard of linear algebra or differential equations. They've heard of calculus: it's that advanced math that scientists use.
I remember in undergrad telling someone that Linear Algebra had Calc 2 as a prereq and they didn’t believe me because “why do you need calculus for y=mx+b” and wouldn’t accept that it was anything other than y=mx+b. Now when I teach linear, I hate telling non-math people for the same reason
I would be just as surprised to learn that Linear Algebra needs calculus as a prerequisite. Don't you just work over arbitrary fields anyways for a pretty long time in the beginning? Then why care about calculus?
It's typically listed as a prerequisite in the United States, but I think it's usually for mathematical maturity rather than the specific content.
It’s also helpful to have calc 2 when you want to give a range of examples of inner products since you can use the integral to define an inner product on continuous functions
It always interests me the slight differences in how math is taught around the world. In the UK, we would always use y = mx + c not + b. I’ve also noticed the differences in the order of operations pneumonics, we would use BIDMAS (Brackets, Indices, Division, Multiplication…) whereas in the US you guys seem to use PEMDAS. Also in the UK we have a weird thing for histograms, my teacher said her husband was a French professor of mathematics and he has never heard of them before, whereas here they are taught when you are ~14 I think? They’re pretty useless imo anyway 🤷♂️
In Sweden, it is y=kx+m, where k is koefficient (coefficient). No idea where the m is from.
M might be multiplier and c might be constant.
I find it pretty interesting too. Here it's y=ax+b. In high school we also didn't learn sec or csc, maybe because they seem like the least useful ones, I guess, but it's hard to say the reason. On the other hand we learned about simple integration in high school, for some reason. The funnier thing was that we hadn't actually encountered the differentiatial operation beforehand, not entirely at least, we used the prime symbol and didn't even mention what variable was affected, it was just assumed to be X. Naturally this created a lot of problems past the first few classes as different letters got added, some of my classmates had trouble properly understanding that the different letters were treated as constants and should be reduced to zero if not tied to an X.
>Most people outside of mathematics don't have any concept of what academic math actually is. When I tell people that I'm a mathematician, it's common for them to ask what I actually do Folks seem to think I must be an accountant or auditor because "being good at math" equates with numbers and money for many people. Even the more technical folks mostly only think of maybe up to calculus and linear algebra for use in engineering. Practically speaking, only other mathematicians have any idea beyond. As a previous teacher, many people just blank when they start seeing symbols, or even when they see too many numbers. It's a culturally reinforced response because everyone instinctively wants to say they are "bad at math" to not feel weird. Most of them can actually do it and if you start talking about sports they'll start quoting statistics and actually analyzing it decently well while telling you so they can't do math. So there's some cultural aspect as well as finding a personal interest in it.
People at work know I have a math degree, and so whenever someone has an arithmetic problem, they ask me. I'm terrible at arithmetic. God awful. I hated math and barely paid attention until I had a great teacher in highschool, which is when I fell in love. My coworkers can't seem to fathom that I studied math and yet can't do arithmetic well at all. It's kind of obnoxious, because I think some of them think I'm making it up.
Out of curiosity, can you give us the elevator pitch? Sometimes it's the case that people just don't pick the right words to connect with an interested person
Sorry, I don't post anything about my research on Reddit because this isn't intended to be a professional account and it's identifying due to how specialized research becomes. It's also not exactly a canned talk. I usually start by asking the other person a little bit about their background and then I explain differently based on what ideas/vocabulary they're familiar with. I do get positive reactions sometimes, so I think that I'm probably not terrible at it. I could also probably be better, but I think the loss of interest comes more from the fact that most people aren't really that interested and just ask to be polite or because they want a one sentence answer that is not really possible for me to give. It's easier in other fields to say something like " I study cancer" or "I study black holes". If I just say the name of an object that I'm thinking about, that's not meaningful to the person asking. Often even the name of my subfield isn't meaningful.
Perfectly understandable, no probs
maybe start with "are you prepared for a more-than-one-sentence speech?"
Haha, I definitely don't start by launching into an elevator pitch. I'll usually start by saying that I work in academia and do a little bit of teaching and mostly research. If they ask about my research, I'll give the name of my subfield and a 2-3 sentence explanation of what that is, usually with an example of an application that I think they'll like (even though it's not related at all to my own research). If they ask further about *my* research, I'll tell them that it requires a little bit of set-up and then start asking about their background if they still seem interested. I have decent enough social skills that I try to give them some polite places to opt out of hearing more. :)
I was about to ask the exact same but out of pure curiosity.
>most people aren't exposed to math beyond calculus or maybe a linear algebra and differential equations course. Would you mind adding what people don't know? What does a mathematician do?
From this post I have learned that mathematicians are very well spoken. On that note, the other 10% stop listening just after you finish the second sentence.
>Most people outside of mathematics don't have any concept of what academic math actually is. While it's true, I'm still quite shocked by how little many experimental people understand how theoretical fields like (pure) math work. I spoke to a group that had mostly (lab-based) Biology/Engineering students and to their credit, labs/PIs and "umbrella/direct-admit programs" also exist in Math because "it's STEM."
If you have any recommendations on sources that serve as an introduction to academic maths and it is not a bother, I would be very glad.
I mean, Perelman turned down that million dollar prize, so I don’t think people like him would have any interest in gaining Twitter followers…
The other day I was watching a video about debunking Terrance Howard appearance on Joe Rogan. At some point Terrance talks about how he found a "new wave and it's conjugates". The youtuber types conjugate into Google and goes "see! This is nonsense! You can't conjugate a wave cause it's not a verb!".
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>Something that someone pointed out once is that the general knowledge of modern/20th century mathematics, compared to other disciplines, is extremely poor. The overwhelming majority of the math we teach children is many, many hundreds of years old. Even for math majors, they won’t learn things less than about 150 years old until they’re seniors. For grad students, decades old. In a lot of fields, research-level work can’t even be explained in a meaningful way until several years into a graduate program. That’s not to say some things aren’t accessible. Some problems in number theory are readily explainable to children, even if their solution techniques are not. The public could probably wrap their heads around “a new model for controlling and managing the spread of a plant disease in orange groves” and at least believe it’s important. But yeah, most math is barely accessible to mathematicians; forget the public.
> Even for math majors, they won’t learn things less than about 150 years old until they’re seniors. This is a bit of an exaggeration -- replace "150 years old" by "90 years old" and it becomes correct. For example, the term "abstract algebra" was coined in the 20th century, ideals in rings were first defined by Noether in the 1920's, and the importance of structures like abstract vector spaces wasn't really understood until the 1930's. Likewise, the first textbook on graph theory was *Graph Theory* by Dénes Kőnig, which was published in 1936. Metric spaces were defined by Fréchet in 1906, and topological spaces were defined by Hausdorff in 1914.
Even 90 years is too much. A lot of the material in a graph theory course will date from the 1950s and 1960s.
Modern category theory and the way it's used in topology and algebra were developed even later than that
Yes, but aside from at the strongest of departments, most undergrads are not going to see category theory, except in so far as they'll here words ending in morphism.
I think the general public could easily get a vague inkling of what some of the important objects in maths are about. Mention a "manifold" at a dinner party, and you'll face bemusement. Mention an electron, Schrodinger's equation, or general relativity, and you'll get cautious nods. But a manifold is probably easier to explain than all the above! I don't really see why there's an objective reason why general relativity or electromagnetism is in the public consciousness, but cohomology groups are not. We shouldn't expect that the public understands these ideas on any high level at all, but an inkling would be nice.
> I don't really see why there's an objective reason why general relativity or electromagnetism is in the public consciousness, but cohomology groups are not. I think it is completely obvious why cohomology groups are not at all in the public consciousness while GR and E&M are. People have had direct tangible experience with E&M their whole lives. Even though GR is a much more abstract thing, people have heard in passing about its unusual *physical* effects. There is nothing physical about cohomology groups. Sure, they have a role in geometry, but not in a way that would ever make them an object of popular fascination like branches of physics are. Why should the public *care* about cohomology groups? In the popular consciousness, atoms are visualized as tiny solar systems with the nucleus as a "sun" and electrons as "planets" even though that idea of atomic structure has been obsolete for about 100 years. And it's even used in the logo of the International Atomic Energy Agency. Such simple images persist despite being in accurate, but I don't see how you would convey a simple idea of cohomology groups (even with some inaccuracies) that the public would care about. On the other hand, the public *does* know what prime numbers are and can appreciate that they somehow play a role in cryptography, which everyone has an appreciation for, even without knowing exactly *how* primes are playing that role. So prime numbers are an example of a serious mathematical concept that is broadly well-known.
I tried explaining what a manifold is to my mom and I think I kind of lost her on the way when mentioning more than three dimensions :/
This is pretty accurate honestly. My first intro to big boi analysis was with a really young professor. He stated that he was annoyed with the fact that he had to teach things to at were nearing 100 years old, and wished he could teach the newer concepts. Unfortunately, you kind of need the “basic” concepts to even start into functional analysis, and then a few more years of refining those skills to think about really understanding cutting edge stuff. I can’t imagine being introduced to Hilbert, Banach, C^* algebras etc. without going through the process of learning the (now) classical concepts. But I also agree with several other comments related to telling someone you have a phd (or BS/MS) in math and getting the “wow, you must be really smart!” Or the obligatory “what’s 687 times 4523?!” Smile and nod boys. Smile and nod. (Edit: Girls too, or just people in general, ya know!)
There’s a lot of counterexamples to your general rule there, and I didn’t even go to a particularly good school for math. Differential equations, vector calculus, abstract algebra, combinatorics, game theory, graph theory, cryptography, analysis (Hilbert), computability theory (Gödel, Turing)… Maybe that last one feels out of place, but I pity the math major who wasn’t required to take a few courses from the CS department. Hell, even physics majors get some modern math before their senior year. You need modern math to learn modern physics…
> Most people have a vague idea of what ideas of Foucault or Said. This takes pretty generous definitions of "most people" and "vague idea".
I was going to comment on the same thing. Are we talking about the French philosopher Michel Foucault or the 19th century physicist Leon? And which Said? The only Said I know is the literary critic Edward Said. I don't know any mathematical Saids.
What bit of common knowledge exists about Foucault only comes from memes or other offhand jokes about everything being a prison.
I only know about Foucault’s boomerang.
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[Relevant xkcd](https://xkcd.com/2501/)
you can safely drop that to <1%. any time someone tries to guess what portion of the population knows x, they tend to wildly overestimate the portion that knows the same things they do.
Calculus is closer to 350 years old (but your point is still taken).
In fact, it is useful to remember that Calculus is younger than Harvard.
I’m a math major, wtf is a grothendieck and why does it sound like and Elden ring boss
He is kinda the final boss of mathematics. Very interesting life.
French person
Username checks out.
> about maths beyond basic calculus (which has been around for 500 years). I sometimes wonder what life would be like if the average science education stopped in the mid 1600s. Darwin is 200 years too advanced. Boyle's Law might be acceptable, but certainly nothing on combustion (1700s), or even conservation of mass. No atoms or periodic table. Certainly no mention of nuclear physics, relativity or quantum mechanics. I think a lot of people get mixed up because their science courses do at least mention the existence of relatively recent science, and some of the products of science are large and obvious. With a typical education we at least get the gist of what happens on an airplane wing or inside a nuclear reactor. So we mentally assume that we were taught similarly recent math, when in reality math education stops centuries before science education.
That famous Carl Sagan quote about his prediction for the looming American Idiocracy sure seems relevant. I’m not gonna quote it, you know which one I’m talking about if you’re on this hellsite. The average science education arguably has stopped in the 1600s in parts of the USA, and replaced with Bible study. No Darwin is a given. I suppose they still get Newton’s laws, for now…
Besides, the way a real mathematician hypes himself is to wait until someone else mentions a result he’s found and reply, “I knew that,” or, “I proved that in 1976, but I didn’t think it was worth publishing.”
That's a thought-provoking comment. That got me thinking though if it would be fair to say then that the diminishing returns of research for mathematics dimminished much faster than other fields. Like the entire modern world is built on mathemics, but all that mathematics was developed so long ago, it is still good, and most people today do not have to learn 20th/21st century mathematics to participate in the 21st century. But then I also remembered statistics and probability, where some parts of it are relatively more recent and they lay the foundations for all the machine learning and deep learning we have today.
Not really. Number theory was useless for hundreds of years, then we developed computers and it suddenly became important. Computational algebraic geometry is becoming more important along with topological data analysis etc.
>Number theory was useless for hundreds of year That was kind of the point I was making that the older stuff produced significantly higher returns to scoiety because they are still being used in the state-of-the-art today. In your example of DNA, it also produced high returns to society, but was also much more recent. >Computational algebraic geometry is becoming more important along with topological data analysis etc. It seems like new mathematics being developed today is only intended to solve a particular niche problem.
>being developed today is only intended to solve a particular niche problem. Well, initially, calculus was just designed for orbital mechanics. It has to start somewhere.
I think the reason that you don’t get more mathematicians hyping their work on social media is i) it often takes a lot of background to describe a problem/solution, and ii) writing for other mathematicians in your niche subfield and writing for a more general audience are distinct skills. Most mathematicians do not practice the latter, so writing for general audiences can be very time consuming. I find that you end up describing mathematical ideas to a general audience using analogy, which can introduce inaccuracies. I have a lot of respect for outlets like Quanta that specialize in finding ways to communicate mathematical thinking with reasonable fidelity to a non-mathematical audience.
> I find that you end up describing mathematical ideas to a general audience using analogy, which can introduce inaccuracies. That's true of physics as well, but people do it anyway.
I’m guessing that the tolerance for inaccuracy is lower for mathematicians than for other fields.
The other problem is that they oversimplify the physics by leaving out all the math. How do you leave the math out of math?
I don't think the concept of inertia requires much math to understand. Neither does the concept of forces attracting or repelling each other. If you want to actually *do* physics then sure, math. But explaining "how do moon go around earth" can be explained as far as anyone will need to understand with basically no math at all
*folds a paper and make a hole What inaccuracies?
I certainly don’t think this tendency has benefited the physicists
Pop physics is physics without the math, how are we going to make math without the math? We have Numberphile and it's great, but compared to pop science it's nothing.
Pop science also mass produces crackpots
that's not nice. everything produces crackpots, just ask math departments who get letters about proving that pi is not irrational. but indeed, i learned discrete math in uni, and i would LOVE to learn more about other areas of mathematics more at a level i can understand. and many other people as well. we are just not as loud and abnoxious as the crackpots
Yes, but those rational-pi crackpots exist because of pop maths talking about irrationality
I wouldn't say "produces". It seems more likely that delusional, arrogant, and egotistical people would exist regardless. Pop science simply makes science accessible to everyone including them
Pop science mass produces crackpots but it also mass produces scientists. Pop science gets people introduced to science it's up to them what they do with that
Never said otherwise. Just said that one thing I don’t like about pop science is the amount of crackpots, way fewer of those in math imo
Well, I guess 99.9% or more of the population won't understand a thing in those works
Not only that, it's very rare than at random two career mathematicians will be able to understand each other's work. That's why seminars exist.
There are some magazines (especially Quanta) that do a fantastic job in trying to appease the general public to enjoy mathematics. I do also believe that some Youtube creators (like 3B1B and Numberphile) do a great job. Mathematics (mainly pure) is always going to be difficult to explain to the general public. The level of research is so advanced, detailed and "out of contact" with the real world (abstract) that it becomes a tremendously difficult task. Physics and biology for example are way easier because people can grasp the fundamentals. Some areas of mathematics (more on the applied side) can perhaps be more easily explained to the general public. I think there has been an increase of content creators that take the approach of Quanta and 3B1B (focus on visualisation) which is very nice. I hope we can take this to more "mainstream" media in the future and maybe attract more people to this beautiful subject.
Advanced math exposition rarely leads to increased understanding. In fact, it's usually the opposite. People with no math background seem to always come away from exposition with loads of misconceptions. There are too many people who genuinely believe 1+2+...=-1/12. Almost everyone thinks fractals are self-similar shapes. Even those who know these things are not true couldn't tell you why. The average math understanding is so poor that communicating about math is like trying to explain things to someone who speaks a different language.
Its magic to 99.99% of people. In the 1700s, Jean-Baptiste Fourier finds that periodic function can be thought of a sum of trigonometric functions, now Fourier series are the basis of the modern music industry. In 1917, Johann Radon defines a new integral transform, it becomes the basis of CT scans. In 1928, Paul Dirac finds 2 solutions to an equation, now PET scans are used to find cancer. The average person knows nothing of this. > It is weird that we live in a world where most people do not know the quantum notations Yes and its the biggest science revolution in the past 100 years. Just mention transistors and people know its important.
1800s for Fourier
This feels true; mention quantum mechanics and people thought of transistors. Mention .jpeg / .mp4 and nobody thought of Jean-Baptiste Fourier. I certain that there's a big problem in mathematics communication between experts and the mass of people.
The general public barely know the alphabet of math. How am I to talk to them about my multi-paragraph long research, or describe the context of a mathematical result? How does one describe the result of research into English to a person who can't spell, or even read? By the time I've reduced math research into something that an undergrad can understand - I've already robbed my statements of meaningful truth, everything becomes obvious and trivial. Plus I've wasted a considerable amount of time producing content that will be ignored or dismissed. For example; I study the normalization of volume forms via generalizations of mean curvature flow within the canonical tractor bundles associated to parabolic geometries. To describe why I study such things is easy for someone who understands the importance of geometric invariants and the difficulty of producing them, but to anyone else such a thing - or why I should be so specific about which geometric invariants is meaningless.
Even mathematicians only speak their own dialect. An analytical number theorist wouldn't even understand the abstract of a paper on symplectic geometry. How on earth do you expect a layman to?
A virologist and a neuroanatomist won't know the state of the art in the others' fields, but they can have a meaningful discussion about their own research with each other because the distance between their fields at least admits a common vocabulary. But if you put a biomathematician like me in a room with an algebraic geometer like you, there's going to be a lot of time in just getting basic definitions out of the way.
mean curvature flow!!! i know that one. don’t know what canonical tractor bundles are tho :(
An Ubuntu Linux distribution for farmer-hackers who root their agricultural equipment and yearn for freedom from the tyranny of John Deere. (Seriously, [they exist](https://en.wikipedia.org/wiki/Right_to_repair#History).)
We should swap knowledge! I know about tractor bundles - but mean curvature flow is doing my head in. Roughly: It is possible to convert an over-determined system of PDE over a manifold into vector bundle (called the prolongation) in such a way that solutions to the PDE correspond to parallel sections of the bundle. If you do this "just right" the resulting bundle has a uniqueness property that implies that it is the associated vector bundle of a Cartan connection where the representation is "nice". When this happens the bundle is called "a tractor bundle". If it is very nice then it is called the "canonical tractor bundle" associated to the prologation. So.... mean curvature flow used to find solutions of PDE on manifolds.
Flow gang rise up 💪
I'm just a junior member - it the other stuff I know about. One day soon I might get a membership card...
Why do you study such invariants? I have heard of canonical tractor bundles appearing in Cartan geometries, but I'm not familiar with the analytical/PDE aspects that you mentioned.
Good question. In Riemannian geometry (geometry of principle bundles with groups that "allow" a metric) we know what all the "equivarent invariants" are. Some research in the 60s and 70s figured this out. We don't know the answer for geometries associated to groups that do not "allow" a metric. Efforts seem to be focussed on conformal geometric and the geometric of projective manifolds (of some type that I don't understand). Both of these structures fall under the heading "projective geometry". Which as you mention is roughly the geometric of Cartan geometries without the restriction that the lie algebra that the connection takes values in is associated to the lie group that gives the bundle.
Just a friendly comment (it's by no means a criticism but more of a question, I don't know anything about your field) because I am probably the type of idiot who would not get what you are talking about but can get it in a few days (i.e., generally what you do, not your papers) if I need to and refer to the definitions: For some reason, "the normalization of volume forms via generalizations of mean curvature flow within the canonical tractor bundles associated to parabolic geometries" does not seem like the friendliest way to explain your research (I would not say that's for sure the case because I do not understand some of the terms and I need to Google it). Usually, people start by explaining the challenges they work on, and then follow up with a high level description of the technique. You, instead, decided that no one will get it because they don't already know the challenge, while the challenge is usually the first part of a post of presentation. Usually, when: "why I should be so specific about which geometric invariants is meaningless.", well, in this case just don't state it in Twitter (?)... I actually appreciate the technical definition as well though, because it can help me to learn the concepts if I need to. It's always clarity vs rigours (well, not always, but many times... Sometimes "simple terms" are a mess).
i’m doing warped product manifolds and the heat kernel / spectrum of the laplacian on cusps induced by a warping function. doing this on S^1 X_f S^3 (warped einstein universe) has implications on thermodynamics, and i can’t explain anything about my research to people outside of math and/or physics. even with those people i’m doing something pretty niche
Ooohhh!!! Cool stuff. Warped manifolds with ?non-smooth? warping? Have I understood that correctly?
has smooth warping, but the warping function applied to the metric causes little “spikes” that extend to infinity but keep the manifold of finite volume. they can be thought of as singularities in the einstein universe
I think there are three main problems. For much of modern mathematics you will need formal training to even hope to understand what a paper is about and even then you will probably have to read up on pre-requisites if the paper wasn't written in your particular field of expertise. How are you going to communicate this to a person who only vaguely remembers what a matrix is. The next issue is making laymen care about your research. To an outsider mathematical research probably seems like a massive waste of time. They probably don't know anything about how often seemingly abstract results have been used for solutions of concrete problems years or decades after. Or how the developed machinery helps in other areas like homology was developed for studying topological invariants but then moved on to applications in other fields. In other fields than mathematics you can at least give a vague idea of how your research could be useful without going too much into details most of the time. Last but not least, people have been conditioned to hate maths. Schools aren't exactly good at making people fall in love with maths. There are too many cases of bad maths communication which is then attempted to be compensated by inflicting pressure on students. Maths being a considerable hurdle in a successful graduation - be it high school or college - which directly impacts your chances of "making it" damaged maths reputation. I've had numerous people tell me that they hate maths immediately after me telling them I study it. With YouTube channels like 3Blue1Brown this has certainly gotten better, but it's still a niche subject not a lot of people will care about unfortunately.
One thing I love about mathematical culture is that we frown on researchers who overhype their work. Of course, some amount of hype is necessary in order to improve funding, but we’re not going to outright lie about what we’re doing. If we cared more about money than honesty, we certainly wouldn’t have become mathematicians. While I certainly think the general public and politicians *should* financially support mathematical research, it’s unethical to trick them into doing so.
>How tf the public going to fund pure mathematics if they cannot imagine what mathematicians are doing. That's not how scientific research gets funded. Soecific branches aren't ran by the public to see which gets funding. It's done by an organ like the NSF and grant proposals are reviewed by the panel. Pure math funding in this sense depends on how much political power mathematicians have on these. Directors of the major institutes also regularly communicate with elected representatives, both formally and informally. Whether math research gets sufficient funding isn't because we don't have good enough instagram pages.
Have you seen the state of math on social media? The majority are trying to do basic algebra using fruit or simplify an arithmetic expression, and failing…
Aside from the fact that it is just part of the nature of modern math that it is VERY hard to communicate in any meaningful way to a non mathematician, as others have already said, I would add that I don’t think it would inspire funding the way you’re hoping. I think for most people, if they had a vague understanding of what mathematicians do, the response would be, “the fuck, this is what we’re paying for?” Fortunately, people see mathematicians as magicians who do the unknowable sorcery that underlies the rest of the sciences, and that’s enough to justify funding. Consider this: if the very dumbest people fully take governmental power (cough-maga-cough), then much of the sciences will be quickly defunded, but I’d say there is a chance that math won’t be, and this is because it is opaque, so it hasn’t been demonized by idiots.
>the fuck, this is what we’re paying for?” To be honest they are not paying very much. Sure, we have nice conferences every so often; but mathematicians are badly underfunded compared to chemists or physicists. It's much easier to get funding for a postdoc or PhD in physics compared to maths. In Europe, at least, mathematics has the funding level of a humanities subject not a science.
The head of the physics department goes to the dean of the university, asking for funding to build a new cyclotron. The dean groans at the tremendous expense, and asks “why can’t you be like the mathematics department? All they need are paper, pencils and a wastebasket! Or the philosophers - they don’t even need the wastebasket!”
Well yeah, that’s true also.
"Fortunately, people see mathematicians as magicians who do the unknowable sorcery that underlies the rest of the sciences" THIS IS SO TRUE. I once encountered a problem; didn't understand the math -> blindly bow-bow-clap-clap convert the formula to programming language and somehow it is true.
sooo.. we should just lying to the public about our magic stuff to get funding? that's not a very healthy way of doing things.
I don’t think I or anyone else is suggesting lying to the public—I’m not really sure what you mean. I think the closest most mathematicians get to lying to the public is when they try to make tenuous claims about real world applications of their research in NSF grant applications. Let me clarify something though: I very much support people’s efforts to try to communicate math to general audiences, I just have doubts that it is an avenue to increased funding. And when it is, that’s probably where you would find a bit of a lie (e.g., knot theory is really cool, here are some pictures, and it’s important because DNA unknotting and stuff). And honestly I think that’s fine.
Some mathematicians do it, I see it often on X and Mathstodon.
No one understands it enough to appreciate it
Other fields need a lot of research funding to survive. If you're a particle physicist, 10% of your job is actually doing particle physics and the other 90% is begging various organisations and government departments for a new particle accelerator. Ultimately, most pop science exists because most scientists want the public to vote to make the funding pot bigger. Mathematicians are content with a few notepads and pens. The really boujee ones might treat themselves to some hagoromo chalk. They therefore don't need to fight for funding in the same way as other scientists - a university can pay salaries for an entire maths department for less than they'd spend on equipment/supplies for a single chemistry lab.
Bougie* as in bourgeois
My parents, both chemical engineers who graduated from [my country's leading technical university](https://en.wikipedia.org/wiki/National_University_of_Engineering), which has a reputation for the brutal amount of math, physics and chemistry you need to know *just to be admitted in*, never mind to survive the first two years... ... even they struggle to understand what I do, when they ask me and I answer them. And I'm also an engineer, so I'm a bit more qualified than the typical mathematician at communicating in terms an engineer would understand. Given this, I hold no illusions that math can be hyped in social media, or that it's worth it to even try.
There's one big reason that I'm a little surprised no one's mentioned yet, although it is something we as a field are generally hesitant to mention: 99% of pure mathematics research has no, and will probably never have any, applicability outside of pure math itself, and that's totally fine to us. When people ask us things about how pure mathematics is "useful", we all have the same rote answers in our back pocket, like how important Fourier transforms are, or how number theory turned out to be key to the development of cryptography decades later. If we want to get into things more esoteric in the general public, we might mention how significant Lie theory has ended up being in mathematical physics, or the fundamental connections between category theory and functional programming. Then we usually cap off with "we can't know what will be useful until the future; there's always a chance that something that seems useless now will turn out to be key to something in a hundred years." This is all true, but we often leave off "but even if my own research never finds an ounce of use, I don't mind, since I just love learning more about this topic for its own sake." Pure mathematics research simply isn't _about_ what benefit it could bring outside providing more insight into mathematics itself. It's research for the sake of learning more about mathematical structures and their properties. And I don't say this to denigrate it, because I think that's awesome, and research for research's sake _should_ be more valued than it is. Honestly, I'd bet this is probably the case for a lot of theoretical scientific researchers too: that they research not because of how it might be useful, but for the sake of learning more about things in and of itself, with applicability as a secondary concern. It's just not as big a "problem" there because...well, the things they're studying are things that exist, not platonic ideals of mathematical structures. Things like "research for the sake of learning more about high-energy particle interactions", or "learning more about ursine genetics", or "learning more about mantle boundary conditions" are blatantly tied to the real world, and so need less justification to laypeople than "learning more about independent set enumeration in trees".
Perfect answer.
My advisor was asked (mostly as a joke) the following question at the end of his PhD defence: "If you're stuck on a plane and were asked about the applicability of your research to the layperson, what would you say ?" His answer ? "Can you get the door for me ?" Jokes aside, the thing about modern maths is that, in order to even state the definitions or communicate the vague ideas, so much prerequisite knowledge and context is needed that, should you take a jab at any kind of explanation, you would have produced a PhD candidate by the end of it.
I think it’s because maths a lot less tangible than any other subject. It requires a lot of abstraction, protons, shakespeare, big bang, it doesn’t require any imagination it’s all there, compared to a riemann surface which isn’t so easy to conceptualise.
>How tf the public going to fund pure mathematics if they cannot imagine what mathematicians are doing. It's not the public who decides, it's the NSF, which has a better idea of what research goes on.
Math isn't very hypable since most people don't even remember algebra. People just won't understand more advanced concepts so it isn't exciting.
There's Mathologer, blackpen redpen, and tons of stuff on well established math. There's like a zillion videos explaining Fourier Transforms, specifically. As for new research, if I were a mathematician, I wouldn't show any work in progress to anybody publicly like that until I had it published. If you show stuff before that, A it could be wrong , and B someone else could publish it before you do.
Pure maths is much less prone to someone else trying to steal it than in the sciences so that isn't really part of the concern
The biggest problem is the level of abstraction involved in pure math that many people find alienating. A large amount of people already struggle with calculus, trigonometry, and high school/early college algebra and these subjects are very commonly used to describe the natural world. Trying to convey concepts and developments in topology, analysis, set theory, algebraic geometry, etc., to the general public would be much harder, especially in short form social media that can be found on twitter, instagram, and tik tok. The best math communication I have found for pure math has been youtubers like numberphile and 3blue1brown (and the channels they inspired), but that is because they spend a lot of time laying the groundwork and developing an intuition for the problem at hand. Due to this, their content requires some level of time investment and interest that many people using social media do not have or want to give to math. They have done a great job at increasing interest in math (i can attest to this personally), but I do not think math will ever have quite the same appeal to the general public as the sciences which are inherently tied to understanding tangible concepts about the world we live in. I think more can be done to increase public interest but it will be an uphill battle in a world where a good amount of people’s immediate reaction to seeing math is either “math is boring/when will i ever need to use this?” or “i’m just bad at math”.
Imagine Banach and Tarski hyping their work on the internet by saying that it is possible to split a soybean into *finitely many* pieces, move them around, reassemble them to obtain a solid ball as large as the entire earth.
Well we have grant sanderson who does a great job and the SoME does exactly what you’re asking. I can’t speak for everyone but what I’ve noticed among people my age and demographic (young black males) is math is scary(I disagree with this), you have to be genius to be successful(I double disagree), it’s boring(disagree), and there is no clear use or point to math(again disagree). When I’m more qualified, after my prospectus or something, I have hopes of being sort of like grant but for people not remotely interested in math, among other things.
I'm doing undergrad courses and I cannot understand the Hyperspecialized problems that mathematicians are talking about let alone the general public
Communicating with the general public is not mathematician's strong suit, and often one of the worst. In addition, explaining to general public on high level pure math is extremely difficult to begin with, and those mathematicians are not able to tell people how their research can be useful because they do not care AND they don't known. Applied math is a whole lot better at least you can tell people how it matters to certain real world problems
Compared to what exactly? Other sciences are heavily grounded in the applications to real world events. I.e. we filter micro plastics but none of the underlying science. Even ML which isn't super complicated and has a lot of eyes on it is entirely framed in its applications. The number of people who think chatgpt is going to be sentient is vastly larger than those that can explain the transformer architecture and why it matters.
Not all scientists are into bullshit. You are being unfair to them.
just because the majority of people do not understand math beyond calculus it does not mean that math is in any jeopardy. everyone knows how difficult it is and know that in some shape or form whether by intuition or belief that math is invaluable to humans and it is here to stay no matter how reclusive it may seem.
Because we abide by the statement “the pleasure of finding things out”, and further refuse to dumb down our theories for the masses the way scientists so publicly do just to get likes. If you want to understand differential equations, we will explain it to you until you understand it, or die trying, but we will not allow you to skip the details.
If there’s a hot new physics result, there’s usually a way to literally point to either some application or something, well, physical. “We’ve detected a black hole merger” means something even if you don’t know how we detected it, what general relativity is, or even what a black hole is. Likewise, if you say we’ve made a breakthrough in fusion energy, they can form an image in their head of what that means even if it’s 99% wrong. Even if all their working definitions of the terminology is completely wrong, a lay person can think they understand a part of it, visualize it, and maybe even grasp why it’s important (like cheaper energy or a better battery). For an important mathematical result, none of the words really mean anything for a lay person. Also, in science, a lay person has an image of someone doing experiments or pointing a telescope at the sky. Someone might think an economist just spends their time trying to balance the government budget, but hey at least the budget is relevant to economics! If you told someone you’re a mathematician, they might unironically think that you just calculate big numbers all day or just purely teach. They have zero cultural exposure to what mathematicians actually do. In contrast, applied mathematicians probably have a much easier job explaining what they do. “I came up with a way to do simulations more accurately” or “I sped up the computer calculations” might be crude but at least gets *a* basic point across.
Terence Tao was on the Colbert Show. I assume his goal was to educate people and promote the field he loves.
"like all of the other scientific fields"? Umm.. I am a heavy social media user, but those hypes are mostly from CS folks imho
It’s also CS people are more united imo. Open source projects etc etc… they need the visibility so people maintained most of the projects while other fields people are way more gatekeeping and greedy. Can’t think of any other field as cooperative as it’s CS
Indeed. I love the open source community, and at the same time, I am not a fan of the overpromising and hype culture of the SF/Bay area.
Is the other side of the coin, but most of them really think that their projects are good. That Bay Area, full of analyst and less of CS
I would argue that the lack of "proper outreach" is an issue for math. I am at a very applied math institute, where our day-to-day work is more computational physics than actual "pure math". However, to explain our work and its importance to people outside the community still takes enormous effort, eventhough our work has direct consequences on i.e. industry applications. The lack of outreach also has consequences on the amount of funding we can obtain. Often even small funds for projects in e.g. experimental physics have budgets of far more than a million €. Meanwhile if the entire math departement gets this much money per year, they can consider themselves lucky. I believe for outreach in math to be effective we might need to start earlier in school and teach math more rigorously but also display the applications to motivate.
Kevin Buzzard hypes his work, sure as sure, and it's annoying as all get out.
>How tf the public going to fund pure mathematics if they cannot imagine what mathematicians are doing. I think you should read some basic political science textbook so that you'd learn that the public is not making decisions about funding anything: the public delegates the power to the government, and it is they who make such decisions. Some of these decisions may be unpopular, other may deal with arcane matters such as funding fundamental science, but it is not the case that everything should be understood by the public to get funded.
The arxiv and stackexchange are our social media lol. Haven't you seen all the Mochizuki shitposting?
I tried and can confirm this very much: > Mathematical research is complicated and takes a very long time to read. Hence, noone will leave any kind of response to these research if being publicized. It even applies to r/math, or any math forums not focused precisely on the topic of research (except when the subject is sufficiently mainstream). About funding.. well, you have to talk to the right people (especially being lucky enough for them to listen to you), I guess. These are usually professors who are paid more for their administrative work and teaching than anything else.
A bit part of it is that there’s a limit on how much math can be taught over the course of a k-12 education. By the time you reach grade 3, most students are still grasping multiplication tables and basic algorithms for larger numbers. By 5th grade you might be starting to get into some basic algebra (solve for X type of problems). Middle school is then mostly an introduction to basic trig, geometry, and more complicated algebra. Over the next four years of high school the furthest that most students will make it is to calculus. To discuss even the concepts of any more advanced math you need to have this foundation. It’s not like chemistry where you can say “there are these things called protons, but don’t worry about how they behave.” You can grasp the concept of a proton without even having a discussion of quantum chromodynamics or the residual strong force. As far as I know, there’s nothing in pure math that can be explained as simply.
There is no clickbait stuff in mathematics. E g. People want to hear wormholes, not the math behind it. People want to watch the AI generated stuff, but not the linear algebra, calculus and loads of other math that made it possible.
Well, the problem is, as many others have said, is that the public has an extremely ignorant view on mathematics. For example, when I say I got my bachelors in mathematics, most people who try to talk about math talk about trigonometry, adding/multiplying arbitrary large numbers, geometry, and equations. No one would understand my interests in non commutative ring theory. Not even half of the undergraduates/graduate students. Another reason relating to the previous note is that is hard to explain research mathematics to laymen. Research mathematics is also very hard for mathematicians that are not even in that field; meaning, mathematicians tend to be very specialized. Lastly, if the general public could understand mathematics, it would definitely reduce its funding. Pure mathematics, even for me, has almost no public utility. For example, nothing in model theory or category theory could be used in real life; what is the application of the Yoneda lemma in real life look like?
Guess you’ve not seen the STEM feed on TikTok?
People simply don't care, and many mathematicians don't want to bore people. Quite simply, we find our fields exciting, most people don't, so why put them through that? As has been pointed out, general mathematical knowledge is thin. People may know what the Pythagorean theorem is, they may vaguely remember the quadratic formula, and that's generally it. The language of math is somewhat dense and doesn't always translate well for general audiences. Physics is exciting when stripped down for general consumption, filled with nest words and intriguing possibilities. Harder to replicate that with math.
I think another aspect is that most mathematicians don’t want to do pop math. Most researchers who are interested in doing something more glitzy are typically drawn into other fields. Part of the joy many pure math professors get is that there’s no bs, they are just messing around trying to solve puzzles they find interesting, and selling people on that is not the point
In my view, it's partially because most interesting mathematical results won't fit in a Tweet (an...X?) or in a TikTok. I think part of it is also because mathematicians, even really good ones, realize that they fit into a community and don't want to hype their stuff without showing deference to mathematicians whose work provided the foundation for theirs. (This is also why even single-author papers tend to use the pronoun "we".)
I mean, it has reached morons like me. So something is working that is hyping us up.
I'll quote Evan Chen: "I think that if the general public understood what mathematicians *actually* do for a career, they just *might* be a little less willing to pay us."
The reality of it is that: • Pure mathematics is very difficult to popularize, because most of it is just playing around with rules of logic, with a specific interpretation for your symbols in mind, with no other application other than producing more results in pure mathematics. • If you're a pure mathematician working on the cutting edge, there's usually just a handful of people in the world, who can *begin* to understand your research, without spending at least a few years studying the preliminary formalisms. And the reason these few people can understand the cutting edge research is due to them already working on the same problems, so they already took the time to master the required information. • Working on modelling drug behaviour (one of your examples) is already in the domain of computational physics, not pure mathematics. • When asked, most pure mathematicians cannot provide an example of where their research could be applied, because quite frankly they don't know. They don't think about it from that perspective. But yes, all of this means thst getting funding is rather difficult in pure mathematics. There have also been quite a few attempts to get rid of pure math departments across different application-oriented universities in the past. And yes, people blab about all kinds of science topics without knowing anything about it, and the result is the spreading of misinformation. The public is not willing to work on mathematics full time, so they could become informed, and therefore tweeting about pure research math to the general public serves no purpose.
Outreach is not as important as papers. If anything I doubt is valued when looking for permanent position.
1) Audience capacity to understand 2) It's sort of seen as gauche? Like there is plenty of ego, don't get me wrong, but there's a culture around it where the work is supposed to stand on its own. If it's significant, it will make itself apparent. 3) Assuming "pure" math - hype doesn't get you much. Other fields of research you need resources ($$$, access to equipment) to get on the cutting edge. Shiny research gets you the shiny toys. Math is cheap. The only thing you really need to fight for is time. So the ROI on self-promotion is low.
Either the result is insanely complicated and can't be understood or its insanely trivial sounding to the point where the public says "so what?" That is the problem with 40 character explanations of math research.
I think Cédric Villani's interview on numberphile (https://www.youtube.com/watch?v=xopM9BFjcNo) gives a quite interesting explanation. Math doesn't really need all that much funding (since pen and paper is infinitely cheaper than particle accelerators, fancy instruments or hard-to-produce chemicals), so the culture in academic math isn't as focused on trying to broadcast how important your work is to try and get grant money, and therefore mathematicians aren't used to trying to explain their research to a non-specialized audience. I will say, quantamag seems to be only outlet genuinely trying to present the weird and wonderful world of math to a general audience.
Because you cannot **integrate** stupid into a subculture that is not so stupid ?!? It will diverge ! :D
if i published the things i did in social media, most people will have no clue of what i’m talking about, and the rest is people i would rather tell in person. also… i don’t know if “like other scientists” is a good comparison. i don’t really think math is a science. and sciences talk about… the real world, and things a lot of people already care about.
Have you heard of Ken Ono? He is always putting out press releases. But most people think he overdoes it a bit.
Exactly. My first thought when reading "Why mathematicians do not hype their research on social media..." was that the OP obviously has not heard of Ono.
Mathematicians are terrible at making social media posts. They are always going off on tangents.
That jokes rather derivative wouldn’t you say
For the funding part, this is usually inherent in their applications. Usually federal funds to research things of interest for the government like cryptography. What is the purpose of hyping it up at all? It's not a product to sell. The people you convince are those likeDoE or DoD not the public . We the researches go to these government departments and convince them, not the public
I work in stochastic analysis, and more recently geometric measure theory. I feel like I could explain most of my projects to a layman with some knowledge of calculus. So yeah I’m not sure why it’s not done more often.
There are a couple hype places (eg Quanta), but they tend to focus on somewhat accessible work and their pieces are pretty clearly being suggested by a small group of sources who are academic mathematicians (eg Gil Kalai). I’d say mainly that math is easier to judge than other subjects, so the hype cycle is just less important to publication decisions. It also means math tends to have a more hierarchical journal system than other subjects, and mathematicians attach a lot of meaning to publication venue (other subjects do this too, but to a slightly lesser extent). As a young mathematician, publishing a paper in Annals, for instance, does more for your career than any publication decision which happens in computer science, for instance.
I spend a fair amount of time finding ways to make my work accessible to a general audience, although I try to be careful about not hyping the results too much. For me, that means maintaining an blog and occasionally making YouTube videos about my work. This is a time intensive process, but I do think it’s worthwhile to do outreach.
I might be wrong, but I believe this has to do with the usefulness of what's being hyped and how easy is for the non researchers to undertand it. For example, news about stuffs arriving in Mars is kinda easy for a normal person to understand what is happening and what's the importance of it, even tho they dont know "how". The same with the progress in the AI field. Now if someone solves the P X NP problem, how would a non mathematician understand the importance of it and what this even means? I guess mathematics has achieved a point where most of the new discoveries are too abstract and complex for a normal person to understand it, not only the "how" of the discoveries (like in most of the other fields), but also WHAT is being discovered
This is extremely taboo in math. Other mathematicians will hear about your work the normal way, via Arxiv and via the community. There are probably only a few dozen specialists on Earth who really understand it anyway.
If they did, it would mean nothing to anyone who isn't a mathematician or studying math in university currently. Without stripping all of what makes it exciting just so it can be accessible. Plus, most math research is not about having some application or potentially benefitting society. The research that gets hyped up involves stuff people either have a vague or basic understanding of, could potentially impact either them or society in some way, or it's just cool. EX: I study active matter in the chemistry department. Many people, when I told them I studied chemistry and math during undergrad, they could appreciate the chemistry because of basic experiencing or understanding of how chemistry as a field has benefitted society. Just look at physics. At the high level, physics is very math heavy. Yet, an average person asked at random will have more appreciation for physics than math. Or how, relative to other fields, mathematicians don't really have to care about speaking to non-mathematians regarding their work all that much if its not applied work. Like, in my chemistry field, I'm being trained to speak to a wide range of people and knowledge. From experts to people who only know high-school chemistry. Even though most of the work I do is theoretical and computational based. Since it's common for chemists to speak to a wide range of audiences. This idea applies to other fields, STEM or not. Math, though, unless you do applied math research of some kind, there's no reason to train a mathematician in stuff like this really
I'm pretty sure they do, people don't find it so interesting but I keep up with plenty of math communication to the public on YouTube and Twitter. I personally don't find the need to speak to an empty room. I'll tell my friends because my friends are also studying math tho, and I welcome any curious people. And I also just don't use social media. And perhaps another thing is that mathematics pertains with *proof* and normal people just don't mesh with formal logic, it takes effort to to tell something informative and engaging to the public that's also *correct*
From my (non-expert) view, it seems like black holes are more comprehensible to a layperson on some basic and oversimplified level than whatever vector calculus/infinite series/whatever the mathematician found.
It's very simple actually. Math isn't science. It's best understood in this situation as a language. Say I study elvish. I read and write it with calligraphy, I speak it, I study all of the Tolkien books, etc. Someone comes up to me and asks "can you show me what you do?" Naturally I start speaking elvish. "But I don't understand, can you show me what you do, but in English?" No, I can't do that. I can just explain that I do elvish. If you want a taste of that you need to put in the effort too.
Lots of complicated math could be made somewhat (if only roughly or vaguely) accessible to much more of the general public. I think the limiting factor is really trying to get people interested in it. It's easier to grab interest if you can make the case that it will lead to warp drives or teleportation or whatever is the current popsci hype. An important part of this is also getting mathematicians excited to share their work to the general public.
Do you understand what he's doing? That's why he's not hyping it. It's much easier to understand "this cancer research will save lives" than it is to understand "this theoretical maths proof will advance other areas of science". Consider computer science - it's all just applied maths. Computers don't work without binary maths. There is, afaik and I'm sure someone will correct me if I'm wrong, basically no value in researching binary maths without other sciences existing to use it.
I remember talking to my professor about something similar. He was actively working on the same conjecture for like 30 years. Although he made an insane amount of progress, he refused to lean in any general direction of suspected outcome. His answer was essentially still, “Yeah, still I have no idea if this is true or false.” Even when pressed on a leaning, he was adamant that he genuinely didn’t know one way or the other. This relates, because I think that math research is very “pure” compared to other fields. Where if I talked to my professors about their research in other fields, there was an obvious leaning, “We suspect this is almost certainly true (or false).” But math was always met with, “I don’t know, and I don’t care. It’s not about being right or wrong, it’s just about the pursuit of truth. I don’t care one way or the other about its truth value. I only care to prove it.”
Coming from the perspective of someone who is certainly not a mathematician or particularly gifted at math, I think it's the failure of public education. Mind you, this is VERY subjective and from a layman's experience but the feeling I get is that many people are taught the "what" and not the "why" or "how" at a young age because math is so damn complex, even though it's important to teach children. In high school there were very few times here I was taught why I was using a cerain equation or how it was discovered. It felt like I was never getting the full picture of why I was doing something which lead to frustration since it was as if I was just doing busy work. I had a long conversation with my friends about this and we all had pretty much agreed despite going to different schools. When I got to college I continued to have not interest in math until I took logic as one of my philosophy course requirements. It felt like everything I did had a reason behind it and I fully understood the steps I was taking through a problem. This was literally the first time I was excited to move into a new unit to see how what I've learned builds on predicate logic, set theory, etc. and what contemporary problems or weirdness happens in logic research. I definately appreciated math much more when I moved onto stats for my psych requirements. The irony of all this is that I, a social worker, am more interested in math than most of my firend group which consists compuer scientists and engineers. They're certainly better at math than me but I still want to learn more than them! TL;DR I think most young people aren't being taught in a way that encourages curiosity which leads to disinterest, misunderstanding and unfortunately hatred for math, leading to low hype for mathematics research among laymen.
I try to, e.g. this was very well received: https://beta.epiplexis.xyz/logs/crystalline Granted that was about the process of doing math research, not really explaining the details, but I do that elsewhere.
I am not saying that it should be provate equity to do it, I am not proposing a change, but lets not act surprised.
Math is a kind of philosophy, but with the real universal language. I think mathicians doesn't really care about the popularity of math, they care about the true and the development of knowledge.
-discover a equation/theory in math -ask if it was discovered before -answer: "probably was"+no source+downvotes when you are a nobody online people will act as such, so don't hype math on social media, take your chances with peers in real life
I don’t understand people saying you’d be lying to the public if you “hyped” mathematics. People can’t be knowledgeable on everything, so it’s very important to simplify the most complex concepts to make them understandable and also fun to learn. Ignoring the funding issue for a second, this is culturally relevant as knowledge enriches people. Also if Math is better understood and publicised, more people will become interested in math which is always a good thing. Being technical and precise isn’t as important as conveying the intuitive aspects of a theory and conveying the sense of wonder only sciences can make people feel. You’re not lying to people, because the premise while doing science communication is that you’re simplifying the concepts (also because in a tweet or a twenty second video you can say only a limited amount of things). Also even in University things are simplified for the sake of understanding (not much for the entertainment value though lol). I study physics, and mathematical and also physical concepts are simplified for the sake of the models I’m studying at any given time. That doesn’t mean what I study is meaningless just because it isn’t the latest model accepted by the scientific community. Not every mathematician should talk about their work to a general public (also because Math is particularly difficult to explain) but people who do it aren’t lying and with the right compromises even very abstract concepts might be understandable by a general public.
Its just very hard to express these really abstract topics to people with no formal mathematical background. Especially if there is (as of yet) no application. We can help ground people in the understanding of certain fairly advanced topics in math by relating them to their associated applications. This is why you see LOTS of popscience media on Fourier transforms, Chaos Theory, Fractals, etc. It’s just very hard to do. Anyone with a significantly advanced degree in math will likely go on to pursue a more lucrative career than trying to hit the lottery and develop a self sustaining career as a math communicator. Being a science communicator and a scientists are VERY different and often take distinctly different talents. I love science/math but I’m not particularly great at science communication, even though I try really hard to be. So in short, I think most mathematicians would love for it to exist, but it’s very hard to do and not very lucrative, so the likelihood of enough people doing it to make any reasonable impact is very low.
Truthfully, and I have to be really, as I’m autistic, I think it’s largely because purely approximating, Maths, along with Philosophy probably, are seen as the most academically-challenging fields. We could argue that that’s because it’s often badly taught and therefore a very low level of Maths is taught to most people. The modal average student leaving school in my country, doesn’t even know how to confidently use the basic level of Maths, that they actually need for ordinary life skills. So how realistic is it that the average person would even think they could understand current Maths research? In my experience the average person, even the average “intelligent lay person” assumes they won’t understand anything about Maths so they don’t even try. They hear the word “Maths” and switch their brains off, deciding that the “mathsy” person is probably terribly clever and smile politely. Let’s be honest: even within an area of Maths, there are few other Mathematicians who properly understand research of their colleagues. Say we randomly selected: 100 Mathematicians and 100 Biologists and 100 Historians and put them, each group separately, in prolonged intense socialising situations. Apart from the fact that the biologists and Historians would socialise marginally better, I believe they would also be successfully discussing their research more with each other. They would probably send each other links to papers and they would read each other’s work. It’s true that there would be the odd word or concept they would have to look up, but they would do it, because it would be largely comprehensible, so it would be worth sharing. The Mathematicians would be there, even within/adjacent fields, largely talking about many other topics because they mostly don’t read each other’s work unless it’s almost exactly their very specific area. They would be doing so very carefully and precisely, correcting tiny errors in their previous phrasings that no ordinary person would even have noticed… (This is my experience anyway, although I admit my knowledge of Biologists and Historians is vastly more limited than my experience of Mathematicians.) The problem is that when Maths is “dumbed down”, we Mathematicians are (rightfully) irate. Sorry I haven’t finished my point, which I haven’t properly got to yet… I’ll edit this tomorrow. It’s late in the land, where Maths is the usual shortened term for Mathematics.
Frankly I think because it's a lot easier to "bullshit" stuff in other sciences. I am not saying that the hyped research itself is BS, but often the headlines and even the articles in pop-sci media use language that is essentially BS and makes something sound awesome to the "general public". In addition, for pop-sci you can take out most of the abstract stuff and math and just use some colorful analogy.... much harder to do with mathematics.
Quite simple actually, public and private schools don't know how to teach math to folks, make it interesting for them and explain to them what is the use of maths, hence why mathematicians don't share their research online; you need to at least understand stuff and if you do, you already check for new studies or reasearch in your given field, therefore there is no need for you to post on socials. People in high towers stuff.
Mathematicians know they know nothing very early compared to people in other fields.
yeah.. we need more math propaganda..
This is interesting
The person who seemingly proved the Riemann problem is posting on twitter and his proof looks promising
I think it’s because math is a language, and most mathematicians do not know how to talk about mathematics in any language but mathematics. They usually can’t translate their achievements or questions, or the significance of those things, into the word-based language the rest of us speak.
Tao is practically a modern-day Feynman with the way he makes state of the art research seem almost understandable to mere mortals. There’s just not that many people who have ever lived, who had that kind of mathematical ability and also the ability to explain it to more than a room full of their contemporaries. Something like the Langlands problem, there can’t be more than a million people currently alive who could even understand the problem statement, never mind how to solve it. Theoretical physics? Well, we all know what atoms are. There’s a tangible interest due to nuclear energy and fusion. It’s not as abstract. So there’s more interest and a greater ability to grok the basic idea. Also, I think AI grifters are setting unrealistic expectations for what a researcher’s Twitter presence should look like…