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this is barely hyperbole, there were times when finding a number higher than 3 arise naturally in a real analysis proof would be a genuinely intriguing event. once we found a 7 and it was so weird we stayed up for hours to figure out why
That's because we use π instead of τ that is a way better ratio to start with. No more pesky 2s and 4s to mess up every formula. Unit circle that actually works as intended.
When you're dealing with an equation derived by integrating a linear function, or when the equation is relating something to a half turn, it makes perfect sense for there to be a 1/2 in the equation.
You mean e^(iτ)=1 ? In other words, when you do a full circle turn, you're going in the same direction. e^(iτ/2) = -1 means when you do a half turn, you're going in the opposite direction.
Using Tau instead of Pi helps better explain what's going on. It's not some esoteric mystery of weird irrational numbers and imaginary powers. It's an explanation of how the exponential constant and the rotational constant interact to change directions on the complex plane.
Yeh, when everything is symbolised in variables, any number turning up is really weird. They're there because they must be there.
"Is there a way I can make this 7 a variable? Have I discovered a new structure?"
I remember when our professor said that we will now put the theory we just discussed to practical use. Us students must have been looking too hopeful because he followed that one up by "...but not using actual numbers".
I swear to god, mathematicians will rather invent new numbering systems than using the existing ones. Double credit for coming up with operations where EVERY element is a neutral element.
You probably can understand the general idea- we sorted all the finite simple groups (groups without a smaller group and normal subgroup as a quotient) into a ton of different categories, like Z_n for primes, and several others. Almost all of these are infinite except a handful, which are really weird. These "categories" of finite simple groups are explicitly defined groups which don't fit neatly into other types. The biggest of these is called the "monster" and has 20 of the others as subgroups. This group happens to have 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 elements. This group might be useful for a bunch of conjectures different fields.
https://simple.wikipedia.org/wiki/Monster_group
the "simple" language can be nice for various STEM topics, if you just want the quickest of run-downs (and it exists.)
Also, I think wikipedia is a terrible place to learn anything from. That's not its purpose. At least for STEM topics, it's a reference for things you already know or have considerable background knowledge about (again: reference.) The goals are not the same as for instance a textbook.
I just have to insert that rant because often (not here but it triggered me) I see people sending folks to wikipedia to supposedly learn about some math topic, and it ringles my jimjams.
TIL Simple Wikipedia exists
And I kinda get linking people to Wikipedia, for advanced math topics it may be one of the only free resources on the internet for that topic, and I know it personally helped me a lot for areas such as elliptic curve properties. But the keyword is advanced, and unless you know most of the terms surrounding that topic, or as you said you know the topic fairly well and are referencing it, it’s confusing to most people and can generally shy them away from the topic
I was gonna say, 2 is normal, 3 happens sometimes, 4 is just 2*2, anything 5+ is weird...
And then you'll get some 10+ digit monstrosities because fuck you.
You might be the only person to appreciate this joke. What is the value of a contour integral around western Europe? Zero! All the poles are in eastern Europe.
One of the biggest open problems in set theory can be summed up as "why the hell is it 4?" (This is a quote from a famous paper about the problem).
The result is that they found that under certain conditions we have that 2^(aleph_w)
First of all, literally Searching `“Why the HELL Is It Four?” set theory` on duck duck go finds the relevant paper in which the quote is from [this paper](https://arxiv.org/abs/math/0102056v1) (the link is to Arxiv page)
The relevant key words are "Shelah inequality", "Shelah PCF theory" and "Shelah aleph omega". [Here is the relevant wiki page](https://en.m.wikipedia.org/wiki/PCF_theory).
7 showed up in my real analysis course. The course, as I'm sure several people have experienced, was one where the professor (sometimes) outlined proofs, and students had to fill in the blanks and present the proofs to the class, and those presentations were our grades in the course. We were chosen randomly, so we ostensibly had to have every proof prepared.
7 showed up because one of the proofs was so involved that the professor divided the proof up into 7 sections. I think it was Radon-Nikodym, but I might be mis-remembering. There were 6 of us in the class, so we each did one part, and the professor did one as well.
My favorite part of the class was when I was picked to do the Caratheodory Extension Theorem.
I think the main reason the fact that alternating groups become simple for degree greater than or equal to 5 is surprising is that we aren't used to numbers larger than 3 being important
Especially once you realize it somehow *has to* be a 7 and no smaller constant and you wonder if you can do better or if the number is truly interesting.
In our theoretical electrodynamics lecture (based on _Jackson_) we solved for some potential and we got a result with a factor of sqrt(127).
Like, that's so random, it gotta be wrong, right? Turns out it was correct.
I did Adderall once during my undergrad for a Real Analysis take home test. Never felt smarter, flying to the moon, boom boom, this is what those PhD bound kids were on! Got a 15% and a conference with the professor. Apparently my sludge laden and constantly complaining brain was more capable of math than I gave it credit for. A good lesson in 'feeling good does not make one correct'.
Adderall is effective for completing tasks you're already an expert at, with maximum enthusiasm and precision, if the biggest barrier was enthusiasm and executive function.
For people with severe ADHD, this is basically all tasks they are experts at: including laundry, hygiene, responding to basic correspondence, grocery shopping, completing basic tasks at work etc etc.
For regular people, these categories of tasks are already not an issue most of the time. This is why Adderall is effective for med and chemistry students but terrible for engineering/physics/math students (broadly).
Med students need to memorize and practice thousands of simple conceptual relationships to the point of perfect, rapid recall. This is boring, but easy to be an expert at, if you put in the work.
Engineering students need to learn a very small number of fairly complex conceptual relationships and be able to generalize that knowledge to a task they have never seen.
The act of studying isn't the use of an expert skill to build basic recall, it's the development of the expert skill in the first place.
Across the board, every person I know, with or without ADHD, when they take stimulants to study these sorts of disciplines or tackle these sorts of problems, just end up cleaning their room and going to the gym instead.
As someone with ADHD literally so severe it pegs the meter (first percentile in focus on my diagnostic test, despite getting anywhere from 77th percentile to 99th percentile on the rest of the cognitive measures), I can confirm: extra stimulants only make your brain more effective in very limited ways. In fact, too much caffeine doesn't give me the shakes, it tends to make me sleepy.
Yeah, unfortunately, stimulants actually make some of the symptoms worse in some contexts, and "psychotropic drug literacy" for the patient isn't really a part of psychiatric medicine.
There's definitely ineffective ways to use (and/or abuse) stimulants as an ADHD person. There's effective ways to use them as an NT. Just for pharmacology broadly I wish there was a greater effort by care providers to holistically introduce drugs into peoples' lives, rather than infodumping risk factors and sending them on their way.
im an engineering student with ADHD and I use ritalin, i'd say it's still effective in our field too; idk if it's actually less than med and chemistry since i'm not in those fields but still.
tbf my dose is tiny at 5mg x2 every day, i don't know how effects would change with more typical doses of 20-30mg
5X2 is pretty small, and, as I said, for some folks the benefit of stimulants are how much easier they make the tasks which are just "given" or "routine" for neurotypicals.
It's not at all that "not engineers should take stimulants". It's more that "stimulants don't give special benefit to studying engineering, but DO give special benefit to studying chemistry or biology"
>Oh yeah 2 is super important, it's numbers higher than 2 that start freaking me out
**7** is important too, because it's **8-1**.
^(**Note:** The set of people who think it's deep is precisely: 3-year-olds, stoners, and math PhD's.)
It's not that it'll pop up in equations, but a lot of things **only** work in dimensions **1**, **3**, and **7** for the same reason that we Cayley algebras beyond octonions are *reeeeeally* not nice (aren't normed division algebras).
For example, the cross-product [can only be extended to seven dimensions](https://en.wikipedia.org/wiki/Seven-dimensional_cross_product) if you want to keep its nice properties.
Seven-dimensional [Exotic Spheres](https://en.wikipedia.org/wiki/Exotic_sphere) were found by John Milnor - something for which he [got the Abel prize](https://en.wikipedia.org/wiki/Exotic_sphere). Those are spheres with smooth structures that are homemorphic, but **not diffeomorphic** to each other.
Unit seven-dimensional spheres have the [largest surface areas](https://en.wikipedia.org/wiki/N-sphere#/media/File:Hypersphere_volume_and_surface_area_graphs.svg) out of all dimensions. Don't know whether this is connected to the existence of exotic spheres, but it's certainly *suspicious*.
What is connected (equivalent, in fact) to existence of normed division algebras in dimensions 1, 2, 4, and 8 is existince of [H-space structures](https://en.wikipedia.org/wiki/H-space) on spheres of dimensions 1, 3, and 7. [**0, 1, 3, 7**](https://oeis.org/A222010) is thefore a famous **finite** sequence.
*Side note:* interesting *infinite* sequences are dime a dozen; but provably **finite** ones are much harder to come by.
An equivalent (and simpler to understand) fact is that spheres are [parallelizeable](https://en.wikipedia.org/wiki/Parallelizable_manifold) **only** in dimensions 1, 3, 7.
This is a generalization of the [Hairy Ball Theorem](https://en.wikipedia.org/wiki/Hairy_ball_theorem), which says that a 2-sphere is **not** parallelizable: every smooth vector field on it must have a singularity. Since wind velocity gives a vector field on a sphere, this math means that at any given time, there *must* be a hurricane on Earth *somewhere*.
Or, in other words, you can't comb a sphere.
Unless its dimension is **1**, **3**, or **7**, that is.
**7** is freaky.
Ah. Makes sense!
The post is absolutely 100% realistic, thanks for making it :D
(The right picture is literally me, though I haven't switched to XR yet)
Yes. Any number n in base n is 10. I’m really bad at explaining that, but if you for example take a number like 389 in base 10, you can write it as 3 x 10^2 + 8 x 10^1 + 9 x 10^0 and other systems would just use a different base. So if you take 10 in base π, you can write it like 1 x π^1 + 0 x π^0
Had friends in engineering, physics, and math in college, I still remember the night when I was hanging out at a their apartment one night playing games with one when his roommate came out from his room where he’d been doing homework “Kyle, do you recognize this symbol?” “…CJ, that’s a 6…” “…a 6…a 6? A 6?!” Followed by manic exhausted laughter.
This reminds me of the time somebody corrected my Linear Algebra lecturer because he’d gotten some basic arithmetic wrong when solving an example problem. The lecturer looked at him with complete confusion - “Are you telling me that 3 plus 2 is 5??!”
After what felt like a lifetime of silence he eventually goes: “Yeah… I think… I think you’re right” and corrects the board. He really still didn’t seem very sure.
Don't! You're not stupid for not knowing much about advanced math - I doubt you know much about, say, Bhutanese history, but you wouldn't feel stupid for not getting a meme about it. You just haven't learned it yet.
I like to think I’m good at math, but then I go to the math subs and they’re all talking about Hurberger’s decimal. Meanwhile I’m like:
https://preview.redd.it/yq07n08sxjmc1.jpeg?width=640&format=pjpg&auto=webp&s=22c17a2815bd975dbbfcb050918bb35bf0c9ea9d
Replying to the woke's question
https://preview.redd.it/9dmaybtlajmc1.jpeg?width=1500&format=pjpg&auto=webp&s=58c662960d5a609c43220b72f1dfed2ee8007cda
Because I'm bad at drawing (especially with a finger), this took longer to write than to calculate.
I did it as 397x46=(400x46)-(3x46)
18,400-138
18,262
397x46=18,262
Edit: Why does Reddit need a blank line between each new line to actually write it as a separate line, let me compact my comment damn you
I love this so much everything about this meme is pure gold. barely hyperbole you say? you're touching the surface. im in honours real analysis 2 (were covering topology rn and haven't seen a single number... so far.) will see 0 in a sec when we go over rienman integral I'm sure of it.
ahh sorry i was being sarcastic
beyond school, being able to multiply big numbers isn't seen as *difficult*, just time consuming and unimportant. mathematicians are profoundly disinterested in it.
in the very rare case one needs to do such a thing, we have calculators
A bit late to the party but I felt very strange when I studied the formula for the variance of a continuous uniform distribution, which naturally contains a 12
People who claim to like math always do random stuff like memorizing a bunch of digits of pi, but if you frequently interact with actual mathematicians, they barely even remember how to count.
I have a lot of pi memorized not because I like math, but because I like cyphers and stuff like that and it’s fun to base random shit off pi (plus I just felt like it)
…I also said that 3 - 1 = -2 the other day
What the fuck is "e" was where I hit my limit in mathematics. Suddenly starts showing up in every Calc problem and no professor could explain it to me.
e comes from taking the limit of (1+1/n)^n as n tends towards infinity. You might recognise that as the formula for compound interest. It’s a transcendental number, and it’s key property for calculus is that as a function f(x)=e^x it is it’s own derivative. It also just appears everywhere
e is an irrational constant (an irrational number that never changes, but we write it as a single character representing it to save space). Just like Pi.
It's equal to *approximately* 2.71828.
It's used in calculus because f(x) = e^x is an exponential function that is equal to it's own derivative and meets the condition that f(0) = 1 [f(0) = e^0 = 1]. Being equal to it's own derivative makes it convenient to work with and gives it some useful properties.
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this is barely hyperbole, there were times when finding a number higher than 3 arise naturally in a real analysis proof would be a genuinely intriguing event. once we found a 7 and it was so weird we stayed up for hours to figure out why
In geometry 4 comes up a lot, usually in some combination with pi. Occasionally, 8 comes up for a similar reason.
Wow, the number 2 frequently appears multiplied by the half-turn circle constant? I wonder why that happens so often.
["2?"](https://static.wikia.nocookie.net/international-entertainment-project/images/3/39/So_Weird_-_Poster.jpg/revision/latest?cb=20230105041433)
lmfao
https://i.redd.it/7itfd495ypmc1.gif Source: smbc- comics: [https://www.smbc-comics.com/comic/2008-02-21](https://www.smbc-comics.com/comic/2008-02-21)
Because we like our exponential 2wPi (can't be arsed to do an omega on phone)
well that’s just 2^2 and 2^3
That's because we use π instead of τ that is a way better ratio to start with. No more pesky 2s and 4s to mess up every formula. Unit circle that actually works as intended.
Would you rather the occasional 1/2? I think i prefer the 2 to be honest Also pi is much easier to draw satisfyingly
I will move the 1/2 on the other side, away from my pretty τ.
When you're dealing with an equation derived by integrating a linear function, or when the equation is relating something to a half turn, it makes perfect sense for there to be a 1/2 in the equation.
> Also pi is much easier to draw satisfyingly Marketing always beats 'better' ;)
ah yes the famous e^(iτ/2)+1=0 that contains no pesky 2s
You mean e^(iτ)=1 ? In other words, when you do a full circle turn, you're going in the same direction. e^(iτ/2) = -1 means when you do a half turn, you're going in the opposite direction. Using Tau instead of Pi helps better explain what's going on. It's not some esoteric mystery of weird irrational numbers and imaginary powers. It's an explanation of how the exponential constant and the rotational constant interact to change directions on the complex plane.
True but isn’t e^iτ = 1 so much cooler?
I think you meant 2^2 and 2^3.
Yeh, when everything is symbolised in variables, any number turning up is really weird. They're there because they must be there. "Is there a way I can make this 7 a variable? Have I discovered a new structure?"
Im picturing that scene from Friends when the doctor brings a team of like 25 doctors to stare at Ross’s ass and figure out what the mole is haha
🙄🍑 👀👀👀👀👀
"You know I have dinner plans, thank you"
I remember when our professor said that we will now put the theory we just discussed to practical use. Us students must have been looking too hopeful because he followed that one up by "...but not using actual numbers". I swear to god, mathematicians will rather invent new numbering systems than using the existing ones. Double credit for coming up with operations where EVERY element is a neutral element.
When 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 appears in group theory 😶 https://en.m.wikipedia.org/wiki/Monster_group
Thanks to my 18 hours of various undergraduate mathematics training I know that this article contains words and many of them are in English.
Ive got a math bachelors and spent a lot of time learning the abstract algebra course specifically, none of those besides group seem familiar at all.
You probably can understand the general idea- we sorted all the finite simple groups (groups without a smaller group and normal subgroup as a quotient) into a ton of different categories, like Z_n for primes, and several others. Almost all of these are infinite except a handful, which are really weird. These "categories" of finite simple groups are explicitly defined groups which don't fit neatly into other types. The biggest of these is called the "monster" and has 20 of the others as subgroups. This group happens to have 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 elements. This group might be useful for a bunch of conjectures different fields.
https://simple.wikipedia.org/wiki/Monster_group the "simple" language can be nice for various STEM topics, if you just want the quickest of run-downs (and it exists.) Also, I think wikipedia is a terrible place to learn anything from. That's not its purpose. At least for STEM topics, it's a reference for things you already know or have considerable background knowledge about (again: reference.) The goals are not the same as for instance a textbook. I just have to insert that rant because often (not here but it triggered me) I see people sending folks to wikipedia to supposedly learn about some math topic, and it ringles my jimjams.
TIL Simple Wikipedia exists And I kinda get linking people to Wikipedia, for advanced math topics it may be one of the only free resources on the internet for that topic, and I know it personally helped me a lot for areas such as elliptic curve properties. But the keyword is advanced, and unless you know most of the terms surrounding that topic, or as you said you know the topic fairly well and are referencing it, it’s confusing to most people and can generally shy them away from the topic
I was gonna say, 2 is normal, 3 happens sometimes, 4 is just 2*2, anything 5+ is weird... And then you'll get some 10+ digit monstrosities because fuck you.
To be fair there's a 1/137 in particle physics
"I can explain what Monstrous Moonshine is in one sentence, it is the voice of God."
You might be the only person to appreciate this joke. What is the value of a contour integral around western Europe? Zero! All the poles are in eastern Europe.
What the hell Europe is holomorphic ???
That joke stopped working after Poland joined the Schengen area.
I learned the joke almost 18 years ago and there are plentiful poles outside Poland. That's why it's a joke.
Polish Air Force - simple poles in complex planes
One of the biggest open problems in set theory can be summed up as "why the hell is it 4?" (This is a quote from a famous paper about the problem). The result is that they found that under certain conditions we have that 2^(aleph_w)
Is there a name/keyword for this problem so I can read into it more?
First of all, literally Searching `“Why the HELL Is It Four?” set theory` on duck duck go finds the relevant paper in which the quote is from [this paper](https://arxiv.org/abs/math/0102056v1) (the link is to Arxiv page) The relevant key words are "Shelah inequality", "Shelah PCF theory" and "Shelah aleph omega". [Here is the relevant wiki page](https://en.m.wikipedia.org/wiki/PCF_theory).
7 showed up in my real analysis course. The course, as I'm sure several people have experienced, was one where the professor (sometimes) outlined proofs, and students had to fill in the blanks and present the proofs to the class, and those presentations were our grades in the course. We were chosen randomly, so we ostensibly had to have every proof prepared. 7 showed up because one of the proofs was so involved that the professor divided the proof up into 7 sections. I think it was Radon-Nikodym, but I might be mis-remembering. There were 6 of us in the class, so we each did one part, and the professor did one as well. My favorite part of the class was when I was picked to do the Caratheodory Extension Theorem.
> there were times when finding a number higher than 3 What does backwards-epsilon mean again?
im pretty sure its made up by engineers as an approximation of pi
I think the main reason the fact that alternating groups become simple for degree greater than or equal to 5 is surprising is that we aren't used to numbers larger than 3 being important
Even when you have a sum or series where one of the numbers increments, they usually put the “…” before they show 7.
Trigonometry?
After thorough peer-review, I can confirm that 7 is indeed higher than 3.
You won't get anywhere in life by rounding Pi to 3, sonny-boy
Especially once you realize it somehow *has to* be a 7 and no smaller constant and you wonder if you can do better or if the number is truly interesting.
well, where did the 7 come from?
In our theoretical electrodynamics lecture (based on _Jackson_) we solved for some potential and we got a result with a factor of sqrt(127). Like, that's so random, it gotta be wrong, right? Turns out it was correct.
https://artgallery.yale.edu/collections/objects/198876
Come on guys, there are so many numbers! There's 0, there's 1, they keep going until 255!
You missed a negative sign 4 steps above. There, I solved it for you.
The number 8 came up in the Jane Street Puzzle last month, those are always fun lol
Some people like using 100 (or maybe a bigger number if needed) as a generic big number in estimates e.g. in harmonic analysis
This is the opposite of my aerospace engineering degree where if an answer was under 10 to the twelfth power I was concerned
Sounds like 2^n - 1 is your case
Me when I get percent yield higher than 1
False, you use at least 100mg of Adderall
Get you, Mr Erdos
I did Adderall once during my undergrad for a Real Analysis take home test. Never felt smarter, flying to the moon, boom boom, this is what those PhD bound kids were on! Got a 15% and a conference with the professor. Apparently my sludge laden and constantly complaining brain was more capable of math than I gave it credit for. A good lesson in 'feeling good does not make one correct'.
Adderall is effective for completing tasks you're already an expert at, with maximum enthusiasm and precision, if the biggest barrier was enthusiasm and executive function. For people with severe ADHD, this is basically all tasks they are experts at: including laundry, hygiene, responding to basic correspondence, grocery shopping, completing basic tasks at work etc etc. For regular people, these categories of tasks are already not an issue most of the time. This is why Adderall is effective for med and chemistry students but terrible for engineering/physics/math students (broadly). Med students need to memorize and practice thousands of simple conceptual relationships to the point of perfect, rapid recall. This is boring, but easy to be an expert at, if you put in the work. Engineering students need to learn a very small number of fairly complex conceptual relationships and be able to generalize that knowledge to a task they have never seen. The act of studying isn't the use of an expert skill to build basic recall, it's the development of the expert skill in the first place. Across the board, every person I know, with or without ADHD, when they take stimulants to study these sorts of disciplines or tackle these sorts of problems, just end up cleaning their room and going to the gym instead.
As someone with ADHD literally so severe it pegs the meter (first percentile in focus on my diagnostic test, despite getting anywhere from 77th percentile to 99th percentile on the rest of the cognitive measures), I can confirm: extra stimulants only make your brain more effective in very limited ways. In fact, too much caffeine doesn't give me the shakes, it tends to make me sleepy.
Yeah, unfortunately, stimulants actually make some of the symptoms worse in some contexts, and "psychotropic drug literacy" for the patient isn't really a part of psychiatric medicine. There's definitely ineffective ways to use (and/or abuse) stimulants as an ADHD person. There's effective ways to use them as an NT. Just for pharmacology broadly I wish there was a greater effort by care providers to holistically introduce drugs into peoples' lives, rather than infodumping risk factors and sending them on their way.
im an engineering student with ADHD and I use ritalin, i'd say it's still effective in our field too; idk if it's actually less than med and chemistry since i'm not in those fields but still. tbf my dose is tiny at 5mg x2 every day, i don't know how effects would change with more typical doses of 20-30mg
5X2 is pretty small, and, as I said, for some folks the benefit of stimulants are how much easier they make the tasks which are just "given" or "routine" for neurotypicals. It's not at all that "not engineers should take stimulants". It's more that "stimulants don't give special benefit to studying engineering, but DO give special benefit to studying chemistry or biology"
That just has a 1 in it. That's fine. If it was 400mg that would be confusing.
Yeah, 30 is daily use. 100 and we're going to the moooooon Source: I'm on 20 mg
He doesn't have anymore cos he's consumed the rest of it.
Since I left school the highest number I saw is 59 on my digital clock
that's because you're using the *old* clocks.*new* clocks go up to 99
Nothing is safe from inflation
Are we trying metric time again?
Not only are the trains running on time, they're running on *metric* time.
Y'all still use numbers? -Me, an engineer
My favorite day as an engineer was when my colleague, who refused to use numbers (time) for naming files, got fired.
Every office has one Kevin. When Kevin is inevitably fired or quits, the universe will make a new one appear out of thin air.
I think mine was like 2^999999999 or smth
Upgrade to an analog, they go up to 360.
3:32 is too real
2 comes up in algebraic number theory all the time. To say that Char(K) != 2.
Oh yeah 2 is super important, it's numbers higher than 2 that start freaking me out
>Oh yeah 2 is super important, it's numbers higher than 2 that start freaking me out **7** is important too, because it's **8-1**. ^(**Note:** The set of people who think it's deep is precisely: 3-year-olds, stoners, and math PhD's.) It's not that it'll pop up in equations, but a lot of things **only** work in dimensions **1**, **3**, and **7** for the same reason that we Cayley algebras beyond octonions are *reeeeeally* not nice (aren't normed division algebras). For example, the cross-product [can only be extended to seven dimensions](https://en.wikipedia.org/wiki/Seven-dimensional_cross_product) if you want to keep its nice properties. Seven-dimensional [Exotic Spheres](https://en.wikipedia.org/wiki/Exotic_sphere) were found by John Milnor - something for which he [got the Abel prize](https://en.wikipedia.org/wiki/Exotic_sphere). Those are spheres with smooth structures that are homemorphic, but **not diffeomorphic** to each other. Unit seven-dimensional spheres have the [largest surface areas](https://en.wikipedia.org/wiki/N-sphere#/media/File:Hypersphere_volume_and_surface_area_graphs.svg) out of all dimensions. Don't know whether this is connected to the existence of exotic spheres, but it's certainly *suspicious*. What is connected (equivalent, in fact) to existence of normed division algebras in dimensions 1, 2, 4, and 8 is existince of [H-space structures](https://en.wikipedia.org/wiki/H-space) on spheres of dimensions 1, 3, and 7. [**0, 1, 3, 7**](https://oeis.org/A222010) is thefore a famous **finite** sequence. *Side note:* interesting *infinite* sequences are dime a dozen; but provably **finite** ones are much harder to come by. An equivalent (and simpler to understand) fact is that spheres are [parallelizeable](https://en.wikipedia.org/wiki/Parallelizable_manifold) **only** in dimensions 1, 3, 7. This is a generalization of the [Hairy Ball Theorem](https://en.wikipedia.org/wiki/Hairy_ball_theorem), which says that a 2-sphere is **not** parallelizable: every smooth vector field on it must have a singularity. Since wind velocity gives a vector field on a sphere, this math means that at any given time, there *must* be a hurricane on Earth *somewhere*. Or, in other words, you can't comb a sphere. Unless its dimension is **1**, **3**, or **7**, that is. **7** is freaky.
This was a fun read, for a math padawan (or maybe the left wojak in ops upload) like me. Thanks!
this is why i included the number 7 in the post lol. finding out that 7 was special was a genuinely psychedelic experience for me
Ah. Makes sense! The post is absolutely 100% realistic, thanks for making it :D (The right picture is literally me, though I haven't switched to XR yet)
The highest number of any importance is pi
I swear, I'm going to start a petition to eliminate pi from math. Who cares about pi. It's just a number.
Signed
That is not nice. Every number is special
I believe only countably many numbers are special.
Decimalising Pi is cringe. Free yourself from Base10, for all that is holy. 
why would anyone put pi into digits, you're giving yourself more symbols to write at the cost of less accuracy
Thank you for understanding so completely.
pi in base pi is jus 10
wait, is that true?
Yes. Any number n in base n is 10. I’m really bad at explaining that, but if you for example take a number like 389 in base 10, you can write it as 3 x 10^2 + 8 x 10^1 + 9 x 10^0 and other systems would just use a different base. So if you take 10 in base π, you can write it like 1 x π^1 + 0 x π^0
So this is proof that pi = 10?
I mean, only in the situation where you're using base pi. The base is important.
1000000 + π ≈ 1000000 + 10 Therefore, π ≈ 10
To be allowed as a base, wouldn't the base required to be a natural number?
Why would I need an approximation for a numerical solution? All those propagating errors...
Ok, binarising π time: 11.00100 10000 11111 10110 10101 00010 00100 00101 10100 01100 00100 01101 00110 00100 11000 11001 10001 01000 10111 00000
https://en.m.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula Every time Pi in binary comes up my mind goes to this
Does it come up a lot??
You would not believe how much it comes up around the water cooler
As an engineer, depending on the application and precision required, I can get away with rounding Pi to 3. /s
Everything is 3. Pi is 3. e is 3. 4 is 3.
Base pi
go back to your cage leo
2.718 crying in the corner
You must mean 2.71828182818281828 oh waitaminit... how did it go again? 459 Dirello Street?
e = 27/10 + 1828/99990
I tried to make that nice and reducible, but the prime factors of 271801 are 47 and 5783. υωυ That makes me a saaaaad panda 😭
Thank god OG mathematicians are ded
Is this a reference to what’s up doc? (I recognize the address from the movie, but is that number 2.718… also in the movie somewhere?)
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aren't Seconds the only "metric" time measurement? since they're what the SI prefixes apply to, e.g. millisecond, microsecond, kilosecond...
1 megaday
1 year ~ 10π megaseconds
Had friends in engineering, physics, and math in college, I still remember the night when I was hanging out at a their apartment one night playing games with one when his roommate came out from his room where he’d been doing homework “Kyle, do you recognize this symbol?” “…CJ, that’s a 6…” “…a 6…a 6? A 6?!” Followed by manic exhausted laughter.
This reminds me of the time somebody corrected my Linear Algebra lecturer because he’d gotten some basic arithmetic wrong when solving an example problem. The lecturer looked at him with complete confusion - “Are you telling me that 3 plus 2 is 5??!” After what felt like a lifetime of silence he eventually goes: “Yeah… I think… I think you’re right” and corrects the board. He really still didn’t seem very sure.
He just like me fr
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Don't! You're not stupid for not knowing much about advanced math - I doubt you know much about, say, Bhutanese history, but you wouldn't feel stupid for not getting a meme about it. You just haven't learned it yet.
You know what's weirder than 7? Seeing a neoliberal in a different subreddit.
o7, gotta leave the DT occasionally
Everybody starts somewhere. As the saying goes, you gotta be bad at something before you can be good at something
I like to think I’m good at math, but then I go to the math subs and they’re all talking about Hurberger’s decimal. Meanwhile I’m like: https://preview.redd.it/yq07n08sxjmc1.jpeg?width=640&format=pjpg&auto=webp&s=22c17a2815bd975dbbfcb050918bb35bf0c9ea9d
Trying to think of what the largest number to appear in my thesis was. If we remove discussions of specific examples… maybe 3?
In my world, half the time pi = 3. The other half of the time, pi =1. Once in a great while, pi^2 = g.
Numbers make math hard.
Replying to the woke's question https://preview.redd.it/9dmaybtlajmc1.jpeg?width=1500&format=pjpg&auto=webp&s=58c662960d5a609c43220b72f1dfed2ee8007cda Because I'm bad at drawing (especially with a finger), this took longer to write than to calculate.
Why are your 0s squares
Now you left me wondering that.
I did it as 397x46=(400x46)-(3x46) 18,400-138 18,262 397x46=18,262 Edit: Why does Reddit need a blank line between each new line to actually write it as a separate line, let me compact my comment damn you
When your math becomes so advanced that you run out of alphabets for your variables you can just use digits as variables. "Let 3 > 0 …"
I mean at that point it’s not like you’re using the digits anyway
Mathematicians literally just can't count. Source: Family of mathematicians.
I love this so much everything about this meme is pure gold. barely hyperbole you say? you're touching the surface. im in honours real analysis 2 (were covering topology rn and haven't seen a single number... so far.) will see 0 in a sec when we go over rienman integral I'm sure of it.
True mathematicians are handling some 3 dimensional graphs and regularly fail basic arithmetic
This is too true
18388, did that in a minute
Wow you must have a PhD in math!!
Wdym, im in 11th grade and have 4 mental disorders
The funniest thing is, i just checked, its off by like 104
ahh sorry i was being sarcastic beyond school, being able to multiply big numbers isn't seen as *difficult*, just time consuming and unimportant. mathematicians are profoundly disinterested in it. in the very rare case one needs to do such a thing, we have calculators
Just comes to show that sarcasm can't be expressed through written text. Especially if the person on the other side is a bit off.
Bazinga!
Btw the answer's 2 3-3=0 0x6=0 0=2=2
(rolled up thesis) **WHAP** Bad Den! Bad Den! **WHAP** Stop confusing the normalized. That's for MATH300 and up.
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Math exam rules say if you can somehow cancel something to zero, you're probably doing something right
Oh my dear peasants, mathematicians don't care for numbers.
This makes me think of microwaves. Do you think you have ever pressed the 7 button?
There are three types of mathmos Those who can count and those who can’t
According to [xkcd](https://xkcd.com/899/), if you encounter numbers higher than about 8.7 you're not doing real math.
That's an upside down L. This "7" you speak of is only mythical. Calm down and take more adderall to calm down.
One time in college, I found myself staring at the board, wondering what that "backwards epsilon" was.
A bit late to the party but I felt very strange when I studied the formula for the variance of a continuous uniform distribution, which naturally contains a 12
‘plier on the ‘eddit doebeit https://preview.redd.it/b2oe7zy0uimc1.png?width=480&format=png&auto=webp&s=4b530ce3094d7243be84124c7c5fc9ddab627c26
Peetah?
People who claim to like math always do random stuff like memorizing a bunch of digits of pi, but if you frequently interact with actual mathematicians, they barely even remember how to count.
I have a lot of pi memorized not because I like math, but because I like cyphers and stuff like that and it’s fun to base random shit off pi (plus I just felt like it) …I also said that 3 - 1 = -2 the other day
Actually I don't remember where but I got a 7 and the teacher told us "brace yourself you should see something weird by the end of the exercise"
Reminds me of this comic about scientists https://www.smbc-comics.com/index.php?db=comics&id=1777
Do the physics trick c = ℏ = e = 7 = 1
Mathematicians have ADHD?
real talk, like bro cringe instagram number theory tricks and hard integrals aren't doing shit sorry I am a snob and Im aware
Arrows pointing to arrows pointing to ARROWS POINTING TO ARROWS POINTING TO ARROWS POINTING TO ARROWS POINTING TO ARROWS
find a number larger than 4 in someone's thesis. i dare you
397x46=(7940+1191)x2=…
π=e=3
7 is a constant that stands for 6+1
The adderall is a nice touch
I would replace his "<3" with (-1/12)
I can't upvote this enough.Lmfourierao
Sad shit too I can’t even do 397*46 in my head anymore the calculator is my crutch
The biggest thing my mathematics course load for engineering school taught me is how little I know about math…
It's hard to get higher than 2. I swear that biatch is on edibles every time I find him in a cyclotomic field
well i live in GF(5), so this '7' thing works like a 2 for me.
Hahaha. Well this made me laugh.
What the fuck is "e" was where I hit my limit in mathematics. Suddenly starts showing up in every Calc problem and no professor could explain it to me.
e comes from taking the limit of (1+1/n)^n as n tends towards infinity. You might recognise that as the formula for compound interest. It’s a transcendental number, and it’s key property for calculus is that as a function f(x)=e^x it is it’s own derivative. It also just appears everywhere
e is an irrational constant (an irrational number that never changes, but we write it as a single character representing it to save space). Just like Pi. It's equal to *approximately* 2.71828. It's used in calculus because f(x) = e^x is an exponential function that is equal to it's own derivative and meets the condition that f(0) = 1 [f(0) = e^0 = 1]. Being equal to it's own derivative makes it convenient to work with and gives it some useful properties.
Radditor math fans in the comment section be like, "uhm the answer to the equation on the left is...."
real mathematicians: 3x+1
The more math strays away from reality, the more it is fun and interesting
https://artgallery.yale.edu/collections/objects/198876 This keeps me up at night
The 30mg adderall is killing me, it’s the only reason I’m still pursuing math studies
my brain doing 397\*46: 397 \* 46 = 46\*4 \*100 - 3\*46 (40+6)\*4 = 160+24 = 184 (40+6)\*3 = 120+18 = 138 397 \* 46 = 18400 - 138 = 18262
No more base ten, decimalizing is cringe.
Left phone answer is -13, right?
Ay Yo that adderall joke hit close to home
ok without a calculator i think the answers are -13 and 18262