Math @ TTT

Category Theory

Category theory is fun, come on guys let's talk about it!
For those who interested but know nothing about it my recommendation is Basic Category Theory, by Tom Leinster, which can be found on arXiv.
My favorite notion is currying, let me explain it.
Give three sets %%%A, B, C%%% and denote the set of functions from %%%A%%% to %%%B%%% by %%%[A, B]%%%, we claim that %%%[[A \times B], C]%%% is actually isomorphic to %%%[A, [B, C]]%%%.
Before I give the proof you can think about it yourself!

77° 2025.05.14 05:07:00 0 replies
Whats 2 + 2?

2

76° 2025.04.01 12:57:57 0 replies
anonymity is not schizophrenia

number of persons: 1
number of pseudonyms: n
rationality of such individual: true
proof: suppose use of only one pseudonym is rational choice. then the first pseudonym is eventually discovered and linked to legal name, making it pointless. contradiction to rational goal of anonymity as protection against would be big brothers. QED

75° 2025.03.04 15:28:22 0 replies
how do i get back into math?

So I recently graduated from Fine Arts studies and realized that I actually miss learning Math but I don't know where to start again. The last thing I remember from highschool is the very basics of calculus. Any books or websites that you might recommend? (Also, i'm quite interested in math for audio/acoustics/sound design)

68° 2022.11.28 04:54:39 3 replies
- other than fm what are you going to be using math for in sound design?
  I guess there is karplus/strong type stuff, but I mean, what does that have to do with anything? What are you doing, vst programming?
  
  69° 2023.03.31 02:47:23
- khan academy
  
  73° 2024.10.03 03:28:15
- deepseek
  
  74° 2025.02.08 07:10:13
jahavvshsisjsbslspsjshsb

jsjssnsbsjsjsnsbsjdjdndldodbsbwkabshsusjsb
these are numbers in base 26
jshshsus
jsjsjsj
dodkdkdjdjs
sjsjshsj sjsjsshsh
dldkddk sjsjsjsj,jsjsbseb
ekejdjd.djdjsbssn
sksjsdj,jejsnsj.sksjsnd,jsjsjseo.eksksjs.sksksj,kskskssk
sksksksks.sksksksksjdjdjd
eodos
sjsjsjsnssnsnsjssjsjsj
slslsksksksoeiwismsmsmzmxmx..,,.,.,.,.nsnsnznzmzmznzmzzmzmzkzksksmmssnsksnsnksskkwowkwowowkiwkwoqqoowwkieueuysyststgssbnsjdnxnxnxmxnxbxmxoxkdkdkdkkklxmxnxvzzbzzmzmznznnnnznznzkkakqiakajsnxnbxbxxvxbx.,..,,.,..,nkm.s.w..ww.w..w.ww..we...w.w.w.w.w.w.e.e.e.ememmemrmrmrmr.r.r.e.e.e.ekekelepwlwlwkwkwklwpqowiwiwueyeygrhdbwjwqklqoqpqpqpalalaksksmzmzmznxnxbxbcskksksksksksksksksksksksksskskkslalalalalaldjdjjdfjfjfjfjhghghghgfjfjfjjdjdjddhdhhddgfgfgfgfjddjjdhdhdhsjsjsjskskskallalallalallallallllallallallllaallallallallallalallalllllighugibuvuvivvuvuvvibuvibvgivugibgihhhiviuvigigpigcpiyckuralutslitswwlurslurslitsitsslitslutslurssislitslursaslurslufslursaalitsljtsljtssslitslitslitssslitslitssisljfssttst
ljgxtxgxyxylkgxdydydyduffigigoiglihdyfufifgdudyxypigxdydhxhxhdyxhddligxlitdlitxddlifxlufzlufxsslufzlufzlufzzzlufzlufztss

70° 2024.04.28 17:55:16 2 replies
- BR CG BO BW
  
  71° 2024.04.28 18:16:49
- 100%25%24%24%24%24%24%24%24%24%24
  
  72° 2024.04.28 18:20:15
Ever since that other anonymous website made a major contribution to mathematics, I feel like we should be able to do it too. I vote that we work on the Riemann Hypothesis.

1° 2019.07.01 03:19:16 10 replies

7 replies omitted in this preview.
- Please do! That would be awesome!
  Not sure I can help...
  
  53° 2022.02.10 18:51:38
- >Ever since that other anonymous website ...
  Which anonymous website?
  
  60° 2022.05.05 06:13:28
- >>60
  > Which anonymous website?
  I found a question on Stack Overflow about the topic of anonymous contributions to math, one of the answers pertained to a certain western anonymous forum:
  https://www.wired.com/story/how-an-anonymous-4chan-post-helped-solve-a-25-year-old-math-puzzle/
  The tl;dr is a post was made asking about what was the least amount of episodes to watch every ordering of episodes in the first season of The Melancholy of Haruhi Suzumiya as it was aired out of order intentionally.
  For the 14 episodes you'd have to watch a minimum of 93,884,313,611 episodes for all orderings.
  This was left unchecked properly until seven years later after Greg Egan proved the upper bound, which drew attention to the original lower bound post.
  The important thing is that both proofs (if you call an imageboard post a proof) apply to a series of any length.
  The lower bound was formalized in a paper written in October, 2018.
  The link to the paper mentioned in the article is broken so here is a working one:
  https://oeis.org/A180632/a180632.pdf
  (Links to the archived post on the board are in the paper)
  Here is the previously stated Stack question:
  https://hsm.stackexchange.com/questions/3001/are-there-any-anonymous-contributions-to-mathematics-that-had-a-great-impact
  Overall, a pretty interesting ordeal, though I'm not sure how surprised I am that anime would be the cause of advancements in mathematics given the audience it tends to draw.
  
  67° 2022.11.07 11:24:43
i am a stupid idiot

how do i learn how to math. I have a GED understanding of math in the very normal range.
Want to be a man, and not an ape.
Please.

63° 2022.07.06 03:04:40 3 replies
- Try improving your understanding of logic first, if you haven't already. It is fundamental to all of mathematics.
  Although I have not read it myself, I have heard good things about the "Book of Proof".
  
  64° 2022.07.29 21:25:37
- i have found some one willing to tutor me in algebra through calculus- where can I find textbooks (not pdf's, they require me to get a book) for cheap? Even if they're older, that would be fine with me.
  
  65° 2022.08.12 16:21:53
- Check out any thrift stores near you?
  
  66° 2022.08.19 17:45:06
How to know if your product will sell X amount of people

LOL

47° 2021.12.11 08:02:05 2 replies
- > sell X amount of people
  This sounds like a slave trading product.
  
  61° 2022.05.05 06:14:28
- >>61
  lol i mean sell to ORz
  
  62° 2022.05.25 02:56:40
ahhh

so you never really gonna be better consistently without any logic....

55° 2022.03.03 01:02:57 1 reply
- x
  
  59° 2022.04.22 07:14:50
Cantor's diagonal argument but for dimensional reduction

As I understand you can also apply Cantor's diagonal argument to a matrix (or well just write columns below eachother), thus proofing that you can always reduce an n-dimensional tensor to a 1 dimensional vector. Similarly, you can reduce an n-dimensional vectorspace to 1 dimension. For example, you could encode all the (natural) numbers in an n-dimensional vector in only one ("1D") number following Gödel, like this: 2^n_1*3^n2*...*p^n_i

54° 2022.02.10 18:56:51 0 replies
For all e>0, there exists a d>0 such that...

e-d statements are rad

9° 2019.08.18 02:42:56 7 replies

4 replies omitted in this preview.
- $\eq$
  
  50° 2022.02.10 18:48:05
- some text $\LaTeX$ more text
  
  51° 2022.02.10 18:48:46
- percent signs are important
  
  52° 2022.02.10 18:49:20
What's your favourite theorem?

4° 2019.07.01 03:38:15 4 replies

1 reply omitted in this preview.
- Ummm, is it normal to know a lot of these theorems offhand?
  
  6° 2019.07.01 05:19:14
- Either Gauss-Bonnet or the Theorema Egregium. Both are classical theorems related to Gaussian curvature, which is like a measure of how twisty a surface is at a point (sphere has positive curvature because it's bent in the same direction, hyperbola has negative curvature because it's bent in opposite directions, plane and cylander have 0 curvature because they're flat in a direction)
  Gauss-Bonnet: if you start with a surface, and you stretch or bend it somehow, the integral of the curvature stays the same. This shows that, for instance, no matter how weirdly you stretch and bend a sphere, it stays a sphere (in some sense)
  Theorema Egregium: if you keep distances between points fixed, then you also keep curvature fixed. This is why it is not possible to have a perfectly accurate map, because the paper is flat everywhere but the sphere is not flat anywhere. So any time you try to map any portion of a sphere, there will be some distortion of distances and area.
  
  44° 2021.02.13 23:35:59
- You guys are awesome. Unfortunately I don't know much. My brain is stained with dirty physics.
  
  48° 2022.02.10 18:46:02
rather go to jail and die than work

can you use math to predict a product's sales? like maybe a certain design and format, and how will it get X amount of people? Maybe a certain mouse design like razor?

46° 2021.12.11 03:41:47 0 replies
Hello!

I love math!

7° 2019.08.15 05:26:48 2 replies
- I love math too!
  
  8° 2019.08.15 05:27:20
- Come to Mathchan (it's not ready yet).
  
  45° 2021.12.04 00:52:25
Math books for kids

I've always wondered about how to get more kids into mathematics. I've even thought about writing math books aimed at children. To do that I want to read the existing literature out there. Let's compile kids' books and resources about teaching math

30° 2020.08.13 07:36:30 11 replies

8 replies omitted in this preview.
- >>38
  customer!
  
  39° 2020.08.18 18:15:34
- http://worrydream.com/SimulationAsAPracticalTool/
  
  40° 2020.08.27 00:39:19
- >>40
  >Mathematics, as currently taught, consists of the manipulation of abstract symbols. For most people, the level of abstraction makes math unpleasant or unusable as a practical tool for exploring the problems of their lives.
  >The simulations represent the problem concretely, without abstractions; provide a broader context, allowing a deeper understanding of the situation
  This is interesting. The way I always saw it was that abstraction is the means by which we make logical thought, and was therefore the most important takeaway from mathematics.
  Certainly learning practical applications is necessary as well, but being able to abstract those applications means they can be applied to more (possibly completely unrelated) situations...
  
  41° 2020.08.27 06:50:38
Is this a thing?

https://www.nytimes.com/2020/02/05/science/quadratic-equations-algebra.html

20° 2020.02.08 18:30:31 4 replies

1 reply omitted in this preview.
- Paywalled.
  Can someone with access to the article, summarize shat the trick is ?
  
  26° 2020.06.24 21:15:27
- >>26
  "This alternate method for solving quadratic equations uses the fact that parabolas are symmetrical.
  For example, in this parabola:
  y = x^2 – 4x – 5
  The two solutions when y = 0 are the symmetrical points r and s, where the parabola crosses the x-axis.
  The midpoint, or average, of r and s is the axis of symmetry of the parabola. We want r + s = –b, which happens when the average of r and s is –b ÷ 2. In this example: 4 ÷ 2 = 2.
  The two solutions to the quadratic equation will be the axis of symmetry plus or minus an unknown amount, which we’ll call u. In this example:
  r = 2 – u and s = 2 + u
  To find u, we want the product of r and s to be equal to c, which in this example is –5. Rewriting r and s in terms of u:
  r × s = –5
  (2 – u) × (2 + u) = –5
  Solving that yields 22 – u2 = –5 or u2 = 9, so u = 3 works.
  The two solutions to this quadratic equation are 2 – u and 2 + u, or –1 and 5. In other words, this parabola intersects the x-axis when x = –1 and x = 5."
  
  28° 2020.06.27 20:21:53
- >>28
  >Solving that yields 22 – u2 = –5 or u2 = 9, so u = 3 works.
  Solving that yields 22 – u^2 = –5 or u^2 = 9, so u = 3 works.
  Sorry. Copy-and-paste mistake.
  
  29° 2020.06.27 20:28:39
The square root of 2 is irrational

Let $x$ be a positive number such that $x^2 = 2$. Assume for the sake of contradiction that $x$ is rational. Then there exist coprime non-negative integers $a,b$, with $b \ne 0$, such that $x = \frac{a}{b}$. Then we have $2 = x^2 = \frac{a^2}{b^2}$, so $a^2 = 2b^2$. Since $2$ is prime and $2$ divides $a^2$, $2$ must divide $a$. Say $a = 2c$ for some integer $c$. Then $4c^2 = a^2 = 2b^2$, so $2c^2 = b^2$, and therefore $2$ divides $b$. But then $a$ and $b$ are not coprime, which is a contradiction. Therefore $x$ is irrational. QED

14° 2019.08.30 02:23:15 1 reply
- Thank you for your wonderful contribution! Always love to see some real maths here.
  
  15° 2019.09.09 00:08:11

Category Theory

Whats 2 + 2?

anonymity is not schizophrenia

how do i get back into math?

jahavvshsisjsbslspsjshsb

i am a stupid idiot

How to know if your product will sell X amount of people

ahhh

Cantor's diagonal argument but for dimensional reduction

For all e>0, there exists a d>0 such that...

rather go to jail and die than work

Hello!

Math books for kids

Is this a thing?

The square root of 2 is irrational