/r/mathematics

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r/mathematics is a subreddit dedicated to focused questions and discussion concerning mathematics.

/r/mathematics is a subreddit dedicated to focused questions and discussion concerning mathematics. Submissions should state and outline problems or questions about a given field or link to an especially insightful article about a mathematical concept.

/r/mathematics is a moderated community. Please read the submission and comment rules before posting.

How to obtain flair on /r/mathematics

Please post:

  • Questions, problems and articles which promote discussion about mathematics. Articles must be accompanied by a comment designed to start discussion.

Please do not post:

  • Requests for help with homework.
  • Homework help
  • Jokes, memes, images, infographics, videos or blogspam.

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/r/mathematics

151,750 Subscribers

1

"Yes, he's good, but he's no..."

Gauss? Euler? I have always remembered this niche idiom as being "He's good but he's no Gauss" — an idiom used to describe someone's skills or intellect as being good but not exceptional. This idiom of course also works outside the field of mathematics, but with the person being replaced with the field's equivalent prominent prodigious figure: "He's good but he's no Mozart," "She's good but she's no Serena Williams," and in math: "He's good but he's no Gauss."

However, a friend of mine contests that the "correct version" is "He's good but he's no Euler." Now I'm curious as to which version is more popular in mathematics. Gauss or Euler? Perhaps even someone else?

I would love to hear which version you have heard the most!

3 Comments
2024/11/03
22:40 UTC

3

Share math learning strategies

Strated relearning math. Currently am at highschool algebra.Need to catch up to complex variables, fourier transform and calculus. It would be helpful, if some you shared your study strategies and techniques.

6 Comments
2024/11/03
20:31 UTC

28

What field of mathematics is related to compilers, languages and logic?

Hi everyone,

I am a sophomore student of Mathematics and always had a passion towards computer science, programming languages and compilers. I decided to study Math because I was inspired by Haskell, functional programming and Category theory; I wanted to learn more about Topology, and I'm liking it so far. It is really difficult for me, but certainly not impossible.

I have learned that I don't have much of a mathematical reasoning, but I do really well on subjects that revolves around coding. In fact, I have been programming since middle school, and love to learn new programming languages. A dream of mine I always wanted to realize is to create my own compiler/interpreter, and find the theory underneath it extremely curious and fascinating.

The next year I'm choosing an Applied Math curriculum (with Logic and computation, Computational Algebra and Geometry, and so on), and during my Master degree, I plan to study subjects related to (programming) languages, logic, etc. A professor I had during my first year teaches a course named "Symbolic computational geometry", which looks really cool; another course I absolutely want to take is "Languages and Codes", which is exactly what I am looking for. Its contents are these "Languages and grammars. Finite state automata and regular languages. Chomsky's hierarchy. Structure of a compiler. Lexical analysis. Syntactic analysis. Syntax-driven translation. Intermediate code generation. Organization of memory.".

My question is: do what I'm passionate about have a name in the mathematical world, or I better look after a CS course for my master degree? I'm trying to figure out what books to read, and to give a name to what I am looking for.

Thank you for your help.

16 Comments
2024/11/03
17:04 UTC

1

How to decide between focusing on math or startups

For me, mathematics is supposed to be a cornerstone of my future endeavors as a fiybder in the startup and innovation world. I aim to found deep tech software startups that will probably involve a lot of computation and mathematics at the core of it (kind of like  current AI startups involve mostly math and coding).

At the same time, I’m 24, and a junior at UC Berkeley – where I study math as an undergrad. I’m so insanely grateful and fortunate to be here, but at the same time I feel like time is working against me. I always feel like I’m wasting time if I’m not trying to make money through building stuff and selling it/raising money, but that would mean that I would focus on startups instead of math (because any type of business requires an insane amount of energy) – which conflicts with my long term vision of math being cornerstone of my innovative endeavors.

I feel like I’m experiencing some type of FOMO – although I may not be right. I feel like time is running out and that is pushing me to sacrifice my long term vision for short term ones.

How do i deal with the fact that I’ll be graduating at 26 years old, and that makes me feel like I’ve already wasted so much of my 20s. Why not fully focus on startups and try to pick up the mathematical foundations necessary for my endeavors later on? Even better yet – why not hire other great mathematicians?

I really need help with a framework of thinking in order to be in internal peace with myself and not resent myself and math while doing it?

3 Comments
2024/11/03
16:45 UTC

3

Story math problem, non-homework math problem

I don't know what tag this would fall under, so sorry if I got it wrong or a question like this is allowed.

I have tried doing this myself, I am working on story and an Academy people are attending is 110 years at the time they began their start year. The Director of the school is speaking to the new student, I want him to say something along the lines of the "32nd class of the school". Tho I want to actuate to the timeline of the story, which isn't base in our world. It is a 4-year school, if I did my math right, I believe it would 3, however I am not sure. I know every 12 years = 3 classes, would 110 years = 30 classes?

Can anyone help me here?

4 Comments
2024/11/03
16:00 UTC

0

how did the first principle was derived?

f(x+h)-f(x)/h
this

tried to search for vids but couldnt find any

pls help

13 Comments
2024/11/03
14:53 UTC

7

Proof derivative of gamma at 1 is minus Euler mascheroni

Would a simple proof, like one page long, that uses nothing but the recursive definition of gamma and basic calculus, of the fact be valuable? The ones I found on the internet all used Euler's product for the factorial or the integral definition of Gamma and long integrals that are not trivially related to the constant.

1 Comment
2024/11/03
13:15 UTC

7

Applied math remotely

What would be best option(s) for acquiring Applied Math degree. I am really debating for studying Data Science but I have met some of the mathematicians that are just clearly showing that getting math degree fundamentally is much better for not only data science degree. Thus, I was curious if there are online degree that would be available to break into a broader spectrum of different industries. I only posses petroleum engineering and realized quite late in my life that knowing applied math could completely cover all of the theories I have been studying...

9 Comments
2024/11/03
05:40 UTC

0

Is Rayo’s Number greater than this?

Would Rayo’s Number be greater than the number of digits of Pi you’d have to go through before you get Rayo’s Number consecutive zeros in the decimal expansion? If so, how? Apologies if this is silly.

36 Comments
2024/11/03
02:21 UTC

5

I want a free online tool which I can use for matrices with variables in it

is there any online tool with which I can insert matrices with variables with which it can compute variables?

4 Comments
2024/11/02
23:12 UTC

3

Should I retake general GRE?

Should I retake general GRE?

I am applying for rank 40-10 PHD programs mathematics around US (msu, Minnesota, uiuc, Ohio state, Purdue, penn state, Bloomington Indiana, u Arizona, UT Austin, and a couple reach schools ).

Just took the general GRE today and I got 165 quant; 168 verbal. Is my score good enough or should I retake the test and try to get a perfect score for quant?

2 Comments
2024/11/02
20:45 UTC

12

How easy is it to pivot into Statistics after a PhD in Mathematics?

5 Comments
2024/11/02
19:36 UTC

66

Did Erdős really sleep 3 hours a day? 😭

The more I learn about this man the cooler he gets

44 Comments
2024/11/02
17:48 UTC

4

Average area of Shadow of Cube; What's wrong with my approach?

This problem arises from a video by 3blue1brown:
https://www.youtube.com/watch?v=ltLUadnCyi0&t=2004s

TL;DW:
What is the average are of the shadow of a cube? The cube has side length of 1, could be in any orientation, and the light source is infinitely far away such that the light rays are parallel to each other.

My approach:

  1. Make a 3D graph of the area of the shadow with respect to rotation angle in x-direction and rotation angle in y-direction.
  2. Perform a double-integration to find the volume under the graph, then divide it by the area of the domain of the graph.

https://preview.redd.it/3us52ftl8iyd1.png?width=808&format=png&auto=webp&s=c1412fce2c2f2927037832d5fc5c4a231661dc04

Remarks on the graph:

  • The graph has maximum at z=sqrt{3} when x=pi/4 and y=pi/4. This is because the area will be maximum when a vertex is directly on top. At this point the shadow will be a hexagon with area sqrt{3}.
  • x and y have domain of {0, pi/2}
  • Maximum in x-direction, when y remains 0 occurs at x=pi/4, is sqrt{2}. This is because the area will be a rectangle when an edge is directly on top. At this point the shadow will have an area of sqrt{2}.
  • The minimum of the graph is 1 as the area of the shadow can't be less than when a face is on top and thus area of 1.

The equation of the graph is:
z = (sqrt{3}-2sqrt{2}+1)*(sin(2x)*sin(2y)) + (sqrt{2} - 1)*(sin(2x)+sin(2y)) + 1

The double integral of this graph from x = {0, pi/2} and y = {0, pi/2} is
1 - 2sqrt{2} + sqrt{3} + pi(sqrt{2} - 1) + (pi^2)/4

The double integral over the area of the domain (pi^2)/4 is ~ 1.488333...

The actual answer is 1.5, so my question is What is wrong with my approach? or What am I missing?

4 Comments
2024/11/02
15:14 UTC

11

A quick animated Polish Olympiad puzzle for anyone interested :)

1 Comment
2024/11/02
11:07 UTC

38

how do I improve my logic at maths

I'm a 17 year old student at high school, I feel like in maths I can only answer questions that are already been told before. it's like I just can find the answer only if the exact same problem has been taught before and only the numbers are changed. When I find a new problem that are new I'm completely clueless,it's like I can only use my memory at maths not my logic. how do I train so I can now what to do when I face a problem?

19 Comments
2024/11/02
06:58 UTC

24

Cauchy the GOAT

Serious question: is Cauchy the GOAT?

32 Comments
2024/11/02
03:49 UTC

2

MIT primes USA

How do you send recommenders info to request LOR for MIT primes USA? The application does not have any instructions to request recommenders

.

0 Comments
2024/11/01
18:01 UTC

10

Suggestions for working on a new branch - for fun

Hi all! I’m a student experimenting with some independent math projects, and I’m trying to invent a new branch of math in my free time. I’m looking for any ideas for unique foundational principles or starting points that could lead to some original theorems and results. For example, one idea I’ve had is creating a new geometry by coming up with a unique fifth postulate about parallel lines, different from Euclidean or non-Euclidean models. But honestly, I’d love any suggestions for a totally new field—or, if you have a cool fifth postulate, that would be a great starting place too! Note that I have read several academic textbooks on maths, so I am familiar to undergrad maths - I know how the logic works. Thanks in advance!

12 Comments
2024/11/01
12:31 UTC

9

Jackson & Johnson Pythagorean Theory Proof

Hi, I recently heard the two highschoolers came with 9 more proofs (after their first one some years ago) of the Pythagorean Theorem by using trigonometry.

I have seen their first proof and I could follow it just fine, but I cannot grasp how in principle it is possible to prove something by using its own theory (if thats fair to say?).

When I hear someone say that they proved some essential part of trigonometry, by using trigonometry, I just instantly think that is impossible. Clearly its not though so im wondering if someone here can explain to me how how it is possible or what im misunderstanding.

16 Comments
2024/10/31
20:43 UTC

7

Optimal packing tips

This might be an incredibly weird question but I'd love for anyone to attempt to answer it, however vague it needs to be.

Because of circumstance I have to work in a supermarket with absolutely lovely coworkers. Though thee tasks I have to do are generally mindnumbingly boring: packing, sorting,... Etc.

So to keep my mind busy while packing products in boxes I have been trying to think about the maths related to packing theory on how to fit certain shapes most efficiently into a box.

From there my question: are there any general ideas/rules/tips/whatever that we know from maths (packing theory?) that would be useful to know for someone who has to pack things daily?

Suppose theres just an average supermarket worker packing things and you'd have to give some tips to help him optimize his packing skills, what would you tell him? Which ideas from maths would be useful to know? Suppose he sees some kind of shape that he has to put in a cardboard box, how would you want him to approach the situation? Even besides all this: what, if anything at all, would you give as a tip?

Like I said this might be kind of impossible to answer, but I encourage you to take this as a non-serious question just purely for fun. I will try out anything you can come up with, even things that arent practically useful but just theoretically interesting would be appreciated to keep my mind occupied.

8 Comments
2024/10/31
20:28 UTC

2

Diffusivity coefficient Vs weight

So i am studying some heat diffusion models, i know the terminology is important
but can this coefficient be regarded just as weight, like what is the differences between weight and diffusivity coefficient aside of weight being the general term used in general equations

0 Comments
2024/10/31
20:16 UTC

29

Is abstract algebra an actual field?

Or is it just algebra applied "abstractly"? If so is "abstraction" something you can do with any mathematics by definition since all math is abstraction? How abstract does abstract algebra go and what are the prerequisites to understand it?

57 Comments
2024/10/31
19:06 UTC

0

Is the RNG system from the Mega Millions not reverse-engineer-able ?

If I take all the past draws can I find the way how the numbers are drawn ?

7 Comments
2024/10/31
17:50 UTC

11

Baby Rudin 1st chapter

I am noobie mathematician, please don't laugh at me. I am trying to learn mathematical analysis on my own. So everyone kept saying that baby Rudin is the way, but his first chapter just throws me off. I understand the material he is showing, and he is trying to sneak in a slick inequality to show that rationals have gaps or incomplete. However, for the love of math I couldn't understand where or how he derived those inequalities at first ‽ I kept going forward and things made sense, like sups and infs, reflexive, transitive properties, etc. But that inequality got stuck on the back of my head like an unfinished business I had, so it kept me turned off from going any further. Primarily the logic I had was that "if I can't figure out that inequality, then I am not worthy of keep on reading this book".

https://preview.redd.it/9f64i3n02dyd1.png?width=870&format=png&auto=webp&s=cb2e0eca66e438e30dbc4235c39d4ba3f813232e

23 Comments
2024/10/31
05:14 UTC

11

The "b" constant in the quadratic equation.

I thought I should share what I had noticed about the "b" constant from the quadratic equation (y = ax^2 + bx + c).

So, we know that the constant "a" widens or narrows the opening of the parabola, the constant "c" shifts the parabola along the y-axis; but, do different values for the "b" constant result in parabola to trace another parabola on the graph?

In this video, look at the parabola's vertex (marked with a red dot), and notice the path it takes as I change the constant "b".

(I don't know if it's an actual parabola, but isn't the path traced still cool?)

10 Comments
2024/10/31
03:35 UTC

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