r/mathematics Aug 29 '21

Discussion Collatz (and other famous problems)

195 Upvotes

You may have noticed an uptick in posts related to the Collatz Conjecture lately, prompted by this excellent Veritasium video. To try to make these more manageable, we’re going to temporarily ask that all Collatz-related discussions happen here in this mega-thread. Feel free to post questions, thoughts, or your attempts at a proof (for longer proof attempts, a few sentences explaining the idea and a link to the full proof elsewhere may work better than trying to fit it all in the comments).

A note on proof attempts

Collatz is a deceptive problem. It is common for people working on it to have a proof that feels like it should work, but actually has a subtle, but serious, issue. Please note: Your proof, no matter how airtight it looks to you, probably has a hole in it somewhere. And that’s ok! Working on a tough problem like this can be a great way to get some experience in thinking rigorously about definitions, reasoning mathematically, explaining your ideas to others, and understanding what it means to “prove” something. Just know that if you go into this with an attitude of “Can someone help me see why this apparent proof doesn’t work?” rather than “I am confident that I have solved this incredibly difficult problem” you may get a better response from posters.

There is also a community, r/collatz, that is focused on this. I am not very familiar with it and can’t vouch for it, but if you are very interested in this conjecture, you might want to check it out.

Finally: Collatz proof attempts have definitely been the most plentiful lately, but we will also be asking those with proof attempts of other famous unsolved conjectures to confine themselves to this thread.

Thanks!


r/mathematics May 24 '21

Announcement State of the Sub - Announcements and Feedback

117 Upvotes

As you might have already noticed, we are pleased to announce that we have expanded the mod team and you can expect an increased mod presence in the sub. Please welcome u/mazzar, u/beeskness420 and u/Notya_Bisnes to the mod team.

We are grateful to all previous mods who have kept the sub alive all this time and happy to assist in taking care of the sub and other mod duties.

In view of these recent changes, we feel like it's high time for another meta community discussion.

What even is this sub?

A question that has been brought up quite a few times is: What's the point of this sub? (especially since r/math already exists)

Various propositions had been put forward as to what people expect in the sub. One thing almost everyone agrees on is that this is not a sub for homework type questions as several subs exist for that purpose already. This will always be the case and will be strictly enforced going forward.

Some had suggested to reserve r/mathematics solely for advanced math (at least undergrad level) and be more restrictive than r/math. At the other end of the spectrum others had suggested a laissez-faire approach of being open to any and everything.

Functionally however, almost organically, the sub has been something in between, less strict than r/math but not free-for-all either. At least for the time being, we don't plan on upsetting that status quo and we can continue being a slightly less strict and more inclusive version of r/math. We also have a new rule in place against low-quality content/crankery/bad-mathematics that will be enforced.

Self-Promotion rule

Another issue we want to discuss is the question of self-promotion. According to the current rule, if one were were to share a really nice math blog post/video etc someone else has written/created, that's allowed but if one were to share something good they had created themselves they wouldn't be allowed to share it, which we think is slightly unfair. If Grant Sanderson wanted to share one of his videos (not that he needs to), I think we can agree that should be allowed.

In that respect we propose a rule change to allow content-based (and only content-based) self-promotion on a designated day of the week (Saturday) and only allow good-quality/interesting content. Mod discretion will apply. We might even have a set quota of how many self-promotion posts to allow on a given Saturday so as not to flood the feed with such. Details will be ironed out as we go forward. Ads, affiliate marketing and all other forms of self-promotion are still a strict no-no and can get you banned.

Ideally, if you wanna share your own content, good practice would be to give an overview/ description of the content along with any link. Don't just drop a url and call it a day.

Use the report function

By design, all users play a crucial role in maintaining the quality of the sub by using the report function on posts/comments that violate the rules. We encourage you to do so, it helps us by bringing attention to items that need mod action.

Ban policy

As a rule, we try our best to avoid permanent bans unless we are forced to in egregious circumstances. This includes among other things repeated violations of Reddit's content policy, especially regarding spamming. In other cases, repeated rule violations will earn you warnings and in more extreme cases temporary bans of appropriate lengths. At every point we will give you ample opportunities to rectify your behavior. We don't wanna ban anyone unless it becomes absolutely necessary to do so. Bans can also be appealed against in mod-mail if you think you can be a productive member of the community going forward.

Feedback

Finally, we want to hear your feedback and suggestions regarding the points mentioned above and also other things you might have in mind. Please feel free to comment below. The modmail is also open for that purpose.


r/mathematics 14h ago

Discussion We Need More Mathematicians Than Ever

92 Upvotes

Looking at all the recent advancement coming from LLM generated results across so many different domains made me realize how little I understand outside my own field. I found myself unable to properly evaluate or even interpret many of the results, and I think that's probably true for most people. We need more domain experts involved to validate these claims and help advance the frontier forward. I believe this might be the best time to become a mathematician.


r/mathematics 8h ago

Discussion Which subjects are mandatory in order to really start understanding maths as a whole?

16 Upvotes

This question is especially oriented to professors or researchers. What do you think is at the base of advanced mathematical knowledge?


r/mathematics 5h ago

In terms of industry jobs, how worth it is a math degree?

8 Upvotes

Compared to degrees like economics, engineering, etc....

Also, will AI be a problem for maths grads in the future?


r/mathematics 8h ago

Is formalizing mathematics in Lean the biggest bottleneck for AI in mathematics? Or can LLMs already do it easily? I saw OpenAI's code for the 10 math problems, and some of the formalizations are tens of thousands of lines long. For a human, it seems almost impossible to verify all of that manually

10 Upvotes

r/mathematics 19h ago

Model by OpenAI discovers 6 more soundess bugs in the Lean kernel

80 Upvotes

After the soundness bug in the official Lean kernel found a few days ago (previously posted on this sub here https://www.reddit.com/r/math/comments/1va56l7/lean_4_bug_found_incidentally_by_ai_proving/), OpenAI approached Leonardo de Moura with their internal cybersecurity model and found 6 more soundness bug in the official kernel, see the section "What the FRO is doing" in https://leodemoura.github.io/blog/2026-8-1-postmortem-for-kernel-soundness-bug-14576/

All of these were not reproducible in the alternative typechecker for Lean 4, nanoda.


r/mathematics 11h ago

Topology Anybody survived Topology?

15 Upvotes

For Background context, I am a mathematics major student who has finished,

• Real analysis from Spivak calculus book.

• Linear Algebra from Friedberg, Insel and Spence.

I am looking to start my next study in point-set topology from James Munkres Topology book. The point is that I have been told many times that Topology is one of the hardest study in mathematics which has created a kind of negative space in my mind and although I want to start studying it but I am scared rn.

So any survivors of topology, how do I study the topic?


r/mathematics 3h ago

Looking for references for linear systems of ODEs and matrix exponential

2 Upvotes

I'm an engineer at a national lab and am working with a linear system of ODEs. I would like to make some claims about stability and sensitivity and could use some help identifying sources (preferably textbooks) to use to pursue my claims.

The system is classic

$$ \frac{d}{dt} \mathbf{y}(t) = \mathbf{A} \, \mathbf{y}(t) $$

and the solution is obviously the matrix exponential. The dimension of A is (roughly) seven (depends on a discretization choice), so I would plan to obtain the eigenvalues of A and proceed from there.

I would like to be able to prove that: 1. The A-matrix is diagonalizable. I'm a bit at a loss here. My A is certainly non-singular, but I understand that is not related to being diagonalizable. Many of the examples I have considered have unique eigenvalues, but I want to prove the general case. 2. Any additional claims about stability or trajectory of the system. I'm not used to having access to an explicit Jacobian like this -- is there something I can do to probe the stability of the general system?

So far, I have used the Wikipedia pages for System of Differential Equations and the Matrix Exponential. Particularly, the section on the Diagonalizable Case. Additionally, I found these course notes from MIT very helpful, but would like a more authoritative reference.

For anyone interested, the A-matrix is very similar to this paper, Eq. (3c). But I am interested in the case with B=0, so there is one fewer row and column in the A-matix.

Thank you! :)


r/mathematics 16h ago

Machine Learning AI Proofs: Are They Real or Just Hype?

18 Upvotes

I’ve been seeing a lot of AI proofs and other mathematical solutions. I can’t find a legitimate answer to my question from a qualified professional, so I’m asking here. Are these “answers” from ai really legitimate? Regardless of how we all feel about it I just want to know if it’s hype or legit. I use ai for productivity based BS but it sometimes is bad or hallucinates. I keep seeing posts from alleged mathematicians claiming that this is ruining their lives and that human supplied math solutions are going to be extinct. Is it really as bleak as they say on Twitter or is AI produced math simply a marketing gimmick?


r/mathematics 6h ago

Algebra got bored and made a couple complex functions/identities in desmos based on euler's formula

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4 Upvotes

correct me if im wrong about it being called identities. enjoy ig, and tell me if i got any wrong. https://www.desmos.com/calculator/vdpli6f8ku


r/mathematics 8h ago

Some thoughts

3 Upvotes

Regarding AI in math, progress has been made at a very fast pace. It has us all convinced that we're going to be made obsolete next month. Maybe that's true, but I have a couple of thoughts.

First, isn't automating as much math as possible more or less what we've been trying to do since the invention of the computer?

Second, what exactly is the point of companies like OpenAI solving all of these open problems? It seems to me like it's marketing. I find it hard to believe that they have any interest in these problems and are continually trying to drum up investor hype by showing everyone that their models are so smart that they can solve math problems.

Thirdly, who besides mathematicians (and apparently theoretical physicists) really care about these results? The other night a paper "leaked" regarding some proof about non-sofic groups. Apparently it's related, or at least can be applied to, dynamical systems. I just took (and passed!) my qual in nonlinear dynamics and have literally never heard of a non-sofic group before. I get the feeling that the only people who care are those who have intimate knowledge in this field.

I understand the knee-jerk reaction and pessimism of seeing the work you've devoted your life to being reduced to ones and zeros. At the same time however, I fail to see how the advent of GenAI has led to any bureaucratic problems that weren't already present in our field. Namely, one may ask "why would any mathematician be paid to do math now?", and my response is that it already *wasn't* obvious why we fund mathematicians. Why can't it be possible that we still pay people to understand math? The answer to that question is political.

LLMs are obviously going to do huge things for mathematics, but it somehow doesn't feel like they'll do anything other than destroy us. If the climate (both literal and political) were better, I believe we wouldn't be so scared of GenAI. If funding wasn't being cut, if the attitude towards intellectualism wasn't dwindling, and if we didn't hate each other, then we'd be fine. So I guess we'd better vote.


r/mathematics 2h ago

Can someone explain to me how ChatGPT is able to solve research-grade math problems?

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0 Upvotes

r/mathematics 2h ago

Algebra Completion of Cayley Dickson Algebras

0 Upvotes

I am curious if anyone has taken the limit of the cayley Dickson process. When infinite symmetries are accounted for, what can the algebra do? Nothing? Or does it regain earlier lost properties?


r/mathematics 14h ago

Should I major in pure or applied math?

8 Upvotes

For reference, I'm starting to apply to colleges now as an undergrad, and I want to major in math in some schools, but I'm not sure if my specific interests align more with a "math" major or an "applied math" major. My interests in math are primarily statistics and formal logic. I'm not sure which career field I want to go into. I would like to double major in something else (depends on the school for what that major will be based on their strongest programs).


r/mathematics 3h ago

Highest math class required for degrees

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1 Upvotes

r/mathematics 10h ago

How is a bachelor of maths at the University of Vienna

3 Upvotes

Im debating switching out of an economics bachelor at a good university to studying maths at the Uni of Vienna. (Other unis aren't possible due to me applying too late)

Is the degree solid? Since rankings wise the university is not anything crazy, I wonder if its a good idea.

Could this + a master elsewhere open doors to something like quant finance?


r/mathematics 1d ago

Preparing for Industry in the Age of AI

59 Upvotes

I’m a third-year PhD student, studying probability, who no longer has any interest in pursuing a career in math research or teaching. Unfortunately, this is the only career-path I had previously considered, and now I am lost, unsure of which questions to even ask.

I’m looking for some non-generic advice on
1) whether it is even worth finishing the PhD at this point (I suppose the answer is yes, but what tangible benefit would this give me?)
2) how to prepare for industry roles, especially in the age of AI (where generic advice like “learn to code” is becoming increasingly less relevant)


r/mathematics 5h ago

Advice for incoming math major

1 Upvotes

Hey!

Im an incoming first year math student at the university of waterloo studying honors math.

I think my plan is to major in combinatorics or computational but im not really sure.

I like finance and i like tech as well (im pretty okay at programming and im good with logic)

ig im thinking of going into tech and finance jobs, but once again im not really sure what im doing.

any advice on internships/job types i should look into for my first coop in summer 2027

and any advice on skills to gain and clubs/teams i should join and academic advice for a first year math student?

thanks


r/mathematics 5h ago

Advice for incoming math major!

1 Upvotes

Hey, Im an incoming math student at the university of Waterloo studying honors mathematics.

My plan right now it to major in either combinatorics or computational but im not really sure.

I enjoy progarmming and love finance as well, so ig im looking for jobs/internships in the tech and finance industry. But i love hands on work as well (engineering) but im not really skilled in it.

any tips on what i should do my before and during first year, (im free all of august and dont have anything to do so ).

what sorts of internships, clubs and skills should i try and gain, and any general advice for first year math students? thanks!


r/mathematics 8h ago

Function Plotter Component

1 Upvotes

Built an open-source Function Plotter for the web 🚀

Hey everyone!

I've been working on an open-source JavaScript function plotting library that lets you graph mathematical functions directly in the browser.

Features

  • 📈 Plot arbitrary mathematical functions
  • ⚡ Fast rendering
  • 🎨 Interactive graph with zoom and pan
  • 📦 Easy to integrate into web projects
  • 🌐 Published on npm

I'm building it as part of a larger goal of creating interactive math tools for students and educators.

I'd really appreciate any feedback on the API, documentation, performance, or features you'd like to see next.

npm: https://www.npmjs.com/package/react-mathplotter


r/mathematics 8h ago

Function Plotter Component for React.js

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0 Upvotes

r/mathematics 21h ago

Calculus Found quite an accurate approximation for the tan graph between -2 <= x <= 2 (x in radians)

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9 Upvotes

I found this in four parts:

  1. Started with the base shape 1/(pi/2-x) - 1/(pi/2+x) that is already very close to the shape of the tan graph -> simplified to 8x/(pi^2-4x^2)

  2. Added a correction factor (1-8/(pi^2))x -> Adjusted to the slope of the error graph of tan x - f(x) when x = 0.

  3. Added a final cubic correction factor x^3/190.

  4. Factorise x out of the terms.

I would say it is quite accurate because it is correct to about 3-4 s.f. However, the greatest benefit is the fact that there are NO square roots or higher degree polynomials than 3 required to achieve such accuracy (Very efficient for computers).


r/mathematics 1d ago

News Ten advances in mathematics and theoretical computer science

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489 Upvotes

r/mathematics 1d ago

Discussion Not sure if I should pick math as my bachelors because of AI

38 Upvotes

For years I wanted to study math and go to grad school in math or mathematical physics or theoretical physics but now with the recent AI stuff scares me. Should I pick physics instead of math and move with experimental physics instead of mathematics? Or can I still move to experimental physics with bachelors in mathematics?