r/math

Many mathematicians have dedicated a good part of their career towards solving a specific problem, whether directly or indirectly. Some examples on top of my head:

Richard Hamilton and the Poincare conjecture

Andrew Wiles and Fermat's last theorem

Thomas Hales and the Kepler conjecture (proof and formal verification)

And perhaps very recently:

Diego Cordoba and the Navier-Stokes equations

How did the careers and research-focus of these mathematicians shift after their career-problem was solved? Did anything particularly interesting happen?

This recurring thread will be for discussion of AI in mathematics. This includes, but is not limited to, the following:

• informal announcements of AI-assisted discoveries, such as those not yet published in a peer-reviewed journal, or not uploaded as a paper to arXiv;
• informal announcements of discoveries related to AI architecture (if relevant to mathematics);
• discussion of such announcements, such as proof breakdowns or other opinion pieces;
• discussion of the impact of AI in mathematics in general.

AI-assisted mathematical papers published in peer-reviewed journals or as arXiv preprints may be submitted as their own posts.

Please keep in mind rules 1 and 6 of our subreddit.

I often ask mathematicians what their favorite shape is; mine is the cone on a trefoil knot, a rather peculiar object.

Why is this my favorite shape? Because it appears naturally in algebraic geometry -- and in fact, the observation that it appeared in algebraic geometry led Milnor, Grothendieck, Goresky, MacPherson, and many more to develop some of the most widely used tools in modern algebraic geometry and singularity theory! If you'd like to know how this trefoil knot appears in algebraic geometry, read this week's hidden-phenomena blogpost!

Hi everyone!

I started a shorts-series about differential forms. This is part 2 so far. I also have a part 1: https://youtube.com/shorts/J20AI3iE4OM

These videos are supposed to be short, concise and most importantly fun, while still being correct! (If you spot a mistake, please let me know)

I have so far introduced differential 1-forms in the previous video, and now I defined the exterior algebra which I used to introduce differential k-forms. Next up, I wish to define the exterior differential and hopefully some day I will also get to Maxwell's equations and de Rham cohomology (but this might take a while).

All feedback is warmly welcome!

(None of the videos are AI generated)

This recurring thread will be for any questions or advice concerning careers and education in mathematics. Please feel free to post a comment below, and sort by new to see comments which may be unanswered.

Please consider including a brief introduction about your background and the context of your question.

Helpful subreddits include /r/GradSchool, /r/AskAcademia, /r/Jobs, and /r/CareerGuidance.

If you wish to discuss the math you've been thinking about, you should post in the most recent What Are You Working On? thread.

This recurring thread is meant for users to share cool recently discovered facts, observations, proofs or concepts which that might not warrant their own threads. Please be encouraging and share as many details as possible as we would like this to be a good place for people to learn!