Brayden Letwin

The KLS constant is O(log^1/4 n)! arxiv.org/pdf/2607.24164. Speaking informally, the KLS conjecture says that the best way to cut a convex shape into two equal volume halves so as to minimize the newly exposed surface area is more or less just a straight cut. The KLS constant measures the gap between the best arbitrary cut and the best straight line cut. Kannan, Lovász, and Simonovits conjectured that this term is O(1). About two weeks ago I had a breakthrough on some adjacently related work, and I had noticed that it would be quite fruitful to study the KLS conjecture through something in convex geometry literature known as a moment measure after I had discovered an interesting formula. This moment measure satisfies a second order PDE known as a Monge–Ampère equation. I used ChatGPT 5.6 Pro to differentiate this equation, and then after a lot of experimentation, ChatGPT 5.6 Pro produced a striking result, which after a some extra work gave what is now Theorem 2.5 in the paper. At the time of uploading this paper, it seems that independently Yuansi Chen and Boaz Klartag had used ChatGPT 5.6 Pro to produce a slightly weaker version of Theorem 2.5, which still is of course the main breakthrough, see here: weizmann.ac.il/math/klartag/s…. Quite remarkable!

@AcerFur I would even be pleased with a black-box yes/no answer of whether KLS is true (so that perhaps, I can stop wasting my time).

If you had access to a much stronger model than those currently available, but not so strong that it could solve a millennium problem, what would you ask it, and why? I am curious about which problems mathematicians care about that are seemingly more tractable than RH, etc.

@AcerFur We were able to get the explicit constant as well, more to reveal in the next month.

@letwinbrayden Nice! Look forward to it.

The wiki section titles have changed now, but to date, there have been 10 previously open Erdős problems fully autonomously solved by LLMs in full intent with an argument not previously published in the literature: They are 205, 281, 401, 524, 543, 635, 652, 728, 729, and 1051.

@wtgowers Are you planning on going to ICM? Boat to the states haha.

This, but adding 1. My main non-plane trips in 2025 were one train journey to Venice, one to Leiden, and one to Saint Jean de Luz in the south west corner of France. All three went smoothly -- as last year my main gripe is that it is more expensive to go by train than to fly.

@CsabaSzepesvari @UAlberta The undergraduate math lounge almost got wiped too, we had to argue for months to even get a new room. The fact that such a fight had to be put up really saddens me, because both Math and CS departments have such a high degree of talent.

@UAlberta pulls the rug under the CS department: 1. Profs get windowless small offices with furniture reminding the 80s 2. Prof floors are inaccessible by grad students outside of office hours. 1/x

@HanWeBlame @SokobanHero @hendrycks For arbitrary complex numbers this is obviously true. Just pick any two numbers and solve for the third because you are in an algebraically closed field...

@SokobanHero @hendrycks i have found solutions for n=1, i think that was the easiest part, but i couldnt prove whether if n>1 had any real solutions. i didnt look into it much but it probably doesnt hold true after 2. now im just curious if theres any value for n in complex plane where it holds true

Yesterday students across the country took the Putnam exam, the hardest undergrad math exam. The exam lasts 6 hours. I gave OpenAI o1 pro the questions, and it took around 0.5 hours. Its answers are in the thread---hopefully experts can help grade to see how well o1 pro did!

@SokobanHero @LombsMr @hendrycks The easiest solution is to without loss of generality assume a, b, c are co-prime. Then after doing this you deduce that one of them are even after manipulation. Then cover the case n = 1 seperately, for n > 1 you can divide through and use similar techniques to get n >1 is bad.

@LombsMr @hendrycks At a glance it doesn’t seem obvious, though usually A1 is the easiest question. What’s your solution?

@littmath Is it known that ZFC can't have logical contradictions?

when you find an error in a proof you were very confident in and you briefly consider that it might signal a contradiction in ZFC

@LeoDelamoJr @AnalysisFact No problem! If you would like to study the subject, I would suggest the book by Rudin. You just need to know vector space theory and real analysis (maybe a bit of complex analysis and point-set topology).

@letwinbrayden @AnalysisFact Thank you!!

There exist separable Banach spaces that do not have a Schauder basis. Proved by Per Enflo in 1973.

@Almost_Sure @littmath Is this an iff? Or could both be false.

@littmath There’s the 2 Hardy-Littlewood conjectures on primes, which contradict each other en.wikipedia.org/wiki/Second_Ha…

I’ve only gotten to do this a few times, but one of my favorite math things is giving a long talk (say ~2 hours) with an intermission, and end the first half on a cliffhanger. A few months ago I got to do this—I explained 2 conjectures which contradict each other, …

@LeoDelamoJr @AnalysisFact Functional Analysis

@AnalysisFact Damn I really don’t know this? Is this topology? Higher linear algebra?

@Ophidian18 @justAfanDavid @QuantaMagazine @GregoryJBarber The more interesting thing is that in high dimensions these are such bodies which are of constant width 1, but the volume of these bodies are extremely small compared to the volume of the sphere of constant width one in the respective direction. It's really surprising and cool.

If you sandwich a ball between two parallel planes, it will roll perfectly. But surprisingly, smaller, pointier shapes can do this too. Do such shapes exist in higher dimensions? A new math proof says yes. @GregoryJBarber reports: quantamagazine.org/mathematicians…

@aryehazan Should a_{n+1} be repeated twice?

@SnowFake3 @JDHamkins How do you know such a division exists? This does not seem obvious.

@JDHamkins Draw a ray through any black/white pair. Now rotate your line through different pairs until you have equal number of black/white on any given side of it. Now repeat the process for the subset of points each side.

My daughter had a nice problem in her high-school math club. Suppose you have 1000 white points and 1000 black points in the plane, no three collinear. Can you draw segments connecting them in pairs, from white to black, using each point just once, without any edges crossing?

@TermehKousha @canmathsociety L’hopitals rule once and then apply the second fundamental theorem.

@neverswimalone Yeah, with this strat, you can deny the entire site outside of the bombsites, so there is no point going for vertical control. The only weakspot I can imagine would be a vertical Theater push to flush the Jager out, but instead all you have to do now is play Jager --- P1

@PolFPS Interesting, my thought is you'd only hold one section of the map vertically instead of going for lots of control. Play Security, Lobby, Triple, Theater x 2 with reinforcements Security & Lobby hatch, Connector, Service, Triple x 2, Theater x 4. An Armor Panel 1F Hall (Tile).

When did teams start creating a rotation Triple/ Lobby on a Kitchen/ Lobby, Coastline defense? I dig the idea but it seems so vulnerable to Security, Blue and Lobby door. Asking for VOD links if you've got them.