Brayden Letwin

phd student in mathematics @UW, I enjoy thinking about probability... probably

[Brayden Letwin @letwinbrayden]

@ConstantinKogl Wow! Very nice.

[Tarun Kathuria @_TarunKathuria]

https://t.co/4CjrYVsPHH lol KLS got solved too! Edit: It hasn't been solved. Only solved for "unconditional" isotropic log-concave measures where "unconditional" is symmetric under coordinate-wise reflections (so certainly not all isotropic LC measures)

[Brayden Letwin @letwinbrayden]

@aparna_gupte Very cool.

[Brayden Letwin @letwinbrayden]

@rrwilliams Thanks Ryan. Hope to see you at a conference sometime! Hopefully I can report next time with some progress.

[Brayden Letwin @letwinbrayden]

@OREAXEAX Noted. Thank you.

[Brayden Letwin @letwinbrayden]

The KLS constant is O(log^1/4 n)!
https://t.co/Luv4z6CjOt.

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: https://t.co/OszLjR9W60. Quite remarkable!

[Brayden Letwin @letwinbrayden]

@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).

[Brayden Letwin @letwinbrayden]

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

[Brayden Letwin @letwinbrayden]

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

[Brayden Letwin @letwinbrayden]

@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.

[Brayden Letwin @letwinbrayden]

@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...

[Brayden Letwin @letwinbrayden]

@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.

[Brayden Letwin @letwinbrayden]

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

[Brayden Letwin @letwinbrayden]

@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).

[Brayden Letwin @letwinbrayden]

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

[Brayden Letwin @letwinbrayden]

@LeoDelamoJr @AnalysisFact Functional Analysis