Hereβs a good read on First Proof, a project designed to test how well publicly available AIs can solve hard math problems. The outcome in my understanding in a sentence: todayβs AIs can sometimes solve hard problems, but theyβre still far from reliable on their own. Link below:
Recently, I have started getting appreciable value from AI for my own mathematics research. While model improvements were necessary for this to happen, I think another key factor was reflecting on recent success cases, in order to build a better mental model for the comparative strengths of AI. Previously I would think in terms like "AI is good at extremal combinatorics, but bad at derived algebraic geometry"; a more nuanced perspective allowed me to identify directions where AI could truly accelerate my work.
A few months ago, Tao described AI as a "junior collaborator". Currently I think of it more as an "alien collaborator", which is already superhuman at certain skills (e.g., assembling puzzle pieces, juggling delicate technical conditions, making local optimizations) but lackluster at certain others (e.g., creating new puzzle pieces, generating diverse ideas).
Much of what I write is in the spirit of taming overhype, but it's important to give credit where credit is due: AI has progressed to the point where AI tools, and education on how best to use them, need to become a core part of any mathematics Ph.D. curriculum.
Very sad to hear of the passing of Misha Kapovich Z"L (March 13, 1963 β June 16, 2026), who lost a lengthy battle with cancer. Our paper on superintegral Kleinian packings and "bugs" was, to me, the "final" word on the subject, and was very instructive for me to learn so much from Misha as we wrote it. I last visited him at his home in May of 2024, when I was giving the Thurston Lectures at UC Davis. While his body was weak, his mind was sharp as ever, and he immediately wanted to jump right into discussing higher rank Patterson-Sullivan theory. He was a great man and a brilliant mathematician. May his memory be a blessing.
I somehow missed this when it was first posted, but Sylvester's Conjecture has been proved by Fan and Wan! Every prime congruent to 4, 7, or 8 mod 9 can be expressed as the sum of two rational cubes.
https://t.co/wAAbGFJb42
Abdullah Ibrahim was a true maestro who embodied a spirit of freedom and experimental artistry that transcended cultural boundaries within his unique musical world.
Today, we mourn the loss of Abdullah Ibrahim (1934-2026).
A giant of South African and global jazz, we are honoured that his final public performance took place on the Rosies Stage at CTIJF on 27 March 2026.
Rest in peace, maestro. Your music lives on. ποΈπΉ