“The core algorithm was found on October 16 by an internal Claude research model with 14M output tokens and no human input. Anthropic researchers worked with Claude to improve the presentation, resulting in this paper.”

Big, big, big, big props for quasiriemann and no Siegel zeroes (with many other beauties in there), I’m kicking myself for talking all over about it being within reach but not actually having pushed. There are some sad stories related to their users getting scooped / conflicts of interest (kakeya maximal comes to mind), and obviously we had some of the problems (without commenting on precise rumours). We should put that aside for today though. It’s obviously the most significant moment in mathematical history.

“we cannot rule out that de-identified data derived from their usage of our products helped improve our models.” i mean props to them for straight coming clean. (so far the proof looks more along the lines of another euler blowup proof we had, off of whose ansatz naming we were making really stupid puns like “smooth criminale”, unlike the much better “ideal fluids explode”, Tristan) so i’ll now give a bit on my thinking here. i actually woulda been pumped to collaborate on this, there are a lot of people at oai i like (ok, clearly some were indirectly dicks to me because of being part of the whole situation, but im a big boy, i still like them), idgaf about authorship on that step anyway, coulda been me Tristan and every fte at oai for all i care (on that Tristan would disagree:p). but on hearing the loud convo in the hallway, especially the part where a millennium prize was offered if i’d just be removed from the paper, it was kinda clear the die had been cast and things were locked. pretty wacky, unstrategic, and unnecessary, since on my side things were mostly me and claude having a good time yoloing random stuff in the corner rather than anything institutional. i also like the idea of the labs cooperating, and even better on scientific progress. it’s a shame!

hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final ((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)