Much more than coding, math appears to be the first field that AI has managed to upturn in a few short years.
Mathematicians have reacted in shock and wonder after OpenAI today published proofs to over 300 open math problems. These included the Quasi Reimann hypothesis, Unique Games conjecture & Hodge Conjecture for CM Abelian varieties.
Alex Kontorovich, Mathematician and Distinguished Professor of Math at Rutgers, could scarcely believe the results. “Quasi-RH?!?!???! Are you kidding me? If a human did this, it would be an instant Fields Medal, no questions asked. RH says zeta has no zeros in Re(s)>1/2. The best we had until a second ago was a region that got thinner and thinner the higher up the imaginary axis you go. I thought maybe they’d fatten that up a bit, that’d be a massive breakthrough. But no. They got a zero free strip!!!! Insane,” he posted on X.
Mathematician and Cornell professor Steven Strogatz called the results “staggering”. “Many staggering results here. But this is a particularly amazing one: the exponent for matrix multiplication is no more than 2.25. The previous world record had been something like 2.37. This leap in progress is like Bob Beamon’s long jump,” he posted on X.
Alvaro Lozano-Robledo, mathematician and professor at the University of Connecticut also called the result “staggering”, but also called it a “takeover of mathematics”. “The scale of this is staggering. But… Why? Why is OpenAI trying to solve hundreds of math problems to be released all at once? I think we got the point when they found a counterexample to Navier-Stokes — internal model = great. I am not sure at this point what this (hostile?) takeover of the mathematical landscape is trying to achieve other than, again, a massive PR stunt,” he posted on X.
Paata Ivanisvili, Professor of Mathematics at UC Irvine, hinted that a single problem from the list was worthy of a Fields Medal. “Kakeya in 3D won a Fields Medal. Kakeya in 4D was solved by AI. Let that sink in,” he posted on X.
Levent Alpoge, who works with Anthropic, and had been involved in a controversy over the Navier Stokes solution, called it the “most significant moment in mathematical history. “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,” he posted on X.
Daniel Litt, Assistant professor (of mathematics) at the University of Toronto, stuck an optimistic note, saying that mathematicians now had a lot of exciting work to do. “Fun! Looks like mathematicians have a lot of exciting work to do. If I understand correctly one of the results is a (very special) case of a conjecture of mine, which is also a consequence of stronger work in progress by a student of mine,” he posted on X.
Thomas Bloom, who is a Research Fellow at the University of Manchester owner of erdosproblems.com, said that all mathematicians should take a brief holiday to recover. “Go outside, touch some grass, bake something delicious and share it with your family. Do a crossword and watch the sunrise. Then we’ll get back to work; lots to do,” he posted.
Rodrigo Porto, who does Math at Princeton and is a former IMO contestant, called the result “very crazy”. “This is very crazy… 1. Quasi Riemann Hypothesis: i cant describe how big this is… its (by very very far) the closest advance in RH. If AI systems can independently get to this result, I dont know how far we can be. 2. Kakeya maximal conjecture solved?! It’s a stronger version of the Kakeya conjecture. Hong Wang literally won a fields medal for making progress on the latter,” he posted on X.
Constantin Kogler, who is Postdoc at Institute of Advanced Study, called the results “superhuman mathematics”. “The OpenAI announcement is insane! Two of my say four or so favourite questions solved! On one of them I’ll publish a paper tomorrow on! This is completely superhuman mathematics! More to follow!” he said.
Kaneenika Sinha, who works on analytic number theory at IISER Pune shared a message she sent to her group. “The analytic number theory group at IISER Pune has a lot to think about this morning. We will think about existential questions later :-)” she posted.
And Scott Armstrong, Math Prof at Courant/NYU, probably put it most pithily. “You guys, I’m starting to consider the possibility that I’m not going to be able to compete against these machines,” he said.