But pumping the gas doesn't just solve famous problems that get newspaper headlines--like the Navier Stokes millennium prize problem--they solve a bunch of other problems collaterally too.

I think I’ve always felt like this for art, but its definitely made me realise I also feel like this about math and it changed my half formed philosophical views on proofs. Oh an AI was so good it solved a millennium prize problem? I genuinely don’t care

With Danny and Sharon Kleitman and Michel Goemans at the MIT Endicott house. Sharing AI progress on mathematics (OpenAI) A few hours ago, Open AI shared solution to a few hundred mathematical problems. Certainly this is an amazing milestone for … Continue reading →

Terry Tao @teorth.bsky.social: Indiscriminate brute-force application of AI to mathematics is depleting the field of good questions without renewing this resource or providing commensurate value.

OpenAI: We hear you. Here's a .zip file with 377 hasty AI solutions to important open problems.

Yea in this case we probably wouldn't learn much from what the LLM tried that didn't work but I think we could start to grasp the contours of what they can and can't do in math.

We could begin to hypothesize the shape of theorems and proof techniques LLMs may or may not be good at.

welcome to the era of good enough. as long as the proof works right, that's all that matters? there is no point in discovery anymore; it's just about finding the end point. smiles.

I am shocked to learn that the Abundance Conjecture has been solved by OpenAI but they couldn't solve Termination of Flips. I always thought it'd be the other way around. I'm even more shocked to learn that the proofs are for compact Kähler varieties and not just for projective ones. #math #algebraicgeometry #mmp #openai #maths

Paper is the most AI written monstrosity ever. Just straight into the proof, no motivation, no connection to other areas, no implications for what this means and why its important.

The "single prompt" part hides the checking. A proof for those math problems can be verified line by line, so a wrong answer gets caught. Most tasks I hand to ChatGPT or Claude have no checker like that, which is why I still read every line

Okay, OpenAI just dropped news that their frontier model is solving open math problems. And get this: they're sharing the Lean proof formalizations and research details on GitHub! Not just results, but how they got there. That's a huge deal for advancing AI in complex fields. 🤯 #AI #Mathematics

I mean I think we all have to get used to this happening. Math is literally the best case scenario for LLMs since it can be easily checked with a proof checker like Lean and therefore put in a loop. It helps that the problems have been thoughtfully written up by humand I imagine.

Oh, cool, OpenAI's AI proved that every regular language has generalized star height (gsh) <= 3. I remember this problem from my time as a computer science student. The bigger open question was, whether there is even any regular language L with gsh(L) > 1 or if all regular languages have gsh(L)<=1. Any CS student can understand this problem, if you know what regular languages and regular…

There's quite a few improvements on methods people will find exciting. First glance is that OpenAI claims to have resolved the UGC in the affirmative, which had you asked people five years ago would probably be at worst debatably more important than any millennium prize problem

[This is a guest post by Ben Antieau, cross-posted from his blog. — T.] There was no personal problem, no world problem, whose eloquent solution did not exist— somewhere in some hexagon. —Jorge Luis Borges, “The Library of Babel” [1] New repository I am writing to announce Hexagon, a new repository for research works in […]

FOR IMMEDIATE RELEASE

SAN FRANCISCO — OpenAI today announced Endings-500, a public GitHub repository containing the final ten minutes of 500 feature films that have never been released, screened, or watched by any human being. Each ending has been formally verified in LeanBack, OpenAI's automated ending-verification system, which confirms that every film does, in fact, end.

OpenAI dropping Millennium Prize-level claims straight to GitHub instead of peer review is a trust problem, not just a format one. Math advances through scrutiny—bulk code dumps skip the step that actually earns credibility.

OpenAI Is Pissing Off a Bunch of Mathematicians—Again

Mathematics is beginning to face a turbulent age due to the rapid advancements of AI systems. A recent Summit on PhD Math Education in the Age of AI (CMSA) discussed recommendations on the adaptations for the Math PhD programs. While I agree with the main points, this post is an opinion on my major objection to the proposed direction of PhD in mathematics. I argue for a radical change in the defin…

[This is a guest post by Thomas Bloom, crossposted from the Erdős problems forum. This blog post was initially written in a different file format and converted using AI. — T.] AI is changing everything, for better and/or worse, and the rate of change is dizzying; in recent months this has been particularly evident in […]

“Large language models (LLMs) first appeared to the general public as a curiosity. Today, everyone uses them, and there is no doubt that their use is radically transforming the nature of our technical activities. This is particularly true in mathematics. […]”

Is mathematics over, or just graduating? ~ Christian Szegedy. https://docs.google.com/document/d/e/2PACX-1vTSh-pyNP3Gi99WMmsinnLmE9V5CDI0HEm6WGbIPMNt3V5SGlClHF8-BetotKHOImrvQDSXmFdiOw8D/pub #AI4Math

“We are in an age in which artificial intelligence is no longer a technological curiosity or a tool used by specialists. Generative AI can now write, summarize, translate, code, solve mathematical problems, and assist with almost every stage of academic work. The opportunities are enormous. […]”

Im not sure i follow, the proof was written in lean. Are you saying that a separate LLM should write the formal proof? Sorry just trying to make sure I better understand

[This is a guest post by Jeremy Avigad. This blog post was initially written in a different file format and converted using AI. — T.] “Mathematics underwent, in the nineteenth century, a transformation so profound that it is not too much to call it a second birth of the subject—its first birth having occurred among […]

Before AI, writing papers and grant applications served as costly signals of a scientist’s ability. Today, they can no longer serve that function. The time has come to return to illegible, subjective human evaluations of scientific quality. Rate-limiting authors is a necessary first step.

Are mathematicians only bearers of truth? I argue not; I argue there is an element of “taste” and “value judgment” behind the scenes that does not appear in the discussion of AI math.

Mathematicians fear being reduced from writers of proofs to mere readers of (machine generated) proofs.

Any writer can feel this: imagine you no longer get to write, but only to proofread what machines have written. Mathematicians feel they’re being LITERALLY reduced to “proof readers.”

I struggle to believe that an AI generates Lean proof constitutes human understanding, however, I think to some (especially those outside the community of academic math) will feel very very differently. And I can see their point because their Lean certificate tells them something is true 3/n

The dumbest part is, they'll use AI to hammer away at a problem in the least efficient, most inelegant way possible, and then show up demanding their Millennium prize. They don't understand why finding the answer they brute-forced was supposed to be interesting.

[This is a guest post by Diego Córdoba and Luis Martínez-Zoroa. This blog post was initially written in a different file format and converted using AI. — T.] Euler formulated the equations for an inviscid incompressible fluid more than 250 years ago. Published in his 1757 memoir, they belong to the earliest systems of partial […]

Some thoughts on what an old folk song can teach us about recent advances in artificial intelligence.

This is fascinating, and those with rusty maths need only get past the intro explanation of the Millennium Prize Problems. Walter Benjamin's place in the discussion steps it up.

The Work of Math in the Age of Artificial Reproduction

• by Dan Rockmore

#maths /1 www.nybooks.com/online/2026/...

[This is a guest post by Jennifer Taback. This blog post was initially written in a different file format and converted using AI. — T.] Recently I have read a stream of articles questioning the future of mathematics: what constitutes a proof, what we value, how we retain the human enterprise of creating knowledge. Many […]

If we are not needed to produce maths, then we can spend our time learning. With the right incentive structure, that does not sound so bad.

i really do not want to hear what llms are doing to the millennium prize problems

I use large language models quite a lot in my research. I ask them to look for references, explain unfamiliar mathematics, write code, suggest approaches, find counterexamples, and try to prove things.

Serious question: do you believe this model output is proof of an emergent understanding of mathematics?

[This is a guest post by Matthew Colbrook. This blog post was initially written in a different file format and converted using AI. — T.] (Disclosure: ChatGPT helped me write and refine this post.) Inspired in part by the recent discussions on this blog, we have started a new project, AIM, an initiative to create […]

So, unlike that fake Buckmaster controversy, here we most likely have an actual credit misassignment.

So we are left guessing how that problem was solved. Which SciAm informs is the case for the original 1978 zeta(3) proof by Apéry as well, who said he found the key parts "in a flower pot".

Especially wrt the Math stuff, there is no "mistaking" a proof. It either is or isn't. It is impossible for the training to have memorized proofs to unsolved problems. I think at that point "it is capable of cognition equivalent of a high-functioning mathematician" ought to be the null hypothesis.

— 1. The Hardy-Littlewood maximal inequality — We work in Euclidean space with Lebesgue measure; we write instead of for the Lebesgue measure of a set . For any and let denote the open ball of radius centred at . Thus for instance . For any , we use to denote the dilate of around […]