Even odds no other millennium prize is solved in September. If announced, has to stand expert review up till 10/31.
OpenAI's AI Breakthroughs Spark Mathematical Debate and Ethical Concerns
Ten thousand agents, eighty-eight hours, one Millennium Prize problem, and a proof Lean checks line by line. So: do you want to win a Nobel Prize? Pick the problem, design the reward, go.
https://davidorban.com/2026/09/do-you-want-to-win-a-nobel-prize/
In my view, If AI can solve a math problem it may mean that the problem is already conceptually understood in terms of how to solve it. What remains is often the tedious work of formal derivation and verification which AI can do much faster.
#science
buff.ly/pFbdIRm
[This is a guest post by Dimitris Koukoulopoulos. This blog post was initially written in a different file format and converted using AI. — T.] At the 2026 World Cup semifinal, England led Argentina 1-0 with less than twenty minutes left. And then the momentum completely changed: England switched to a much more defensive formation, […]
Regarding The Clay Mathematics Institute Millennium Prize Rules. The short answer is no, an AI or non-human entity cannot legally or officially be awarded the prize, but the human creators or users of that AI could potentially be recognized. share.google/aimode/J5OLe...
@kimmonismus
OpenAI is close to solving another math problem from the Millennium Prize Problems, the Hodge Conjecture. Via The Information
For solving the first Millenium Prize Problem "OpenAI used a variant of its next pre-trained model, codename...
More details on OpenAI claiming it had solved a famous outstanding math problem: One of the human mathematicians working on it said he had 3 ChatGPT accounts but only opted out of training the LLM with two of them. That means the model may have well ingested his work and used it to solve the problem. Attribution mess is messy. (Story by Davide Castelvecchi, who happens to have a PhD in math himsel…
OpenAI is close to solving the Hodge Conjecture as it tests whether frontier AI models can handle some of mathematics’ hardest unsolved problems.
Read more in today's AI Agenda: https://thein.fo/46vQYm9
[This is a guest post by Timothy Gowers, crossposted from his blog. This blog post was initially written in a different file format and converted using AI. — T.] When I was around 11 I heard for the first time about Fermat’s Last Theorem. I was immediately captivated by the problem statement, as well as […]
Fields medal winner Jacob Tsimerman is now working on # AI safety for OpenAI and giving talk on "Open source game theory" https://www.youtube.com/watch?v=dLQZWMH4u0k # math # mathematics # gametheory
[This is a guest post by Talia Ringer. This blog post was initially written in a different file format and converted using AI. — T.] When I was wrapping up graduate school in computer science in Spring 2021, I was given access to a curious little programming model on OpenAI’s “playground.” The model, called Codex, […]
Richard Evan Schwartz, Professor at Brown University My short story, The Fate of the Riemann Hypothesis, recently got a lot of attention on social media. Many people liked the story and many people did not. The story precisely expresses my feelings about AI-driven mathematics but my scientific views about it are more nuanced. In this […]
OpenAI said an unreleased internal model resolved Navier-Stokes existence and smoothness.
Source: Last Week in AI
@kimmonismus
Want to see how quickly AI progress can make expert forecasts look outdated?
As late as December 2024, AI researchers’ aggregate forecasts put a 50% chance of AI solving a Millennium Prize problem around 2054, finding and patching a s...
I've written a blog post responding to the letter about maths and AI signed by 25 Fields medallists. As with the Leiden Declaration, I didn't sign it, but I agree with much of it and welcome its existence.
gowers.wordpress.com/2026/09/17/w...
When I was around 11 I heard for the first time about Fermat’s Last Theorem. I was immediately captivated by the problem statement, as well as by the accompanying story, and made a fairly serious attempt to prove it. And while, unsurprisingly, I failed, I learned a lot from the attempt. Blissfully ignorant of the […]
Ben Green, Professor at the University of Oxford The rapid development of AI is of enormous public interest right now, with the possible existential risk to humanity being reported by mainstream news organisations. However, the discussion is often tempered with questions such as ‘haven’t we heard this before?’ or ‘isn’t this just hype from the […]
Anthropic says Claude translated a proof of Fermat's Last Theorem into Lean.
Lean is a computer program mathematicians use to check proofs.
We’re excited to launch Stage 1 of the Lean Kernel Challenge, a multi-stage competition to improve the performance of verified computation in the Lean 4 kernel that the whole community can benefit from. The Lean Kernel Challenge brings the community together to develop faster algorithms and better representations for verified computation. Through these collective contributions, […]
Let's generalize : this post is groundbreaking proof that you can add an arbitrary amount of LinkedIn bullshit to any existing equation without changing its value.
Corollary is trivial.
(…) This is prompted by a friend informing me this morning of two annoying additional stories that taint the recent public success of AI generated proofs and will hopefully lead the mathematical community to address the question of predation and plagiarism. mathstodon.xyz/@antoinecham... #AI #Math ⏚ Antoine Chambert-Loir (@anto...
I'm not anti-AI but OpenAI solving a Millennium Prize as a marketing stunt is beyond lame. It's theft from human potential and accomplishment.
The other reason I want us using Microsoft AI tools at work rather than OpenAI's or Anthropic's, if I can't stop the AI use entirely, is because as we've seen with the recent Navier–Stokes Millennium Prize kerfuffle, OpenAI and Anthropic will definitely use any data you give them to train their […]
Nihar Shah did a heroic experiment for TMLR: he spent 20-25 hours over two weeks interviewing authors of seemingly low-quality submissions about their own papers.
He confirmed what we all suspected: people submitting these papers have no idea what is going on in them.
It would be helpful and it would accelerate progress, because open questions tend to accrete conditional theorems (this is true if Riemann is true, e.g.).
It would certainly spoil some fun, but idk if it would do so more or less than generating a proof does!
A place to read up on AI in mathematics, understand new perspectives, and develop answers to the challenges we face. https:// ai.math.ms/
one idea in it that stuck with me is that the purpose of a proof is not to determine if a statement is true or false
it's to break the statement down into a collection of substatements, joined by argument, which can be mapped onto existing mathematical knowledge
There really isn't any reason that proofs of theorems must be simple enough for a single human (or even the entire mathematics community) to understand, at some point we may actually need ai and some measure of faith in formal verification to progress.
I don’t know that I’m getting across the scale of a millennium prize problem if it’s getting compared to writing a paper.
I mean by this metric I guess everything is on a continuum so nothing is any better than anything else, even solving one of the canonical millennium prize unsolved math problems. “Some math problem” indeed.
speaking to an applied mathematician friend at work, the OpenAI NS proof is non-constructive, so while the counter-example has been proven to exist, it's actually non-trivial to simulate it.
I wonder if porting it (via dedukti?) to Agda might be a valuable thing to do?
The blog @ proofsandprompts is also on mastodon now. It's a community project about # AI and # math .
A genAI math proof might actually be correct, it might actually do what it said it could do and not just be stolen from a human mathematician.
What it doesn't do, and can never do, is create a mental model in a human's head that makes them go "holy shit this is the same as ___"
Formal verification is often treated as a finish line: prove the code once, then trust it forever. That is not what it gives you. It proves that one version of a program matches one version of a specification.
Programs change, and so do their goals.
[This is a guest post by the editors of the communal blog Proofs and Prompts. This blog post was initially written in a different file format and converted using AI. — T.] In the mathematical community, AI became a central conversation topic months before we started our communal blog, called Proofs and Prompts. Some of […]
[This is a guest post by Noah Giansiracusa. This blog post was initially written in a different file format and converted using AI. — T.] Imagine a tech company announces new robot workers that can prepare food better than human chefs. If you think of dining out as sitting at a table and having your […]
[This is a guest post by Ben Green. I support the letter, and am also a (corresponding) Fellow, but I have worked in various collaborations with the AI industry and so was not eligible to be a signatory. — T.] The rapid development of AI is of enormous public interest right now, with the possible existential […]
Anthropic's solution to Fermat's Last Theorem is a constructive proof; the AI generated 29,510 "sub proofs," each one of which has to hold, for its conclusion to Fermat's Last Theorem to be true. Having grad students confirm each step is a chore, but it will have to be done to validate it.
In a list of absolutely remarkable things, what stands out to me is this: Zhang's proof was so carefully and beautifully written that it could be read, understood, vetted, reproduced and published in five weeks. Most modern proofs take a year or more.
Compare that to the recent AI press.