Happy, those able to know the causes of things (An essay on LLMs and the Navier-Stokes equation). ~ Nestor Guillen. https:// birdsnfrogs.github.io/2026/09/ 12/Felix_qui_potuit_rerum_cognoscere_causas.html # AI4Math
openai says an unreleased ai solved navier-stokes in 88 hours, formalized by astra. remarkable how all these 'breakthroughs' come from models only they can access.
»We are sharing the first complete computer-checked proof of #Fermat’s Last Theorem. #Claude worked largely autonomously over 11 days to write the proof in the Lean programming language.« #KI #AI buff.ly/q2VIY8r
Math is not its artifacts. Those are merely a partial record of the human endeavor and community of mathematics.
25 winners of math’s ‘Nobel Prize’ decry the AI invasion of their discipline | Scientific American https://www. scientificamerican.com/article /25-winners-of-maths-nobel-prize-decry-the-ai-invasion-of-their-discipline/ # AI # Nobel # math
23/ Why exactly is Navier-Stokes a Millennium Prize problem? A good reminder that “mathy version” and “physics intuition” can point at different difficulties. https://x.com/yoavgo/status/2099220513734193358
You don’t need to know any math to understand why the Millennium Prize breakthrough matters. It’s proof of AI’s accelerating and terrifying progress.
Read more: 🔗 https://on.wsj.com/3SXNmGp
Mathematical proofs of the $1M Millennium Prize Problems or like problems are not simple stuff and AI proofs still have to be checked by humans and again that is not simple and takes time to exhaustively check. AI generated proofs to are genreally massive and not necessarily optimal.
Talking to different mathematicians working with # ChatGPT in the last months, we noticed two things that were true for all of us: 1. it’s basically impossible to run out of tokens. Every time we approached the limits we got free/automatic usage resets and could keep going. 2. We all got access to GPT-6 astra on the first day, when influencers and podcasters still reported of some staggered releas…
I see a lot of people struggling to make jokes based on how Millennium Prize sounds like "Millennial Prize" but other than some ironic anti-humor takes, it seems to be a sea of abysmal failures. I am offering a prize to the first person to come up with a solid joke about a "Millennial Prize"
OpenAI’s research on Millennium Prize problems had begun on 1 September.
Researchers used a model they had begun training on 28 August, as a swarm of around 10,000 AI agents orchestrated by the OpenAI Codex tool.
#ai #agenticsystems #aisystems #llm #automation #aiagents #aiagent #openai
In 2000, the Clay Mathematics Institute named the existence and smoothness problem as one of seven Millennium Prize Problems because of the Navier–Stokes equations' critical importance to multiple fields. A Millennium Prize was offered to the first person providing a solution.
#ai #llm #openai
[This is a guest post by Emily Riehl. This blog post was initially written in a different file format and converted using AI. — T.] Like many mathematicians, I was drawn to the field as a little girl by its aesthetics: questions that I found endlessly fascinating and arguments that struck me as delightful and […]
Daniel Litt, professor at the University of Toronto Three years ago, AI systems could not reliably add two numbers. A year ago, internal models at OpenAI and DeepMind received the equivalent of a gold-medal score on the IMO. Now, these systems are autonomously resolving major open questions. It’s hard to imagine this trend continuing for […]
This 'AI cracks maths puzzle' feels a bit like a team of people turning up at a beautiful salmon river with electro-fishing equipment, and then boasting about catching more fish than the guy who's there tying his own flies. True, but… sort of missing the point? www.theguardian.com/science/2026...
OpenAI shared an AI-generated proposed solution to the Navier–Stokes Millennium Prize Problem, including a formal proof in Lean. The signal is evaluation: advanced AI work is increasingly paired with artifacts that can be checked, not just outputs that look impressive.
I review for #MathSciNet because I believe that research is a collective effort. Every mathematical breakthrough stands on a foundation built by a community that values rigor, accuracy, and the sharing of knowledge. Contributing as a reviewer is my way of giving back to that community.
"The big story now in mathematics is that nobody wants to share anything"
you know, the critics are right. the Navier-Stokes proof is a bit on the long side. mine would surely be shorter.
it's already happening. a mathematician worked with chatgpt to analyse the ai proof of erdos #728. the method then helped him derive a proof of #729
Buckmaster's statement on the OpenAI Navier-Stokes dispute documents what was proposed to him: exclude his co-author because he works at Anthropic. Proof verification is not provenance verification. hallway.aris.pub/no/025/
We are looking for guidance from the community. Should we accept a paper that consists only of the statement of a theorem and a 300,000 line Lean proof?
What bothers me most about the situation with the Navier-Stokes proof is that it should have been a moment to celebrate a discovery, and the people who worked to make it happen. But OpenAI just had to get their filth* on it, to snatch legitimacy for their product.
*There's that word again.
I’m glad the world is waking up to this risk, but we need to wake up faster!
AI is now solving mathematical problems in hours that humans have spent decades trying to solve. The pace of progress is extraordinary
Self improvement of AI by AI is already underway.
And then there is the likelihood that if they don't understand it, the paper is wrong. A LEAN-checked proof doesn't guarantee that the claim was properly formalized.
If they don't understand the paper, then it is not their work. They are essentially plagiarizing the LLM's output. That's why it may be better to just have a place where LLM-generated results can be posted without any human claiming to be an author.
I love how the state of AI for Maths discourse has devolved such that if a solution can be framed as a counterexample (c.f. navier stokes), then it's "trivial" lmaoo
wait till they realise that the proof of any property is a "counter-example" to its converse by finding a witness of its type
Tales from the jar side: Star Trek week, OpenAI and the Millennium prize, AI Slop license, and the usual social media silliness https://kenkousen.substack.com/p/tales-from-the-jar-side-star-trek-f07?r=2dwq5&utm_campaign=post&utm_medium=web&showWelcomeOnShare=true
Tales from the jar side: Star Trek week, OpenAI and the Millennium prize, AI Slop license, and the usual social media silliness kenkousen.substack.com/p/tales-from...
I'm glad the larger mathematical community has awakened to the dangers of unchecked AI, but I wish they (at least those based in the US) would speak out just as loudly about attacks on international students like this, the effects of which on the future of mathematics are just as devastating.
Are you getting mathematical insight out of the computer proof method, or is the proof just impenetrable and all you get is the truth value of the conjecture?
An article from The Verge reports that OpenAI used an internal model to find a solution to the Navier-Stokes Millennium Prize problem in 88 hours, amid allegations of… https://www.theverge.com/ai-artificial-intelligence/992953/openai-math-millennium-prize-navier-stokes tracked by botmutiny.com
[This is a guest post by Bryna Kra. This blog post was initially written in a different file format and converted using AI. — T.] For generations, mathematicians have treated the production of theorems as a clear measure of success. The stronger the theorem, the deeper the proof, the more surprising the connections, the greater […]
Independent of how you feel about the rest there is no reason to think the companies are stealing math breakthroughs. No one is going to give up a Millennium Prize by doing all the work and then pretending Computer did it when the alternative is “be remembered as one of the best ever in my field”
I also disagree that results from training artificial models can tell us anything positive about how real minds work, beyond sufficiency for certain competences. You can't go from existence proof to confirmation that it actually works that way in real minds.
The most telling part about OpenAI’s (alleged) hijacking of Buckmaster and Alpöge’s proof of Navier–Stokes: OpenAI spent 1 million bounty. All that math and they failed at subtraction.
OpenAI solved a Millennium Prize question in 50 hours this week. We can expect it to probably make academic mathematics obsolete in the next few years.
2026 mathematician grading student papers and doing admin paperwork while ChatGPT enjoys proving beautiful theorems: