"The big story now in mathematics is that nobody wants to share anything"

www.theguardian.com/science/2026...

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

www.erdosproblems.com/forum/thread...

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.

www.wsj.com/tech/ai/ai-m...

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

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 $22.5 million in tokens for a$1 million bounty. All that math and they failed at subtraction.

Math # AI 28/n Anthropic did not share any information about the energy consumption needed by this accomplishment. Figures that I obtained independently, for another challenge, lead me to the following rough estimations: - an electricity consumption of 250Wh per day, which would made 2.5GWh, hence, at current price in France, 200,000€. Just for running these computers. And this does not take int…

Math # AI 27/n One week ago, on September 4th, Anthropic announced that it had more or less done the same job, namely generated a complete formalization of the proof of Fermat's Last Theorem. They claim the work took 11 days, “largely autonomously”, so that we now have 13 million lines of Lean code that contains a complete proof of that theorem. Those files compile, but require 20 more times…

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.

www.science.org/content/arti...

2026 mathematician grading student papers and doing admin paperwork while ChatGPT enjoys proving beautiful theorems:

Just finished "The Proof in the Code", about the development of Lean and formal verification of proofs. Great book!

An alternative is to create a new kind of venue where AI-written and verified results could be submitted and made available to the research community for examination and analysis. Like aiXiv, there would be no human author, only a "corresponding human". 5/

Another approach might be to conduct an oral examination of the author to test their understanding of the paper. Could this scale, perhaps by requiring authors to provide a letter from a known authority certifying that the authority has conducted such an exam? 4/

How should the scientific enterprise handle this? We could try to decide whether the author understands the work. E.g., if the author lacks a publication record or credentials in the research area, we could reject the submission. 3/

ArXiv policy is that a human author must take responsibility for a submission. But obviously an author cannot take responsibility (or claim credit) for a result that they do not understand. 2/

Daily briefing: OpenAI claims a huge maths breakthrough ->Nature | More on "OpenAI's breakthrough on fluid equations" at BigEarthData.ai | #OpenAI

The Four-Color Theorem Gets a Rare New Proof www.quantamagazine.org/the-four-col...

The proof contains 13 million lines of Lean code, work that had been expected to take years to complete.

“Dr. Buckmaster posted 3 papers on the internet describing the results he & Dr. Alpöge had completed. He also posted an 1,870-word treatise describing the history of the research & apologizing that he had not had time to polish the manuscripts up to his usual standards.

Formal verification is moving from academic research into shipped tools for AI agent authorization. Here is what is real, and what is still missing. #aiagents

The solution of the Millennium Prize math problem by AI announced last week is genuinely disturbing because it's an extraordinary and original accomplishment in a domain representing the highest levels of human creativity and difficulty. The math research community is freaking over this.

Meet the accountant who cracked a 40-year-old math problem, with no math degree, just a MacBook, AI agents, and curiosity. Discover how Richie Sater did it in the latest Math Values: https://maa.org/math-values/im-an-accountant-why-am-i-solving-open-math-problems/

They can make proofs for theorem provers such as Lean. No Lean, no proof. Lean is human readable.

"To solve a problem with a proof is exciting and rewarding because it is true forever." – Marie-France Vignéras (1946-) #quote #mathematics #math #maths

Brand New AI Solves a Millennium Prize

Anthropic's Claude formalized Fermat's Last Theorem "like never before," churning out 13M lines of Lean code in 11 days. An impressive feat for formal verification, even for a known proof. The sheer scale is mind-boggling. 🤯 #AI #Math

How Claude AI Formalized Fermat’s Last Theorem in 11 Days with 13 Million Lines of Code

That depends. On how surprising the result was. On how useful the result was. On the complexity and length of the proof. If the proof was written purely by LLM, or already fed into a proof assistant system. And so on...