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...
Claude proved Fermat's Last Theorem this week, unsolved for 358 years, thirteen million lines of proof. It only counts because a mathematician at Imperial College London checked it line by line. Not AI replacing judgement, AI alongside it, with a human still saying yes.
OpenAI shared a solution to the Navier-Stokes Millennium Prize Problem, produced in 88 hours by around 10,000 agents on a new internal model, and says Tristan Buckmaster's Codex prompts could not have influenced the system
After Math via @ mseri https:// lobste.rs/s/ojls0p # ai # math # philosophy https:// terrytao.wordpress.com/2026/09 /12/after-math/
Restructuring how mathematics academia works wouldn't necessarily be a bad thing. But humans being humans, there must be a period of wailing and gnashing of teeth first. 🙂 # aiinmaths # math
AI Is Breaking Our Proxies for Expertise, by @seangoedecke.bsky.social: https://www. seangoedecke.com/ai-is-breakin g-our-proxies-for-expertise/?ref=frontenddogma.com # ai # math
Too bad the part about the controversity is paywalled. The internet is going wild to what extent the proof was stolen or not. There is quite some complexity involved who did what and to what extent openai models used other people’s work.
"A Severe Misalignment of AI in Mathematics" - a declaration signed by 25 Fields Medal recipients https:// lemmy.ml/post/52673676
Uri Bader, Professor at Maryland University and Weizmann Institute Math exists. We explore it.We do not invent math. We invent ways of understanding and communicating it. We choose which parts of it to study, and we develop an adequate language for that that suits us, humans. But we explore an objectively existing domain. Empirical fact: our abstract […]
A 14 million line proof does not advance human understanding of math, because humans cannot parse the structure of a text that long in a way that provides for understanding
The mess around the Navier-Stokes proof has been sitting with me for days now.
🤖 OpenAI's Millennium Prize proof has turned into a credit dispute, and Fields Medalists are now getting involved
An NYU mathematician named Tristan Buckmaster announced earlier this week that he and Anthropic mathematician Levent Alpöge had made progress on the Navier-Stokes existence and […]
It might have solved the equation just a step earlier, because it had much much MUCH more input to work with. And some of this input was from the math scientists working on the same proof. But it hasn't solved the equation completely on its onw.
OpenAI announced a solution to the Navier–Stokes Millennium Prize Problem, but mathematicians and rival AI firms contest the originality and attribution of the work. #tech #OpenAI #NavierStokes
A useful read for anyone who doesn’t want to be swept away by AI hype. An impressive answer is not proof that AI understands or reasons. Always ask: what exactly can it do, how was that tested, and when does it fail? Iris van Rooij explains why. 👌
I have. Some AI math claims deserve criticism. But that doesn’t justify dismissing the entire evidence base. Eg First Proof used unpublished research problems with answers withheld beforehand and expert mathematical review and an ETH-led system solved 6/10. That’s empirical and falsifiable.
The team of researchers who used AI within OpenAI to find this proof are also humans and also have as much right to any and all parts math as anyone else, using whatever methods they would like to use in order to pursue it.
We can object to the company receiving clout here separately.
Interesting piece on the suspicions of the math community regarding AI companies having access to your chats. Relevant for scientists increasingly relying on AI tools: www.theverge.com/ai-artificia... 🧪
OpenAI says one of its AI models solved a Millennium Prize problem, the unsolved math puzzles that carry a $1 million reward each.
Mathematicians who reviewed it say the AI got to an answer but shows no real sign it understood the proof it produced.
Indeed. Another good take: bsky.app/profile/josh... (e.g. pointing to the only previous Millennium Prize solution announcement, by Perelman, who wasn't super integrated with "the mathematical community" either, and left the "proper writeup" to others as well - just like those super evil AI bros)
GPT-6 is a groundbreaking leap over its predecessors and its successor has been in training for two weeks and just solved a Millennium Prize.
🤣 Ah, yes, the grand revelation that # AI and # math have different "goals." Because we all know AI's main ambition is to # overthrow # humanity , not solve calculus problems.🤖📚 Twenty-five mathematicians with too much time on their hands unite to point out the obvious—AI companies aren't exactly in it for the quadratic equations. 👏 https:// liorpachter.wordpress.com/2026 /09/12/align-ai-and-m…
And while Buckmaster tries to emphasize the importance of humans, it's unclear to what extent they produced the ideas since it seems to have been so hard to even understand the proofs LLMs generated for them.