What Lean checked and Astra didn't: two kinds of verification, one week apart. ~ Scott J. McCormick. https://www. researchgate.net/publication/4 14030431_What_Lean_Checked_and_Astra_Didn't_Two_Kinds_of_Verification_One_Week_Apart # AI4Math
The Real Story in OpenAI's Navier-Stokes Proof: Formal Verification Got 10,000x Cheaper
explainx.ai/blog/lean-4-...
Marcolli writes: "What is for us humans the act of doing mathematics? I’d say mathematics is two very important things at once: a language to make sense of reality and a form of self-expression, much like the arts. When seen from this perspective, the existence of artificial intelligences that can generate solutions to mathematical problems becomes essentially irrelevant, and is just left to…
Mathilde Marcolli writes: "What is it about all of these famous and less famous, invariably hard, Big Problems™? There is an undeniable sense in which these questions are interesting. Typically they are because, in the process of thinking about a particularly hard question, a lot of new mathematics gets developed that advances the field as a whole. The Riemann hypothesis is currently unsolved…
[JP] OpenAIがナビエ・ストークス方程式の証明でLean 4形式証明を同時公開！検証時間を13万時間から17時間へ激減させた革命 [EN] OpenAI Releases Lean 4 Formal Proof for Navier-Stokes Equation, Slashing Verification T…
#Lean4 #OpenAI #形式検証 #AI #Tech
mathematicians now feel like they have to be secretive about what they do in case it gets stolen by AI. graph theorists arent too worried about this though because they’ve already been doing discreet mathematics
Professor Lew Ludwig's new Math Values post asks: When does AI help students learn, and when does it just help them finish? Read more: https://maa.org/math-values/there-and-back-again-the-cost-of-a-fast-answer/
AI software completes a formal proof of Fermat’s Last Theorem. ~ David H Bailey. https:// mathscholar.org/2026/09/ai-sof tware-complete-a-formal-proof-of-fermats-last-theorem/ # AI4Math
We need to separate the "are models good at math?" question from the "do they steal unpublished ideas from users?" question. Of course they're not totally unrelated, but one can concede they have gotten good at attacking math problems while still believing they take ideas from users.
"if we strip away the humans from mathematics the subject will loose its soul. Math is a deeply human endeavor." - words to thrive by
A Lean 4 formalization of Scott's continuous lattices (1972). ~ Lars Warren Ericson. https:// arxiv.org/abs/2606.30782v2 # LeanProver # ITP # AI4Math
AI has solved one of math’s $1 million Millennium Prize Problems. ~ Konstantin Kakaes. https://www. quantamagazine.org/ai-has-solv ed-one-of-maths-1-million-millennium-prize-problems-20260908/ # AI4Math
This is exactly what those companies are after: tricking everybody into the perception that 'all math is solved by AI'. Here's my reply to this.
web.mathi.uni-heidelberg.de/media/Meanin...
3/3 Some thoughts on the use of AI * Intelligence of this kind should not be treated as an ordinary consumer product whose conditions are set entirely by a few companies. A provider should not be able to collect people’s ideas and information, control all evidence about how they were used, and then exploit that advantage against its own users. Once intelligence becomes basic infrastructure for soc…
2/3 Some thoughts on the use of AI * The more important question is therefore what someone contributes to human mathematical understanding. This includes explaining why an argument works, separating the main idea from technical details, connecting a result with other areas, finding the right questions, teaching new methods, and helping other mathematicians make use of them. Such contributions may…
1/3 Some thoughts on the use of AI A mathematical publication used to bring together three things. It announced a result, identified the people who had produced it, and added something to our human understanding of mathematics. It could therefore serve at the same time as a record of knowledge, a basis for assigning credit, and evidence of a mathematician’s ability. AI breaks this connection. * An…
Ii's near-impossible to show direct evidence for stealing ideas, because AI's are black boxes. But circumstantial evidence (which @gro-tsen.bsky.social 's thread catalogues is piling up, no? And OpenAI explicitly did not rule out the possibility that it made use of unpublished ideas from users.
So it's getting clear that some of the math abilities AI models have become ❝superhuman❞ at is “not giving credit where credit is due”, like “failing to cite previous work on the subject that inspired you” and, worse, “stealing colleagues' ideas”.
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the controversy thickens—now other openai results are being questioned 😈 mathstodon.xyz/@andreasthom... mathstodon.xyz/@andreasthom... mathstodon.xyz/@andreasthom...
What is mathematics now, and what should it be? ~ Jeremy Avigad. https:// proofsandprompts.com/2026/09/0 7/what-is-mathematics-now-and-what-should-it-be/ # AI4Math
(Auto)formalization, but why? ~ Seewoo Lee. https:// proofsandprompts.com/2026/09/0 8/autoformalization-but-why/ # AI4Math # LeanProver # ITP
On the Navier–Stokes Millennium Prize Problem. ~ OpenAI. https:// openai.com/index/navier-stokes -solution/ # AI4Math
AI may have just solved a million-dollar math problem. The field will never be the same. ~ Joseph Howlett. https://www. scientificamerican.com/article /ai-may-have-just-solved-a-million-dollar-math-problem-the-field-will-never-be-the-same/ # AI4Math
Clay Institute won't call Navier-Stokes solved after OpenAI proof claim. ~ Marcus Schuler. https://www. implicator.ai/clay-institute-n avier-stokes-openai-proof-claim/ # AI4Math
Wrote up my thoughts on the whole OpenAI Navier–Stokes Millennium Prize Problem story, and how it highlights the still confusing question of what using my data "to improve model performance" actually means simonwillison.net/2026/Sep/8/o...
RE: https:// mastodon.social/@tristanbuckma ster/117233413705701198 Many of you have already heard about the controversial backstory involving the race between OpenAI and Tristan Buckmaster and Levent Alpöge (who works for Anthropic). If not, read this: https:// mathstodon.xyz/@tristanbuckmas ter@mastodon.social/117233413735526010 and this: https:// mathstodon.xyz/@tao/1172335276 38291447 (2/2)
News flash: OpenAI claims formal proof that Navier-Stokes solutions can blow up. They used 10,000 agents simultaneously, who sent 2.7 million messages and used ~130 billion output tokens. They will not claim the $1,000,000 Millennium Prize for this result. This prize is not going as expected. The first winner refused to take it, saying the math establishment is corrupt. The second possible winner…
I’ve posted an AI-assisted preprint proposing an almost-all-primes lower bound of c(log p)^3 / log log p for strictly ordered Type-II Erdős–Straus solution counts. A restricted prime-side proof is checked in Lean; independent human review and originality checks remain outstanding. Does anyone know prior work already implying this bound? References welcome. https:// zenodo.org/records/22556477 # Nu…
RE: https:// mathstodon.xyz/@tao/1172309839 38174038 @ tao writes: "For the first time in the history of mathematics, we are faced with the situation that open problems in pure mathematics -- one of the primary fuels for mathematical discovery -- are being mined as a non-renewable resource". Very important thought! But maybe it's renewable if one is willing to solve an already solved…
Verification, formalisation and canonisation: formal theorem proving in the age of AI. ~ Sidharth Hariharan. https:// thefundamentaltheor3m.github.i o/beamers/tifr-2026/slides.pdf # AI4Math # ITP
Li's criterion for the Riemann Hypothesis, in Lean 4. ~ Nicholas Bulka. https:// github.com/nicholasbulka/li-cr iterion-rh-equivalence-lean # LeanProver # ITP # AI4Math
The global Kronecker–Weber theorem in Lean 4. ~ Naganori Yamaguchi. https:// github.com/n-yamaguchi-0729/Kr oneckerWeber # LeanProver # ITP # AI4Math
Erdős problem #501 in Lean 4. ~ Elliot Glazer. https:// github.com/elliotglazer/erdos5 01 # LeanProver # ITP # AI4Math
MathINsiD — a bridge layer between bibliographic and formalized mathematical knowledge You can browse mathlib or Palomar and see what is formalized. You cannot take a published paper and ask whether it has been. MathINsiD indexes that direction: it starts from the literature, not from a repository. ~5M zbMATH Open records — 97.7% of zbMATH — with formalizations attached to the papers they formaliz…
FLT: Anthropic has beaten me to it (one of their internal models, using the prove2.me platform, has formalized a complete proof of Fermat’s Last Theorem (FLT) in Lean). ~ Kevin Buzzard. https:// xenaproject.wordpress.com/2026 /09/04/flt-anthropic-has-beaten-me-to-it/ # AI4Math # LeanProver # ITP
Formalizing Fermat's Last Theorem. ~ Anthropic. https://www. anthropic.com/research/formali zing-fermats-last-theorem # AI4Math # LeanProver # ITP
Kevin Buzzard's thoughts on Fermat's Last Theorem being autoformalized in Lean.
xenaproject.wordpress.com/2026/09/04/f...
Proof of the Lyons-White conjecture. ~ Colin Defant, Ken Ono. https:// arxiv.org/abs/2608.27708v1 # LeanProver # ITP # AI4Math
FrontierMath Erdős (A benchmark of Erdős problems formalized in Lean). ~ Tom Adamczewski, Greg Burnham. https:// epoch.ai/files/frontiermath-er dos.pdf # LeanProver # ITP # AI4Math
Announcing FrontierMath Erdős (A benchmark of 68 significant Erdős problems, open as of August 2026, curated by Thomas Bloom and formalized in Lean). ~ Tom Adamczewski, Greg Burnham. https:// epoch.ai/latest/announcing-fro ntiermath-erdos # LeanProver # ITP # AI4Math