math

Tens of millions? You're thinking specifically of the proof of Navier-Stokes. According to https://github.com/openai/math/blob/main/README.md: "On average, each result used three hours of ChatGPT Pro thinking compute with that model. Over the course of the evaluation, the model was posed approximately 4,000 problems. Aggregating the output into result families and manuscripts and requiring an appropriate level of significance led to the catalog outlined above." I will note that this includes the Quasi Riemann Hypothesis. The model that solved NS was significantly dumber and less efficient that OpenAIs more recent math-models and you shouldn't over index on "it's expensive now". AI has advanced so quickly that your <2 month old opinion is out of date by 5+ orders of magnitude!

ETH is false! I really would not have believed it. [0]: > We give a deterministic algorithm for exactly counting the satisfying assignments of an arbitrary k-CNF formula. For every fixed k ⩾ 2, on a formula with n variables and m clauses, our algorithm uses $poly_k (n, m)$ space and runs in time $(n + m)^{O_k(1)} 2^{n/(\log n)^{1/2 + o(1)}}$ The dominant term there is (roughly) $2^{n / (\log n)^{0.5}}$, so still superpolynomial but less than exponential. Fucking wild. [0] https://github.com/openai/math/blob/main/preprints/The-Expon...

I was confused too, but it looks like https://github.com/openai/math/blob/main/lean/ComparatorChal... (with the sorry at the end) is just the problem statement; the actual proof is a big pile of lean in the Algorithms folder, with the final theorem stated here https://github.com/openai/math/blob/7ef5c0cc5ca4b0e072b7a050...

They do that to make it easier for readers to verify the statement (which is entirely contained in that file) separately from the proof (which is spread over thousands of files and github can't even show them all). Proof is at https://github.com/openai/math/tree/main/lean/OAI/Algorithms...

https://github.com/openai/math/blob/7ef5c0cc5ca4b0e072b7a050... looks like the real proof is in this file

See also: Announcing three new discoveries in mathematics, computer science, and physics - https://news.ycombinator.com/item?id=50251344

https://github.com/openai/math/tree/main/preprints/The-Expon... >We give a deterministic algorithm for exactly counting the satisfying assignments of an arbitrary k-CNF formula [in superpolynomial but subexponential time]

I'd like to have a look through the lean4 proof from openAI's recent paper: Modularity of elliptic curves over imaginary quadratic fields <https://github.com/openai/math/blob/main/preprints/Modularity-of-elliptic-curves-o…>. I've had a look round the openai github but i can't find the lean4 proof. did openai publish the lean4 code? if so, could you link it to me?

The history of the term is actually really interesting. There has been debate about whether or not its the correct name basically since the advent of computer science departments in the 60s. I don't think the author is "wrong" about the gap between theoretical discussions computation and the actual design constraints of building usable computers. I don't know if that's really a general refutation of proving new things mathematically though. The word "computer" doesn't appear once in the paper OpenAI released, nor do they make any claims specifically about "computer science": https://github.com/openai/math/blob/main/preprints/An-explic... It's a novel bit of math. Whether or not it means anything in the context of writing software realistically is an interesting conversation, but it doesn't have much bearing on the substance of the result

To be fair, they aren't wrong... https://github.com/openai/math/blob/main/lean/ComparatorChal...

They're doing both. Some results were initially published without Lean. But they continue adding the proofs where they're missing: https://github.com/openai/math/tree/main/lean

> Over the year, nothing they've released with a lean proof attached has turned out false That's not true. [0] > On July 25, Ramana Kumar published a repository containing a sorry-free "disproof" of the Collatz conjecture, produced with AI assistance. It is not a valid proof because it exploits a bug in the kernel's handling of nested inductive types. Even in this dump we're talking about, it hasn't been true. [1] > In “Algebraicity of Weil classes on split abelian eightfolds” a sign error invalidates a stabilization-trace cancellation argument and the construction used by two dependent papers. [0] https://leodemoura.github.io/blog/2026-8-24-postmortem-for-t... [1] https://github.com/openai/math/blob/main/history.md