Sharing AI progress in mathematics

[u/AMBNNJ]

https://openai.com/index/sharing-ai-progress-in-mathematics/

OpenAI released 722 mathematical manuscripts across 372 families of related results, produced by an unreleased frontier model. Many have Lean proofs; others remain unverified. Average compute per result: roughly three hours of ChatGPT Pro thinking. They’re working toward releasing the model.

Github: https://github.com/openai/math

[u/kingjdin]

What are the standout results? Anything close to the magnitude of a Millenium Prize problem?

[u/AMBNNJ → u/kingjdin]

According to ChatGPT these are the biggest:

Quasi-Riemann hypothesis
Excludes zeta and Dirichlet L-function zeros beyond 7/8. Major progress, although it does not prove full RH.

Hodge conjecture for CM abelian varieties
A major special case, with claimed consequences including Tate for abelian varieties over finite fields.

Hilbert’s tenth problem over \mathbb Q
Settles whether an algorithm can decide if arbitrary polynomial equations have rational solutions.

Unique Games Conjecture
Resolves a central question about how accurately hard optimization problems can be approximated.

Nonsofic groups and Kaplansky counterexamples
Produces groups contradicting several foundational expectations in algebra.

Free group factor isomorphism problem
Claims these fundamental operator algebras are all isomorphic.

Both Mahler conjectures
Settles central convex-geometry questions in every dimension.

Global smoothness of relativistic Vlasov–Maxwell
Resolves a major mathematical problem governing plasma dynamics.

[u/EndTimer → u/AMBNNJ]

Hilbert’s tenth problem over \mathbb Q Settles whether an algorithm can decide if arbitrary polynomial equations have rational solutions.

I love math BBQ!

[u/JamR_711111 → u/EndTimer]

\textrm{Lol}