OpenAI Releases 722 Math Manuscripts in One Night, Spanning Riemann, Hodge and BSD

Summary

OpenAI has released 722 mathematics manuscripts produced by a single unreleased internal model, grouped into 372 results across 17 areas. According to the company, the model tried roughly 4,000 research problems, with each result consuming compute equal to about three hours of ChatGPT Pro thinking. Papers, source code and some Lean proofs were posted to GitHub, along with 10 model reasoning summaries. Headline claims include: no zeros for the zeta function and all Dirichlet L-functions where the real part exceeds 7/8, with a separate independent proof covering real parts above 11/12 that also rules out Siegel zeros; no general algorithm for the rational version of Hilbert's tenth problem; a complete formula for BSD-type elliptic curves under conditions such as Selmer rank 0 or 1; Hodge conjecture manuscripts restricted to complex-multiplication abelian varieties and products of K3 surfaces; an irrationality measure of exactly 2 for pi; irrationality of Catalan's constant; and a claimed proof of the Unique Games Conjecture. The repository states that verification status varies, some results lack Lean formalization, and two items did not follow the standard pipeline. An independent advisory group of nine scholars, including three Fields medalists, said its earlier advice does not constitute endorsement of the results or the process.