OpenAI’s 722 Math Manuscripts: The Results, Proofs, Compute and Costs

Release examined: October 6, 2026. Evidence status: Source reporting and selected static proof-artifact inspection; no independent Lean execution by Kingy.

OpenAI has published a mathematics repository containing 722 manuscripts grouped into 372 result families. Its catalogue claims resolutions of problems across number theory, geometry, theoretical computer science, algebra, mathematical physics and differential equations. Among them are the Mahler conjectures, an exact irrationality exponent for π, the Unique Games Conjecture, the free group factor isomorphism problem and large-data global regularity for the relativistic Vlasov–Maxwell system.

The release also contains Lean proof artifacts and ten abridged reasoning summaries. That makes it possible to examine considerably more than a list of impressive theorem names. It does not make every manuscript an independently accepted result.

The most useful reading of this release is a large collection of mathematical claims with differing levels of supporting evidence. Some claims have selected formal statements and proposed proof implementations; others currently rely on manuscripts. OpenAI itself warns that unformalized results may contain issues. The formalization manifest records partial progress and an unchecked review status.