A major burst of machine-generated mathematics arrived when an internal OpenAI model produced formalized solutions to hundreds of longstanding open problems, including a Lean-certified proof claimed for Subhash Khot’s Unique Games Conjecture. The claimed proofs are often opaque and poorly written, requiring human teams to reconstruct and verify key steps; Scott Aaronson relays his complexity-theorist wife’s reaction that the manuscripts are chaotic and need AI-assisted synthesis to extract coherent claims. OpenAI reportedly ran about 8,000 problems and solved roughly 5% after about three hours of GPT-Pro compute per problem. Two dissemination patterns emerged: the “OpenAI dump,” which releases many raw proofs and ignites a race to interpret them, and the “Anthropic” model, which instead partners with selected human authors to polish and announce results (exemplified by Virginia Williams and Josh Alman’s speedups for 3SUM and APSP).
The haul contains deep, specific advances across theory and algorithms: L=BPL derandomization; faster-than-classic FFT/integer multiplication improvements; a positive solution to the Unitary Synthesis Problem; parity separation from QAC0; near-fourth-power randomized-vs-quantum query separations; superquadratic sensitivity separations; area law for 2D gapped Hamiltonians; randomized nearly-linear-time maximum-matching and approximate counting algorithms; O(n9/4) matrix multiplication via new techniques; Ω(n3) determinantal lower bound for the permanent; and uncomputability of solving rational polynomial equations, plus partial progress on several Millennium-style conjectures. P vs NP remains unsolved. The immediate consequence is a global sprint by mathematicians and theorists to verify, interpret, credit, and integrate machine-produced ideas while rethinking professional norms for collaboration with powerful AI tools.
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