An AI system built by OpenAI reportedly produced a proof resolving a case of the Navier-Stokes blowup problem, one of the seven Millennium Prize problems, by constructing a counterexample rather than new theoretical machinery. The work built partly on prior human research, including contributions from mathematicians Tristan Buckmaster and Levent Alpoge, and marks the first Millennium problem tackled by an AI attempting all seven in parallel.
logangraves.com
· 2026-09-17
OpenAI announced its AI resolved a long-standing open question about the Navier-Stokes equations, one of the Clay Mathematics Institute's Millennium Prize Problems, claiming it did so within days using roughly 10,000 agents. Mathematician Tristan Buckmaster disputes the credit, saying he and Anthropic researcher Levent Alpöge had already developed the key approach before OpenAI learned of it and rushed to finish the proof over a weekend.
entrepreneur.com
· 2026-09-09
A repository has been published presenting a formal, machine-checked proof addressing the Hopf problem, showing the six-sphere admits a complex manifold structure compatible with its standard topology. The work builds on the paper 'A compact complex threefold fibred by tori over the projective line, and the six-sphere,' shared originally by Levent Alpöge, and includes a Comparator tool adapted from the Formal Conjectures project to verify the statement.
github.com
· 2026-08-27
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