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Anthropic researcher and mathematician Levent Alpöge used Claude Fable during the World Cup final to produce a concrete, checkable counterexample to the Jacobian Conjecture — a problem on Smale's 1998 list of Mathematical Problems for the Next Century. The map is three polynomials in three variables. The Jacobian determinant is -2. The conjecture is false.
Read more →A UC Berkeley IEOR researcher used GPT-5.6 Sol Pro over two chat sessions totaling roughly four hours to prove a lower bound in zeroth-order convex optimization that had resisted attempts for 30 years, then formalized the result in Lean 4. A different kind of AI-does-math story than the CDC proof: one expert, one model, one hard problem.
Read more →OpenAI claims GPT-5.6 Sol Ultra produced a three-page proof of the Cycle Double Cover Conjecture — a 50-year-old open problem in graph theory — in under an hour, using 64 parallel subagents. The math community hasn't had a chance to stress-test it yet, and the details of how much human guidance went in are unclear. Worth watching, cautiously.
Read more →GPT-5.4 Pro solved Erdős Problem #1196 — a 1968 conjecture about primitive sets — when a 23-year-old amateur fed it the problem in a single prompt. The AI's approach used von Mangoldt weights and a downward Markov chain, a framing that existed in analytic number theory for ninety years but had never been applied here. Terence Tao's explanation for why experts missed it is the most telling part of the story.
Read more →In 2023, Terence Tao predicted that 2026-level AI would be a trustworthy co-author in mathematical research. This month he credited ChatGPT Pro with a proof in a real analysis paper — and published a philosophical essay arguing AI is a natural extension of humanity's tool-building tradition. Both together are a data point, not a verdict.
Read more →Donald Knuth published a paper in early March titled "Claude's Cycles" — named after the AI that spent an hour finding an algorithm for a directed graph decomposition problem he had been stuck on for weeks. Knuth wrote the formal proof himself; Claude did the search. Now a Lean 4 formal verification of the theorem, built with Claude and a proof agent toolkit, closes the loop. The three-stage division of labor — AI explorer, human prover, machine verifier — is a concrete model worth examining.
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