RefAI and Mathematics

AI and Mathematics

AI and Mathematics

Major discoveries and milestones where AI systems have contributed to — or independently produced — mathematical proofs, conjecture disproofs, and original research.

2025–2026: The acceleration

  • May 2026 — OpenAI's internal reasoning model disproves Erdős's unit-distance conjecture (planar unit distance problem). External mathematician Tim Gowers: "if a human had written the paper and submitted it to the Annals… I would have recommended acceptance without any hesitation. No previous AI-generated proof has come close to that." openai-unit-distance-problem-ai-proof
  • July 20, 2026 — Levent Alpöge proves the Jacobian conjecture is false (87 years open, since 1939). Terence Tao: not brute force, required genuine creative insight.
  • July 22, 2026 — Dmitry Rybin disproves Dinitz-Garg-Goemans conjecture (~30 years open) by literally asking ChatGPT for a counterexample and insisting it keep going.
  • July 23, 2026 — Jared Zoneraich proves Graffiti Conjectures 39 & 40 (40 years old); also refutes Brandt's Regular Supergraph Problem (~20 years).
  • July 23, 2026 — Shouqiao Wang solves 6 open Erdős problems in 5 days using GPT-5.6 Sol.
  • July 24, 2026 — Prabhanjan Ananth and Amit Sahai solve the unclonable encryption problem (6 years open, quantum cryptography) with GPT-5.6 Sol Ultra.
  • July 25, 2026 — Digvijay Bokey disproves Levit–Mandrescu conjecture (~20 years open).
  • July 26, 2026 — Three groups independently solve the same 26-year-old quantum information theory problem; two used GPT-5.6 Sol with basic prompts.
  • July 28, 2026 — Zhengqing proves a 22-year-old probability problem with GPT-5.6 Pro (37% chance bound on sums of independent random variables).
  • July 30, 2026 — Tencent's Hyra research agent solves a 57-year-old combinatorics problem (distinct sums vs. distinct differences); arXiv:2607.27199.
  • July 30, 2026 — Dominik Peters uses GPT-5.6 Sol Ultra to settle a 25-year-old voting theory question (combining 3 ranked choices is fundamentally hard).
  • July 31, 2026 — Philip Arathoon disproves the Maxwell conjecture (153 years open) via counterexample found by GPT-5.6 Sol.
  • August 1, 2026 — OpenAI's Astra model solves 10 major open problems in mathematics, quantum complexity, and theoretical computer science. Cost: <$2,000 at Sol API prices. Includes flagship problems of entire fields.

Context

These are not AI "solving math" in the sense of finding entirely new branches or conjectures — but they are AI systems conducting original research across entire fields, producing proofs that mathematicians describe with Fields-medal-level framing. The 10 Astra proofs alone would, if produced by a single human, be considered "an entire generation's worth of research across several fields compressed into a single person's output."

See also

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