An internal "reasoning" model from OpenAI disproved, from a single prompt, a conjecture that Hungarian mathematician Paul Erdős formulated back in 1946 — the so-called unit distance problem in the plane (how many pairs of points can, at most, be exactly a unit distance apart). The model found a construction that exceeds the previously assumed bound, meaning there can be noticeably more such pairs than was thought. The company announced this on May 20. OpenAI ↗ Scientific American ↗
The model drew on deep number theory — infinite class field towers. Nine independent mathematicians, including Fields Medal recipient Tim Gowers, verified the result and completed it into a 19-page paper; Gowers wrote that "no AI-generated proof to date has come close to this." However, the model did not find the optimal solution, and it was humans who brought it into publishable form. Live Science ↗ arXiv ↗
This is precisely what fuels the dispute. A group of mathematicians, in the "Leiden Declaration," point out that corporate models are closed off — lacking transparency, reproducibility, and any overview of their failures. British mathematician Ursula Martin adds that we learn nothing about the model's failures — and the fact that "a model finds a match" does not yet mean it "understands mathematics." Who will verify AI-generated proofs remains an open question. NZZ ↗
OpenAI Model Disproves 80-Year-Old Erdős Conjecture — Sparking Debate Over Whether AI Really Understands Mathematics
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