OpenAI's general-purpose reasoning model autonomously disproves an 80-year-old Erdős conjecture in discrete geometry

OpenAI announced that one of its general-purpose reasoning models autonomously disproved a central conjecture in discrete geometry — the planar unit-distance problem posed by Paul Erdős in 1946. The model found a new family of point configurations beating the square-grid arrangement and produced a mathematical proof. A subsequent refinement by Princeton's Will Sawin showed δ ≥ 0.014 is achievable from the construction.

This is the first time a prominent open problem central to an active subfield of mathematics has been solved autonomously by a general-purpose AI system. Crucially, the model was not fine-tuned for mathematics; it was given the written statement of the conjecture and produced both the construction and its proof. The capability claim is therefore broader than 'AI does math' — it's that the reasoning machinery generalizes to research-frontier problems without specialization.

The competitive frame is sharp. The Anthropic disclose-hold posture on Mythos sits next to OpenAI shipping a research-grade autonomous-mathematics result on the same day Anthropic announced its $1.25B/month Colossus compute deal. The two labs are racing on different axes — Anthropic on compute capacity to push the ceiling, OpenAI on autonomous-reasoning narrative to position the brand. Both bets get tested over the next two quarters. See our analysis →.

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