Landmark discovery claim · Mathematics
An OpenAI model disproves the planar unit-distance conjecture
An infinite family of planar point configurations that disproves Erdős's longstanding conjectured near-linear upper bound for the number of unit-distance pairs.
Summary
OpenAI released an AI-generated construction disproving the prevailing unit-distance conjecture in combinatorial geometry. The argument imports tools from algebraic number theory to build infinitely many planar configurations with polynomially more unit-distance pairs than the conjecture allowed, and external mathematicians published companion remarks checking and contextualizing the result.
AI role
OpenAI reports that an unreleased general-purpose reasoning model autonomously constructed the proof while being evaluated on Erdős problems, without a math-specific search scaffold.
Narrative role
This is the direct precursor to the later Astra portfolio and a standalone milestone: a general-purpose model produced a surprising counterexample to a prominent field-level open problem, followed by substantive expert checking and new human follow-up work.
Caveat
The proof and companion review were released through OpenAI rather than a journal, and the result disproves a specific conjectured bound rather than solving every aspect of the planar unit-distance problem. The model and full evaluation protocol are not public.