Eighty Years, One Model, One New Idea
An internal OpenAI reasoning model disproved a conjecture in discrete geometry that had been open since 1946. It found a polynomial improvement to the best known lower bound for the planar unit distance problem — n^(1+δ) with δ = 0.014 — by importing tools from algebraic number theory that no human mathematician had previously applied to this problem. The proof was verified and endorsed by several leading mathematicians, including Fields Medalist Tim Gowers.
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