Amazing stuff! More to come! This is only the beginning!
"OpenAI model finds proof resolving famous mathematics problem
An OpenAI reasoning model has resolved the planar unit distance problem, a central question in discrete geometry posed by legendary mathematician Paul Erdős in 1946.
The conjecture held that square grid constructions were essentially optimal for maximizing unit-distance pairs among points in a plane, a belief that stood unchallenged for nearly 80 years.
The model instead found an infinite family of configurations yielding polynomial improvements over the grid approach, disproving the assumption.
What makes the breakthrough unusual is not just the result itself, but how it was found: a general-purpose reasoning model, not a system specialized for mathematics, produced a proof that external mathematicians have verified. The proof brings sophisticated tools from algebraic number theory to bear on an elementary geometric question, revealing unexpected connections between distant mathematical domains. Fields medalist Tim Gowers called it “a milestone in AI mathematics,” while number theorist Arul Shankar argued the result shows AI models “are capable of having original ingenious ideas, and then carrying them out to fruition.”" (Source)
Paul Erdos (Source)
Previously known construction of many unit distances from a rescaled square grid.
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