Combinatorics · May 20, 2026

Erdős unit-distance conjecture

A fixed δ>0 and infinitely many n with ν(n)≥n^(1+δ), disproving that asymptotic conjecture.

Scope and what remains

A disproof does not determine the exact maximum. The later real sum-product disproof is a separate human follow-up.

Contributors

OpenAI's unnamed model generated the construction; the announcement names Noga Alon, Tim Gowers, Arul Shankar and Jacob Tsimerman as external readers. Later human extensions require their own credits.

Sources