AI Model Challenges 80-Year-Old Erdős Conjecture on Unit Distance Problem

OpenAI's AI model has found a better arrangement for the planar unit distance problem, challenging Paul Erdős' 1946 conjecture. The problem asks how many pairs of points on a plane can be exactly the same distance apart. Erdős believed a grid-like arrangement maximized pairs. The AI discovered a strategy using algebraic number theory that produces more pairs. Mathematicians Daniel Litt, Noga Alon, Will Sawin, and Thomas Bloom reviewed the result. Bloom and Sawin used similar techniques to solve another Erdős problem, the sum-product conjecture. OpenAI published a rewritten summary and proof, not the original output. The Leiden Declaration on Artificial Intelligence and Mathematics, published June 2, warns about unvetted AI results and urges transparency. Co-author Rodrigo Ochigame criticized OpenAI for secrecy. The AI's success is attributed to cross-domain knowledge and tireless computation.