OpenAI announced that one of its internal reasoning models autonomously disproved the planar unit distance conjecture, a problem first posed by Hungarian mathematician Paul Erdős in 1946. The conjecture asked: what is the maximum number of pairs of points exactly one unit apart on a two-dimensional plane?
The AI produced a new family of geometric constructions that outperform the previously assumed optimal square-grid configurations, effectively disproving the conjecture. The proof draws on infinite class field towers and the Golod-Shafarevich theorem.
Fields Medalist Timothy Gowers described the approach as “clever” and “elegant,” and other reviewers stated the proof could be published in a top-tier mathematical journal on its own merits. The AI pulled from algebraic number theory to solve a problem in combinatorial geometry, a cross-disciplinary leap most human mathematicians would not instinctively attempt.
The announcement was made public between May 20 and May 21, 2026.