Tim Gowers

OpenAI Model Disproves Erdos Unit Distance Conjecture

An internal OpenAI model disproved Erdos's 1946 planar unit distance conjecture, with Princeton's Sawin extracting an explicit exponent delta=0.014 in a constructive refinement, and Gowers calling it Annals-of-Mathematics quality. The bigger signal isn't the proof. It's Shankar's CoT observation: most of the model's reasoning attempted counterexamples to the conjecture, not validations of it. That's calibrated contrarianism — a scorable behavioral property and the math-grounded analogue to sycophancy detection. Verifier-rich domains are where autonomous AI lands first; counterexample-seeking is how we'll measure whether reasoning is real or performative.