A proof posted May 20 on OpenAI.com says an OpenAI reasoning model found a counterexample to Paul Erdős’ 1946 unit-distance conjecture, overturning a result many mathematicians had assumed was true.
OpenAI said the general-purpose model used no math-specific software and, across repeated runs on the same prompt, produced the correct disproof in 50% of trials.
Outside experts said the result is mathematically significant because it links a geometry problem to algebra and number theory, though several argued it reflects exhaustive search more than human-style creative insight.
A June 2 declaration urging tighter AI guardrails in mathematics had gathered 1,590 signatures by June 5, citing verification, attribution and access concerns as powerful models remain private and their failure rates undisclosed.
If an AI's mind is a black box, can cryptography provide the key to trusting its discoveries?
As AI solves humanity's greatest puzzles, is it eroding our own ability to think critically?
The End of an 80-Year Conjecture: How AI Disproved Erdős’ Unit Distance Problem in 2026
Overview
In May 2026, OpenAI's advanced AI model made history by autonomously disproving the 80-year-old Erdős unit distance conjecture. The AI achieved this breakthrough by breaking down the complex problem into smaller steps and discovering a counterexample, all through a fully automated process. Its 'superhuman levels of patience' and broad technical knowledge enabled it to meet challenging conditions and even introduce new mathematical tools, like harmonic analysis, to the problem. This achievement not only proved the conjecture false but also showcased how AI can drive innovation and reshape the future of mathematical discovery.