OpenAI's general-purpose model solves 80-year-old Erdős math problem
First time AI autonomously disproves a major math conjecture from 1946
OpenAI revealed today that one of its general-purpose reasoning models has achieved a historic milestone in mathematics: it autonomously solved the planar unit distance problem, a famous open question first posed by mathematician Paul Erdős in 1946. For nearly 80 years, mathematicians believed the optimal configurations for this problem roughly resembled square grids. The OpenAI model disproved that belief by discovering an entirely new family of constructions that outperforms the previous best solutions. The model was not built specifically for math or for this problem—it is a general-purpose reasoning system—making the achievement a landmark for both AI and mathematics.
The breakthrough demonstrates that AI systems are now capable of sustaining long, difficult chains of reasoning, connecting ideas across distant mathematical fields, and surfacing paths researchers had not explored. OpenAI noted that these same capabilities will soon accelerate work in biology, physics, engineering, and medicine. However, they emphasized that human judgment remains essential: expertise becomes more valuable as AI assists in searching, suggesting, and verifying. People still choose the problems that matter, interpret results, and decide what questions to pursue next. The full proof, the model's chain of thought, and accompanying remarks have been published by OpenAI.
- Solved the planar unit distance problem posed by Paul Erdős in 1946, an open problem for nearly 80 years.
- Disproved the long-standing belief that square grids yield the best solutions, discovering a superior new family of constructions.
- Achieved by a general-purpose reasoning model, not one specialized for mathematics, marking a first for autonomous AI problem-solving.
Why It Matters
AI can now autonomously solve open mathematical problems, promising to accelerate discovery across sciences.