Lijie Chen
Assistant Professor of Electrical Engineering and Computer Sciences at UC Berkeley and theoretical computer scientist whose work focuses on computational complexity, quantum computing, pseudorandomness, derandomization, and applications of theory to AI safety.
OpenAI Model Disproves Erdős’s 80-Year-Old Unit Distance Conjecture
OpenAI reasoning researchers Alexander Wei, Hongxun Wu and Lijie Chen say a general-purpose model disproved Paul Erdős’s 80-year-old unit distance conjecture, a central problem in discrete geometry, by finding a construction that beat the square-grid arrangement Erdős had proposed as essentially optimal. In the podcast, they argue the result is significant not just because of the problem’s status, but because the model was not a bespoke math system: given enough inference-time compute, it produced a proof idea that internal reviewers initially doubted and that other mathematicians quickly began using. Their broader claim is that AI is moving beyond contest math toward a collaborative role in research, where models solve hard problems and humans verify, interpret and extend the ideas.
General-Purpose AI Finds Better Construction for Planar Unit Distance Problem
OpenAI says a general-purpose reasoning model has found a new family of constructions for the planar unit distance problem, a combinatorial geometry question posed by Paul Erdős in 1946. The result challenges a decades-old expectation that roughly square-grid arrangements were essentially best possible, and mathematicians including Timothy Gowers and Mark Sellke describe it as a clear case of AI producing a breakthrough on a prominent open problem. OpenAI frames the result as evidence that AI can accelerate research by exploring long, delicate chains of reasoning, while leaving problem choice and interpretation to human experts.