OpenAI Model Disproves the Exponential Time Hypothesis

OpenAI says its internal model disproved the Exponential Time Hypothesis, or ETH, a long-standing hypothesis about the computational complexity of certain problems. Many papers in databases and geometry treated ETH as true. On October 16, OpenAI announced they had disproved it. Then, on October 17, mathematicians checked the result using Lean, a program for automated proof verification. Lean does not care about your elegant reasoning. It either believes you or it does not, and there is nothing you can do about that. The same model then proved another mathematical conjecture, Sogge's conjecture, which concerns wave regularity in arbitrary dimensions. Finally, there is a third result tied to four-dimensional quantum field theory. It has not been published yet, because OpenAI wants other physicists to double-check it first.

OpenAI is not taking all the credit. The company offered the Simons Foundation, a research institute that funds basic science and mathematics, $5 million to pay independent mathematicians to verify these proofs. For AI-agent coding, this is not a tool to use right now, but it gives a sense of what is coming. It is worth remembering that trusting an AI agent to write correct code is not at all the same as trusting a math model to prove theorems.