AI Models Crack Three Foundational Problems in Mathematics and Physics—Opening New Questions About Computational Limits

OpenAI's AI systems have produced machine-verified proofs of three blockbuster problems in mathematics, computer science, and physics, challenging decades-old assumptions about what computers can solve. The claims, announced October 26, include disproving the Exponential Time Hypothesis, a 1999 conjecture that underpins cryptographic security and computational complexity theory, and proving the local smoothing conjecture in harmonic analysis for the first time in all spatial dimensions. The lab also released a mathematically rigorous proof in quantum chromodynamics. MIT computational complexity theorist Ryan Williams, who won the 2024 Gödel Prize, is leading the academic community's verification effort.