OpenAI’s New Mathematical Proofs: Has AI Crossed a Scientific Frontier?
From the Exponential Time Hypothesis to quantum chromodynamics, three remarkable claims test both the mathematical capabilities of AI and the scientific community’s ability to evaluate them. Editorial image generated by the author. In theoretical computer science, some problems are believed to demand exponentially growing computation even from the best algorithms. In quantum physics, theories that explain experiments with extraordinary accuracy still lack fully rigorous mathematical foundations. And in harmonic analysis, seemingly simple questions about how waves behave have occupied leading mathematicians for decades. On October 26, 2026, OpenAI announced that its AI models had made major breakthroughs in all three areas: a claimed refutation of the Exponential Time Hypothesis, existence proofs for important four-dimensional quantum field theories, and a proof of the local smoothing conjecture with consequences for several other longstanding mathematical problem...