OpenAI claims new AI proofs covering half a Millennium Prize problem, the Kakeya conjecture and a core complexity hypothesis.

These problems are in math, computer science and physics, problems top experts had worked on for decades.

The biggest: for about 25 years, the Exponential Time Hypothesis held that certain logic puzzles take time that explodes as they grow. OpenAI’s AI says it proved the hypothesis false, and hundreds of research papers rest on it.

In math, the AI claims to have cracked the local smoothing conjecture, a 35-year-old puzzle about how waves focus, which also settles the famous Kakeya conjecture. Humans had only solved smaller versions.

In physics, the AI claims it proved, with full mathematical rigor, that quantum chromodynamics, the theory of the force holding atoms’ cores together, stands on solid math. Its Yang-Mills proof covers half of the $1M “Yang-Mills Existence and Mass Gap” Millennium Prize problem.