On October 26, OpenAI announced that its internal models had produced solutions to long-open problems in three separate fields. The one that made the most noise was the refutation of a conjecture in computer science known as the Exponential Time Hypothesis (ETH).
What happened?
According to OpenAI, the three results are these: in mathematics, a proof in every dimension of the "local smoothing" conjecture, which also resolves the Kakeya conjecture; in computer science, the refutation of ETH; and in physics, a mathematical proof that some four-dimensional quantum field theories, including quantum chromodynamics, exist. The physics result is also related to Yang-Mills, one of the Clay Institute's Millennium Prize problems.
ETH, proposed in 1999, says that solving certain logic puzzles takes exponentially longer as the number of variables grows. According to TechCrunch, OpenAI, and Anthropic, which published its own refutation a few hours later, claim their models found algorithms that solve these puzzles faster than expected. Ryan Williams of MIT, called in to interpret the result, said that alongside routine parts the proof has a few "alien-looking" sections and that checking it will require the whole community to work together. OpenAI said it is reasonably confident the finding does not break known encryption systems.
A different path was taken for each field: the mathematics output was put on GitHub, an outside working group was set up for computer science and OpenAI will fund a conference, while publication of the physics result was left to physicists.
Why does it matter?
If the results are verified, many scientific papers of the past decade that rely on ETH will need to be reexamined. The bigger question concerns science itself: when AI starts producing proofs, the role of humans may be to understand and verify those proofs and to ask new questions that raise the bar.