New Math from OpenAI

OpenAI has put a sprawling batch of new mathematical results on GitHub, and the size of it is the first shock. The release started as 722 manuscripts, now 719 after three were withdrawn because they lacked Lean proofs, and the set is organized into 372 families. According to the source, one internal frontier model produced the lot, mostly from a single prompt, after roughly 4,000 attempts at problems and about three hours of compute per solution found.

The headline results are not all the same kind of win. The Riemann result is described as a major tightening of bounds, not a proof of the hypothesis itself. Matrix multiplication got down to exponent 2.25 from a previous world record of about 2.37, and integer multiplication also saw an asymptotic improvement. There’s a pi result that gets described as especially fun, plus work on unique games, Hodge, Birch, Hilbert’s 10th, Hadwiger, and other problems that sit close to some of the deepest questions in math and theoretical computer science.

What makes the release hard to dismiss is the breadth. The source says 90 of the top 500 open problems were touched, and several prominent mathematicians reacted as if the field had just been hit by something historic. Even the more sober read from inside the discussion is that verification still matters, and that AI is not yet clearly better at final checking than at generating candidate proofs. But there’s already a lot of evidence, the source argues, that the models are doing serious work rather than spewing random text.

There’s also a practical angle. The source cites possible spillovers into fusion research, body scanners, matching systems, tissue scans, quantum sensors, and safety checks for self-driving cars and robots. And beneath the math drama sits a bigger point: if a model can chew through this many hard problems in a verified domain, the old excuse that AI is only good at fuzzy chores starts looking thin.