Only a few weeks after posting more than 700 pages of manuscripts covering 372 major math problems, OpenAI is back with a second set of results. This time they go beyond pure mathematics into theoretical computer science and physics. If even part of it holds up, it would be among the most significant claims any AI lab has made so far.
The computer science result is the one that should get people’s attention. OpenAI says its models have produced a proof that the Exponential Time Hypothesis is false. ETH, proposed by Russell Impagliazzo and Ramamohan Paturi around the turn of the millennium, is the working assumption that certain problems, starting with the satisfiability problem known as 3-SAT, can’t be solved meaningfully faster than brute force. It hasn’t been proven, but it’s widely believed, and hundreds of papers in fields from database theory to computational biology and geometry treat it as a foundation. If it falls, many hardness results built on it fall too, and better algorithms could become possible.
The second manuscript tackles Sogge’s local smoothing conjecture, which concerns how solutions to the wave equation behave. OpenAI claims the conjecture now holds in every spatial dimension. Human mathematicians have settled it only in limited cases, including a celebrated 2020 proof for two spatial dimensions, so a result for all dimensions would be a major leap.
The physics claim is the most ambitious and the least visible. It involves a rigorous construction of interacting quantum field theories with gauge fields and fermions in four dimensions. Building such theories with full mathematical rigour is an open problem closely tied to the Yang-Mills question, one of the Clay Millennium Prize problems. Nothing has been published yet. OpenAI has handed control of the release to an outside group of physicists.
That points to the most interesting part of the announcement, which is how OpenAI is handling it. The math manuscripts are on GitHub for anyone to examine. The computer science output is public too, with an expert group writing its own explanations, and that group includes the researchers who originally proposed ETH. The company says it won’t seek academic credit for the discoveries. Credit goes to the people producing the write-ups, and they’re also responsible for making sure the AI output properly credits the prior work and techniques it drew on.
It’s a smart move for credibility, because claims this large will face intense scrutiny. Disproving a conjecture the field has relied on for 25 years is the kind of result where one flawed step can sink the whole thing. None of this has passed peer review yet. Whether these results change their fields or end up as cautionary tales will be decided over the coming months, as outside mathematicians check the proofs line by line.
