OpenAI claims AI proofs in maths, computer science and physics

OpenAI has announced three new results it says were generated by its AI models, spanning mathematics, computer science and physics. The company is asking outside experts to examine and explain them rather than simply declaring victory. None of the claims has yet been independently confirmed.

What OpenAI says it found

The announcement comes just weeks after OpenAI released manuscripts with over 700 pages of solutions and progress for 372 major maths problems ^[1]. This time there are two new manuscripts on GitHub. One establishes Sogge's local smoothing for waves in every spatial dimension, a conjecture about how solutions to the wave equation behave ^[1]. According to The Verge, OpenAI says this also resolves the Kakeya conjecture and Stein's restriction conjecture in all dimensions ^[2].

The second is the headline claim: a proof that the Exponential Time Hypothesis (ETH) is false. ETH is an assumption in computer science that some problems are simply too hard to solve quickly, and it is widely believed to be true ^[1]. OpenAI says it has been the basis of hundreds of papers across fields including databases, computational biology and geometry ^[1]. If it really is false, Engadget notes, we could in theory find more efficient algorithms for problems in those fields ^[1].

The third result, in physics, is described as a mathematically rigorous existence proof of certain interacting quantum field theories in four dimensions, including quantum chromodynamics ^[2]. The physics materials have not been released in full ^[2].

A different way of releasing results

What stands out is the process. OpenAI formed groups of external experts it calls "shepherds". The computer science group includes Russell Impagliazzo and Ramamohan Paturi, who were part of the team that originally proposed ETH, and MIT professor Ryan Williams ^[2]. For physics, OpenAI says David Gross will lead a group that includes Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov ^[2].

OpenAI also says it will not seek academic credit for its models' discoveries. The people in each group get credit for the write-ups they produce, and are responsible for making sure the results credit the researchers and ideas the models drew on ^[1].

The approach is already contested. The Verge reports that an advisory panel of mathematicians OpenAI assembled said a day earlier that it recommends AI companies do not adopt the practice of giving selected people early access, citing unequal access, borrowed reputation and biased selection ^[2]. The panel suggested releasing results on scholarly repositories with formally checked proofs and funding for those working to understand them ^[2].

Why it matters for business

For non-specialists, the point is that AI labs are now publishing claims that human experts will need time to check. A claim of this kind is not a result until independent specialists have verified it, so treat headlines accordingly.

If the ETH result stands, it could eventually influence how software is designed for hard optimisation problems, though the sources do not say when or whether that would reach products. For businesses relying on AI for research or analysis, the lesson is about verification: the more impressive the output, the more it needs a qualified human to check it.

OpenAI has also published an open letter asking the research community three questions: what rules should govern early access to AI-generated results, how credit should be shared between discoverers and checkers, and how to support students and researchers as methods change ^[2].

Source: Engadget — OpenAI announces new discoveries in mathematics, computer science and physics