OpenAI says an internal model resolved Navier-Stokes, but has published no proof
OpenAI says an internal model it began training on August 28 has resolved the Navier-Stokes Millennium Prize problem, and more than 100 other long-standing open problems across most areas of mathematics. OpenAI has published no proof, no paper, no list of those problems and no outside verification, so the whole claim rests on the company's word.
OpenAI's cover image for its September 21 post on the new mathematics advisory group. Image: OpenAI
The claim arrived on September 21, in a post announcing that OpenAI is working with mathematicians who have set up an independent advisory group. OpenAI does not name the model, and it does not say that anyone outside the company has checked the results.
OpenAI names no model and shows no working
"The pace of its progress in mathematics has surprised the mathematicians within OpenAI," the company writes. It describes the system only as "a new internal model", gives it no name, and does not say whether it is related to anything you can use in ChatGPT today.
Navier-Stokes is one of seven problems the Clay Mathematics Institute announced in Paris on May 24, 2000, each carrying a $1 million prize. The equations describe how fluids move, from the waves behind a boat to the turbulent air around a jet, and Clay's own description of the problem says our understanding of them "remains minimal".
A Millennium Prize claim normally arrives as a manuscript that other mathematicians can attack for months or years. OpenAI has released nothing of the kind, so nobody outside the company can say what its model resolved, how, or how much of it holds up.
Clay has awarded nothing, and its own rules take years
The Clay Mathematics Institute published its own statement on the problem on September 11, ten days before OpenAI's post. Clay says it "shares in the excitement of the global mathematical community as we contemplate the announcement that the Navier-Stokes problem has apparently been settled", and that it hopes "to see waves of new human understanding unleashed as the innovations behind this work are analysed and interrogated".
That statement names nobody and mentions no company, and OpenAI's post does not mention Clay. What Clay does say is that its rules cover "the process for evaluating what has been achieved and for assigning credit", and that the process is "deliberately unhurried".
Those rules set three conditions before Clay will even consider a proposed solution: it must be published in a qualifying outlet, at least two years must have passed since publication, and it must have received general acceptance in the global mathematics community. Nothing OpenAI describes has been published anywhere, so the two-year clock has not started.
Nine mathematicians will advise, and none of them is paid
The Advisory Group on Mathematics and Artificial Intelligence is hosted at the Institute for Advanced Study, and OpenAI lists nine initial members: François Charles (ENS-PSL), Camillo De Lellis (IAS, GSSI), Timothy Gowers (Collège de France, Cambridge), Martin Hairer (EPFL, Imperial College London), Nikhil Srivastava (Berkeley, Simons Institute), Ulrike Tillmann (Oxford, INI), Ravi Vakil (Stanford), Edward Witten (IAS) and Melanie Matchett Wood (Harvard).
Gowers gave one of the three lectures at the Paris meeting where the Millennium Prizes were announced in 2000. He is now on a group whose job includes helping OpenAI assess how significant its own results are.
OpenAI says the group will operate independently, that its members "will not be paid by OpenAI", that it can change its own membership, and that it is free to "offer advice we have not requested" and publish that advice. One limit is written into the remit: the group "will not be responsible for advising us on how to pace our internal progress on mathematics".
OpenAI is answering an open letter from mathematicians
OpenAI points to a recent open letter, "A Severe Misalignment of AI in Mathematics", in which mathematicians raise concerns about the negative externalities of solving open problems as a benchmark for new AI systems. The advisory group is OpenAI's answer, and the company calls it "a first step".
The remit covers reviewing and communicating emerging results, coordinating how they are shared, academic and professional standards, and how OpenAI's tools can support mathematical research and learning.
OpenAI has been making large claims all month. On September 19 we reported its statement that GPT-6 Astra cracked a 1941 Enigma message that had resisted solution since 2005, and the same week it published its first reports of models inventing data and using a leaked API key in testing.
A Millennium Prize problem is a long way above an Enigma message. Until OpenAI publishes something mathematicians can read, the only part of its announcement anyone outside the company can check is the membership list.
