What's going on with OpenAI and the Navier-Stokes controversy?

Artificial intelligence has solved a major mathematics problem, but credit for the accomplishment is murky.

OpenAI announced today that it has found a solution to the Navier-Stokes problem, one of the longest-standing puzzles in mathematics. It's a major accomplishment, but the news has been marred by a debate over whether the company acted based on unpublished research from other parties. Additionally, OpenAI has been accused of attempting to influence who will receive credit for the achievement in publication.

First, some background. The Millennium Prize Problems are a group of seven complex questions established by the Clay Mathematics Institute in 2000. The organization is offering a reward of $1 million for solutions to each of these questions, all of which have stymied mathematicians for decades, if not centuries. Since the prize's creation, only one of the other problems from the collection had previously been solved.

The Navier-Stokes problem centers on fluid dynamics, the rules for analyzing the behavior of both liquids and gasses. The angle that had been posed to mathematicians, in extreme layperson terms, is whether there are any edge cases where the original set of Navier-Stokes equations lead to results that cannot happen in reality.

Having a solution to a second Millennium Prize Problem is a massive accomplishment when it comes to applying artificial intelligence and large language models to solving some of the most perplexing quandaries in mathematics. However, the use of tools made by rival AI businesses in developing those solutions has created friction in the field regarding who gets to claim responsibility for the work and how.

Tristan Buckmaster, a mathematician at New York University, and Levent Alpöge, a researcher employed at Anthropic but working in a personal capacity, had been developing their own solution and made use of multiple different LLMs in their efforts, including Anthropic Claude, OpenAI's Codex tool and its Astra frontier model . According to a statement by Buckmaster, OpenAI may have doubled down on its efforts regarding Navier-Stokes after learning that a team including rival Anthropic was close to a solution. He questioned whether OpenAI had leveraged the work he and his colleague had done with Codex to obtain its own breakthrough.

"I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer," the statement reads.

Buckmaster then said he spoke with Sebastien Bubeck, a mathematician and AI researcher at OpenAI, and another unnamed party and was offered two options for claiming credit for the work. One was to publish a partial development, with OpenAI to publish its Navier-Stokes solution the following day. The other was to write a solo paper that credited the use of an OpenAI LLM in the Navier-Stokes solution without the inclusion of Alpöge's name. Buckmaster said he declined both proposals.