Mathematicians worldwide have scratched their heads over the Navier-Stokes Millenium Prize Problem for 90 years; now, OpenAI’s agents claim to have solved it in 88 hours.
The Millenium Prize Problems are a set of seven difficult problems spanning Mathematics, released by the Clay Maths Institute to celebrate the year 2000. Each problem comes with a million-dollar reward for its solution, intended by the Institute to “emphasise the importance of working towards a solution of the deepest, most difficult problems.” On this list is “proving the existence and smoothness of Navier-Stokes,” a system of equations which describe how the pressure, density and temperature of a moving fluid are related. These equations form the foundation of modern fluid dynamics, and are used in a huge variety of scientific and technical disciplines; from modelling blood flow to the design of aircraft and cars.
However, despite many attempts, there has been no proof that these equations can ever ‘break down;’ beginning
from some valid initial conditions and ending with something physically impossible, like fluids reaching near-infinite speeds. That is, until 8 September this year, when OpenAI, the company behind ChatGPT, claimed to have found such a counterexample. This discovery left mathematicians everywhere reeling. It’s the first time AI agents have been used so heavily to solve a problem of such magnitude and importance before. OpenAI spent an estimated $15m setting 10,000 internal agents on the problem. However, it’s important to note that this result has not yet been verified by the independent mathematical community.
OpenAI’s proof sparked public discourse about possible plagiarism. New York University mathematician, Tristan Buckmaster, had been working on Navier-Stokes in secret alongside Anthropic mathematician Levent Alpöge. The pair had been using Codex, an OpenAI-developed tool, to store their work. Buckmaster claimed OpenAI could have trained their agents on his user data, before throwing immense computational power at the problem (essentially beating him to the punch) and refusing to credit him for any of his work. OpenAI quickly denied these claims, insisting that its solution differed “significantly”; however, they “cannot rule out that de-identified data derived from [Buckmaster’s] usage of our products helped improve our models.”
Responses from leading figures of the mathematical community are cautionary. 25 recipients of the Fields Medal – often called the Nobel Prize of Mathematics and the most prestigious award in the field – signed an open letter titled “A Severe Misalignment of AI in Mathematics,” warning that AI companies’ goals are “severely misaligned” with the mathematical community. The letter urges that AI poses a threat to intellectual discovery; how the pursuit of knowledge is not just important for its end goal, but for the process itself. As the letter puts it: “Solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight.” New questions and ideas in mathematics often arise from the slow, intentional study of problems. Such ideas often grow and develop into entire new areas of research, furthering our understanding of the natural world. But this entire process would not be possible without the natural curiosity of humans, and the creativity that is fostered while sitting with a problem for a long time. To this end, the highest honoured group of mathematicians called for meaningful discussions about the use of AI in intellectual work, in mathematics and beyond.
As the capabilities of AI continue to grow, we should ask ourselves: what does this mean for the future of academic research? Will AI be used as a powerful new tool, or could it irrevocably stifle the creative spirit of the next generation of academics?
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