EMS statement on Navier–Stokes announcement
The European Mathematical Society reflects on OpenAI’s recent announcement to the Navier–Stokes Millennium Prize Problem, its potential significance for mathematics, and the questions it raises about human–AI collaboration, authorship, credit, and open access to research tools.
The announcement of the solution by OpenAI to the Navier-Stokes millennium problem is a milestone in the history of mathematics. This is not only because a major open problem may finally have been resolved. It is also because of the manner in which the paper evolved. It is authored by OpenAI but acknowledges that it is the output of mathematicians and AI models working together. It is important to understand that this solution does not come out of a vacuum but follows a strategy closely related to that suggested by mathematicians Diego Córdoba, Luis Martínez-Zoroa, and Fan Zheng (references [6-8] in the OpenAI paper). Progress had also recently been made by mathematicians Levent Alpöge from Anthropic and Tristan Buckmaster from NYU. This of course in turn relied on decades-long progress by mathematicians across the world.
That OpenAI stood on the shoulders of giants is unquestionable, but the speed with which their team of mathematicians and machines arrived at their solution is remarkable. Questions of authorship and credit in the new world of mathematics produced by human-machine interaction will need to be resolved. One worrisome aspect is the fact that the model used in this current situation is internal to OpenAI and not generally accessible. In the spirit of open science and equal opportunities in science this is a major problem that the mathematical community needs to address. But, without dismissing any of these difficulties, at this moment we join in admiration and celebration of this achievement.
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