AI and Mathematicians Clash Over Navier-Stokes Problem

Tristan Buckmaster, a mathematician at New York University, has been working with Levent Alpöge on the Navier-Stokes equations. The pair finds themselves at odds with OpenAI, which claims to have solved these longstanding mathematical questions.

OpenAI announced that its AI model tackled one of the most challenging math problems, stating a goal to advance research for humanity’s benefit. However, the mathematical community has yet to gain substantial insights from this solution, despite the technical accuracy of OpenAI’s 166-page document.

James Maynard from the University of Oxford remarked that the AI-produced paper is difficult for humans to comprehend. Javier Gómez-Serrano from Brown University believes the proof could enhance the field with significant rewriting. Yet, as it stands, the paper provides little educational value.

AI’s recent surge in mathematical potential is noted, with language models beginning to produce genuine results. Despite this, few view OpenAI’s announcement as indicative of successful collaboration between AI and mathematicians.

The Navier-Stokes problem is famed for its complexity, relevant across physics and engineering. Understanding these equations better could improve models of fluid dynamics and aircraft lift. Researchers have been identifying scenarios where these equations break down, forming part of the Millennium Prize Problems with a $1 million reward.

“Among the seven Millennium Problems, everyone agreed Navier-Stokes would be next to be solved,” said Martin Hairer from EPFL, signing a statement of opposition to current AI-math collaborations.

Buckmaster and Alpöge, nearing a solution themselves, were surprised by OpenAI’s move. OpenAI amassed 10,000 AI agents, working extensively to tackle the Navier-Stokes issue. The solution’s complexity involves hundreds of billions of computational tokens, with significant financial cost implications.

Controversy arose when Buckmaster revealed OpenAI’s approach to exclude Alpöge from their paper. OpenAI denies using ideas from Buckmaster and Alpöge, but suspicions linger about their awareness of the solution pathway.

Mathematicians critique OpenAI’s documentation as practically unreadable. Buckmaster himself hurriedly published AI-influenced findings in response, unsatisfied with their clarity. The document’s Lean formalization, a tool for verifying mathematical proofs, confirmed its correctness, supporting its technical soundness.

Despite the correctness, the episode highlights the gap between solution finding and genuine understanding. Maynard emphasizes that explaining solutions remains crucial to the discipline of mathematics.