Navier-Stokes – Tristan Buckmaster [pdf] (cims.nyu.edu)

Tristan Buckmaster and Levent Alpoge have publicly shared significant results concerning finite-time blowup solutions for key equations in fluid dynamics, specifically the incompressible Navier-Stokes equations and others. Their work builds on the foundational ideas of Diego Córdoba and Luis Martínez-Zoroa, but introduces the use of Large Language Models (LLMs) to enhance and generate proofs with smooth forcing. This collaboration culminates in results for the Boussinesq equations and suggests a potential path toward understanding unforced Euler equations, highlighting a noteworthy intersection of advanced mathematics and AI technology. The implications of this development resonate deeply within the AI/ML community, as it exemplifies how LLMs, like OpenAI's models, can expedite complex mathematical work, potentially reshaping educational methodologies around mathematics. Buckmaster’s commentary on the quality and presentation of the proofs underscores a crucial point about the responsibility of researchers to maintain clarity and rigor, even when leveraging AI tools. This scenario is reminiscent of iconic moments in the history of technology, raising questions about authorship, credit, and the evolving role of AI in academic scholarship, marking this as a pivotal moment for future interactions between mathematics and artificial intelligence.