Why AI Will Not Make Mathematicians Obsolete

Summary

Sergiu Klainerman examines the claim that an unreleased OpenAI model solved the Navier–Stokes problem, one of the Clay Millennium Prize Problems. He explains that the result addressed a weaker, artificially forced version: the model found a smooth external force that drives a fluid initially at rest to a finite-time singularity, where its speed becomes infinite. Although this is technically substantial and fits a provision in Charlie Fefferman’s official formulation, it does not resolve the central question about whether smooth, unforced fluid flow can break down. Klainerman argues that the unforced problem is probably governed by a more nuanced statement: most smooth initial states may remain regular forever, while highly unstable exceptional solutions could exist. That conjecture remains unproved, and neither experiments nor numerical simulations have observed the extreme behavior in question. He places the achievement within a broader pattern in which AI searches through extraordinarily large spaces to produce difficult examples, usually after human mathematicians have identified the relevant structure and target. The article notes that the reported effort involved as many as 10,000 AI agents and millions of dollars in computing, but treats those resources as evidence of search power rather than independent mathematical judgment. Klainerman argues that deciding which questions matter, designing the right mathematical framework, and determining what would count as a meaningful answer remain human responsibilities. He concludes that AI is itself built on mathematics and may help establish deeper results, but current evidence does not suggest that mathematics as a human activity is nearing extinction.