AI will not make mathematicians obsolete
8 hours ago
- OpenAI's unreleased model solved a weaker version of the Navier–Stokes problem, the second Clay Millennium Prize Problem ever resolved and the first by a machine.
- The machine demonstrated that an artificial external force can drive a fluid from rest to a finite-time breakdown, where speed becomes infinite, satisfying a criterion in the official problem formulation.
- The original problem's formulation is seen as a mistake, because the machine's result does not address the real, unforced equations, and the belief that unforced fluids flow smoothly forever is likely wrong.
- Extreme solutions may exist but be so unstable that experiments and computations cannot detect them, suggesting a refined conjecture about smooth flow for all but exceptional states.
- AI achievements in mathematics typically produce specific, complex examples through human-guided but exhaustive searches, rather than proving broad theorems.
- Young mathematicians fear AI will make them obsolete, but the author argues they are categorically still needed for choosing important questions and defining what answers look like.
- AI is a triumph of mathematics itself, built on linear algebra, calculus, and probability, and the extinction of human mathematics is not among AI's risks.
- Formulating profound, solvable questions remains a distinctly human strength, even if AI dominates solution-finding.
- The author cautions against underestimating AI's future capabilities, given rapid progress on one-year timescales.