The Navier–Stokes Problem and the Agents

Gonzalo C. and Günther Klambauer on AI’s mathematical breakthroughs—and the human work still ahead.

Did OpenAI really solve the Navier–Stokes problem? In this episode, we ask mathematician Gonzalo Caolabora and AI professor Günther Klambauer what the proof means, why it has been difficult to verify, and whether large language models are discovering mathematics or combining ideas from existing research.

We also discuss why AI can excel at problems with verifiable answers, where today’s systems still struggle, and how AI could reshape mathematical research and careers. The big question: as proofs become more automated, what will mathematicians focus on next?

OpenAI

https://openai.com/

Navier–Stokes existence and smoothness

https://www.claymath.org/millennium/navier-stokes-equation/

Lean

https://lean-lang.org/

Terry Tao

https://www.math.ucla.edu/~tao/

EPFL

https://www.epfl.ch/

Johannes Kepler University Linz

https://www.jku.at/en/

Transformer

https://arxiv.org/abs/1706.03762