Episode 2: Navier-Stokes and that crazy week in mathematics
Guest: Javier Gómez-Serrano
Listen to Episode 2.
Listen to Episode 2 on YouTube.
This interview was recorded on September 14, 2026.
Podcast release date: September 22, 2026.
See more episodes at academiaontheline.com.
Podcast abstract
Two weeks ago, on Labor Day, NYU mathematician Tristan Buckmaster posted three preprints and a statement detailing
some troubling interactions with OpenAI and a need to rush to get his results out with collaborator
Levent Alpöge (who works for Anthropic). The next day, OpenAI announced a solution to the Navier-Stokes Millennium
prize problem. The previous week, they had announced a substantial improvement on bounded gaps between primes,
a problem related to the famous twin prime conjecture. Both results (and some others over the summer) came on the heels
of breakthrough progress by mathematicians in the field. In this episode, we discuss this crazy week in mathematics
and take a deeper dive into the Navier-Stokes news. Our guest, Javier Gómez-Serrano, is a mathematician at
Brown University who is a leading expert on Navier-Stokes and AI-assisted mathematics.
Podcast timeline
00:00 Introduction
02:15 Progress on bounded gaps between primes
06:42 Navier-Stokes bombshell news
14:50 Additional questions on the Jacobian conjecture and non-sofic groups results
24:00 Guest Javier Gómez-Serrano comes on the line
28:30 AlphaEvolve and first LLMs
36:00 Javier's collaboration with DeepMind on Navier-Stokes
39:00 When did the community start to believe there would be blow-up solutions?
43:42 Statement of the Millennium problem, Euler vs. Navier-Stokes, 2d vs. 3d, forced vs. unforced, etc.
54:28 How should we think about the OpenAI solutions?
58:00 How do the OpenAI results relate to prior work by mathematicians?
1:02:30 How original are the OpenAI solutions?
1:04:40 Why was OpenAI able to find unforced blow-up in the Euler case but not in Navier-Stokes?
1:07:08 Where does the field go from here?
1:09:40 What do you think of the 25 Fields medalists' misalignment letter?
1:14:00 What would you like AI companies to do to be more helpful to the math community?
1:22:22 What are you recommending to math students as far as using AI?
1:27:45 Credits
Theme Music:
Ophelia's Blues by Jason Shaw (Audionautix.com), licensed under Creative Commons.
Related materials
1. Julia Stadlmann's preprint on bounded gaps between primes.
2. Tristan Buckmaster's statement on September 7, 2026.
(See also here.)
3. OpenAI's Navier-Stokes announcement
on September 8, 2026.
Note: this has been edited since September 8. The original announcement
contained the line: "While unlikely, we cannot rule out that de-identified data derived from their usage of our products
helped improve our models." (Referring to work by Tristan Buckmaster and Levent Alpöge.)
4. The new Jacobian conjecture paper (see pages 160-161 for statements about AI).
5. Andreas Thom's post on the non-sofic groups result: page 1,
page 2, and page 3.
6. Javier Gómez-Serrano's talk at Harvard on September 11, 2026.
7. Two slides from the Harvard talk: Javi's message to OpenAI and
the statement of the Navier-Stokes Millennium problem.
8. The 25 Fields medalists' "Severe Misalignment" open letter.
About our Guest
Javier Gómez-Serrano
is a professor of mathematics at Brown University. His research interests lie on the boundary between machine learning,
analysis, partial differential equations, fluid mechanics, spectral geometry, numerical computation and rigorous computer-assisted proofs.
Javier was recently awarded the Ramon E. Moore Prize, the MCA Prize, the Antonio Ambrosetti Medal, the Antonio Valle Prize,
the Vicent Caselles Prize, and the Princeton Junior Faculty Teaching award.