Academia on the Line is a podcast where two mathematicians talk with academics about mathematics, STEM, and higher education.

Episode Summary:
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

Links to Referenced 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.

Theme Music:
Ophelia's Blues by Jason Shaw (Audionautix.com), licensed under Creative Commons.

Academia on the Line is a podcast where two mathematicians talk with academics about mathematics, STEM, and higher education.

Episode Summary:
OpenAI's recent disproof of Erdős' unit distance conjecture surprised much of the mathematics community and prompted many researchers to reconsider the capabilities of modern reasoning models. In our inaugural episode, Melanie Matchett Wood and Daniel Litt join us to discuss the mathematics behind the result, the nine-author companion paper written by leading mathematicians, and the broader implications of AI for mathematical research and graduate education.

Podcast timeline
0:00 - Introduction
4:12 - Guests: Melanie Matchett Wood & Daniel Litt
16:51 - The Unit Distance Problem
25:15 - OpenAI's Disproof
58:41 - Do We Still Need Professional Mathematicians?
1:12:02 - AI and the Future of Research
1:19:47 - Human Understanding and Education
1:32:06 - Funding AI in Mathematics
1:45:34 - Final Thoughts

Links to Referenced Materials
0. OpenAI's announcement on May 20, 2026.
1. OpenAI's research paper with the disproof of Erdös' unit distance conjecture.
2. The nine author companion paper.
3. Twitter source for the projected lattice image that Daniel mentions in the episode.
4. Find your Erdős-number, or collaboration distance more generally.

Theme Music:
Ophelia's Blues by Jason Shaw (Audionautix.com), licensed under Creative Commons.