As of: 2026-10-12 22:30 CEST.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code). Human editor: Adam Bicz.
Canonical page: https://postcutoff.com/v/numberphile2-navier-stokes-solved-by-ai-extra/

# Navier-Stokes solved by AI (extra) - Numberphile

Numberphile2, 18 September 2026, YouTube. 92,928 views as of 12 October 2026.
Kind: Review.
Watch: https://www.youtube.com/watch?v=aom4269UgSM

## Why it is here

Extra footage for Numberphile's Navier–Stokes video (Tony Padilla).

## Description (written by Gemini from the video)

**Summary**  
Physicist Tony Padilla discusses with interviewer Brady Haran the implications of artificial intelligence claiming solutions to fundamental mathematics and physics problems, specifically addressing OpenAI's work on the Navier–Stokes existence and smoothness problem. Padilla argues that automated proofs risk bypassing the mathematical "journey" that traditionally spurs new conceptual breakthroughs, while analyzing the physical plausibility of the proposed finite-time blow-up vortex solutions.

**What is shown**  
* [00:00] Title card reading "Further discussion with Tony Padilla about AI cracking the Navier-Stokes problem."
* [00:07] Tony Padilla seated in his university office discussing the role of AI in mathematics and theoretical physics.
* [01:35] Handwritten notes and diagrams on large butcher paper across Padilla's desk detailing fluid dynamics and Navier–Stokes equations.
* [09:20] A diagram credited to OpenAI depicting a complex fluid vortex structure labeled with "inward spiral" and "axial stretching" illustrating the blow-up vortex mechanism.
* [10:40] End credit cards noting support by Jane Street, featuring Tony Padilla and video by Brady Haran.

**Claims & numbers**  
* Tony Padilla states that the journey of solving difficult problems is what drives mathematical discovery, citing Ramanujan's investigations of Fermat's Last Theorem, which led to developments in elliptic curves that are now applied in string compactifications [00:52].
* Tony Padilla notes that Terence Tao recently wrote a blog post arguing that AI tools must be applied in ways that are genuinely useful, interpretable, and verifiable for the mathematical community [05:37].
* Tony Padilla mentions that he actively uses AI in his own research ("I'm using it like crazy at the moment") [07:34].
* Tony Padilla claims that the finely tuned "wild core" blow-up vortices generated in the OpenAI Navier–Stokes construction would physically collapse and smooth out (similar to Leray smoothing) if disturbed by macroscopic matter such as a person entering the fluid [09:26].

**Notable quotes**  
* [00:36] "The journey to solving them is the important thing, because that journey can take you in so many directions."
* [05:52] "What's the point in an AI proof that no mathematician can understand? There is no point in that. What's the point in an AI proof that no mathematician can verify?"
* [06:14] "If you're now building new mathematics based on mathematics you don't understand because you were handed to it by an AI, then that's a weak foundation."

**Assessment**  
This is an informal academic discussion and commentary video exploring the philosophical and practical impact of AI-assisted mathematical proofs following OpenAI's Navier–Stokes announcement. No interactive software demos or real-time model executions are run on camera; the video consists of Padilla analyzing the methodology, physical interpretations, and institutional implications of the published findings.

_Described by gemini-3.8-flash on 2026-10-12 from the video's audio and frames._

## Related

- 2026-09-08: [OpenAI claims a Millennium Prize problem](https://postcutoff.com/e/2026-09-08-openai-navier-stokes-blowup/)

## People in it

- [Terence Tao](https://postcutoff.com/person/terence-tao/), Professor of mathematics, UCLA