The Controversy Behind AI Solving A Million Dollar Math Problem

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Summary
Jade Tan-Holmes of the YouTube channel Up and Atom breaks down OpenAI's September 2026 announcement that an internal multi-agent system solved a version of the Navier–Stokes Millennium Prize problem. She explains the underlying mathematics of fluid singularity formation and delves into the controversy and priority dispute between OpenAI and mathematicians Tristan Buckmaster and Levent Alpoge.

What is shown

• [00:00] Display of OpenAI's social media post on X announcing a solution to the Navier–Stokes Millennium Prize problem.
• [01:22] Mathematical animations explaining the Navier–Stokes equation, terms (advection, pressure, viscosity, external force), fluid smoothness, vortex stretching, and finite-time blowup/singularities.
• [03:51] OpenAI’s official research announcement page showing details of the proof and Lean formalization.
• [04:07] Visualizations and 3D simulations of the blowup vortex solution (inward spiral and axial stretching).
• [04:25] Excerpts from OpenAI's blog describing the 10,000 coordinating agents and compute resources used.
• [05:20] Statements and social media posts from Tristan Buckmaster (Courant/NYU) and Levent Alpoge (Anthropic) alleging data leakage and priority issues.
• [06:00] Excerpts of responses on X from OpenAI leadership, including Sam Altman and Sebastien Bubeck.

Claims & numbers

• OpenAI announced on Tuesday, September 8, 2026, that an internal next-generation model system significantly more capable than GPT-6 Astra resolved the Navier–Stokes Millennium Prize problem (statement C/D, forced blowup in finite time).
• The system utilized an ensemble on the order of 10,000 concurrent agents, sending 2.7 million messages and generating approximately 130 billion output tokens to solve the Navier–Stokes problem (out of 4.9 million messages and ~300 billion output tokens across all attempted problems).
• The proof was obtained ~88 hours after launch (Saturday, September 5), with Lean formalization and verification taking an additional 17 hours via GPT-6 Astra.
• The presenter notes that with GPT-6 Astra priced at $50 per million output tokens on the OpenAI API, 130 billion tokens would equate to roughly $6.5 to $7 million in output compute alone.
• Tristan Buckmaster and Levent Alpoge had been working on a related blowup proof for the hypodissipative Navier–Stokes and Euler equations using Anthropic and OpenAI tools (Codex).
• OpenAI stated they do not intend to claim the Clay Mathematics Institute's $1 million Millennium Prize.

Notable quotes

• [00:09] "This is a really big deal, like a monumental moment in mathematics."
• [03:30] "The Navier–Stokes problem is: can an initially smooth fluid develop a singularity in a finite time?"
• [05:07] "So that's about $7 million just in output tokens if we were using Astra, and they were using an internal model more powerful than Astra."

Assessment
This is an independent educational and analytical review video examining public claims, technical statements, and social media exchanges. No live technical benchmarks or code executions were performed on screen; all depictions rely on OpenAI's published announcements, third-party visualizations, and public correspondence from the involved researchers.

Described by gemini-3.8-flash on 2026-10-07 from the video's audio and frames.