The Moment AI Changed Mathematics Forever | World Science Festival

Summary
In this World Science Festival interview, physicist Brian Greene speaks with NYU Courant Institute mathematics professor Tristan Buckmaster about the landmark use of AI systems to tackle Millennium Prize fluid dynamics equations (Navier–Stokes and Euler). Buckmaster describes how multi-agent LLM harnesses, computer-assisted proofs, and formal verification in Lean produced correct mathematical proofs in an unreadable, non-human language, and recounts the high-stakes August–September 2026 rivalry between Anthropic and OpenAI over claiming a singularity blow-up solution.

What is shown

• [00:48] Host Brian Greene introduces the debate over AI creativity, benchmarks (such as solving the 2025 International Math Olympiad), and the Clay Millennium Prize problems.
• [06:24] Discussion of AI’s expanding role in mathematics, framed by Buckmaster as a “Deep Blue vs. Kasparov moment” for the discipline.
• [14:42] Explanation of the Euler and Navier–Stokes equations, fluid turbulence, partial differential equations, and the question of whether smooth solutions develop finite-time singularities (blow-up).
• [22:45] Historical overview of weak solutions, from Jean Leray’s 1930s Leray–Hopf solutions to Buckmaster and Vlad Vicol’s 2017 non-uniqueness (“nightmare”) solutions.
• [30:15] Review of computer-assisted proofs, error bounds below $10^{-13}$, and Hou et al.’s numerical blow-up results within a cylindrical boundary.
• [40:05] Account of Buckmaster supervising undergraduate work on Antarctic ice sheet dynamics and using neural networks as search mechanisms for singularity configurations.
• [50:02] Analysis of smooth forcing versus unforced equations, Boussinesq models, and the Córdoba–Martínez-Zoroa work on the incompressible porous media equation.
• [56:37] Description of multi-agent swarms orchestrated by LLMs producing proofs that Lean verified, despite reading like gibberish to human mathematicians.
• [68:50] Retrospective account of the corporate race and information leaks between Anthropic and OpenAI in late summer 2026, including OpenAI claiming an Euler/Navier–Stokes singularity solution.
• [82:00] Deliberation on how AI tools are reshaping the future role, training, and value system of human research mathematicians.

Claims & numbers

• Greene states that AI systems solved problems from the International Mathematical Olympiad in summer 2025 [02:18].
• Greene notes that the Clay Mathematics Institute established a $1 million prize for each of seven Millennium Prize problems, of which only one had been solved over the preceding quarter-century [03:04].
• Greene reports that in August 2026, a solution concerning Navier–Stokes/Euler blow-up was announced with AI as a primary author [04:02].
• Buckmaster states that rigorous interval-arithmetic computer-assisted proofs require demonstrating calculation errors are strictly bounded below $10^{-13}$ [30:33].
• Buckmaster explains that converting a standard 3-page human paper into a formal Lean proof can result in roughly 10,000 lines of code [61:36].
• Buckmaster notes that an early leak suggested Anthropic had solved two Millennium Prize problems [69:09].
• Buckmaster asserts that while experts believed resolving Navier–Stokes singularities remained 5 to 10 years away, major breakthroughs occurred within a little over a month due to massive AI compute and agent swarms [82:35, 82:45].

Notable quotes

• “It was the worst mathematics I’ve ever seen in my life, but it was actually correct.” — Tristan Buckmaster [00:06 / 60:42]
• “If I used Gemini or ChatGPT or Claude, they could all understand this complete nonsense, yet a human wouldn’t view it as actual English.” — Tristan Buckmaster [22:27]
• “I think the math of today is not the same as the math of tomorrow.” — Tristan Buckmaster [82:53]

Assessment
This is an authentic, professionally produced long-form interview by the World Science Festival. No direct software demonstrations, code runs, or screen captures are shown; the content consists entirely of personal retrospective testimony and conceptual analysis by one of the researchers involved.

Described by gemini-3.8-flash on 2026-10-08 from the video’s audio and frames.