The Millennium Prize Problems are seven of the most famous open problems in mathematics, selected by the Clay Mathematics Institute at the beginning of the millennium. A prize of one million dollars was offered for the solution of each problem.

For more than twenty years, only one had been solved: the Poincaré Conjecture, proved by Grigori Perelman in 2003.

Then, on September 8, 2026, OpenAI announced a proposed solution to the Navier–Stokes Millennium Problem, obtained by an internal AI system involving thousands of agents working for 88 hours.

What actually happened? What is the Navier–Stokes problem, what has been proved, and what does the result mean for mathematics?

This mini workshop will discuss these questions with two leading experts in the field:

Michele Coti Zelati — Imperial College London 
Diego Córdoba — ICMAT, Madrid

The event will consist of two talks.

The first talk will be aimed at a broad audience and will introduce the Navier–Stokes Millennium Problem, its mathematical significance, and the recent developments. No specialized background in fluid dynamics will be assumed. Students and researchers from all fields are warmly encouraged to attend. 

The second talk will be a colloquium-style seminar, focusing more closely on the mathematics of the blow-up problem and the recent solution.

ABSTRACTS

Michele Coti Zelati.
The motion of water and air is part of everyday experience, but understanding it mathematically has led to some of the deepest questions in analysis. This lecture will introduce the equations of fluid motion through their historical development, from Euler’s description of ideal fluids to the Navier–Stokes equations and the Millennium Prize Problem. I will explain the physical ideas behind these equations, what it means for a solution to develop a singularity, and why deciding whether this can happen has proved so difficult. This perspective will help place the recent announcement in context and clarify its significance for mathematics and our understanding of fluid motion. 

The talk is aimed at a broad audience, and no background in fluid dynamics will be assumed.

Diego Córdoba. 
"Vortex Cascades and Singularity Formation in Incompressible Fluids"
Can an initially regular fluid flow destroy its own regularity in finite time? In this colloquium, I will discuss this question for classical solutions of incompressible fluid equations, focusing on singularities that arise within regimes of local existence and uniqueness. The central idea is a cascade of interacting vortex layers: each layer generates a flow that amplifies the next at a smaller spatial scale. By arranging these interactions over progressively shorter time intervals, the cascade can produce unbounded growth of vorticity in finite time. I will explain how this mechanism has led to singularity constructions for the three-dimensional Euler equations and related incompressible fluid models. I will also describe how the construction can accommodate dissipation, despite its tendency to suppress the growth. Finally, I will place these constructions in the context of recent advances on AI- assisted on Euler and Navier–Stokes.

Funded by the European Union. This work is supported by ERC grant n. 101219635 - MIND - ERC-2025-STG

For further information please contact elisur.magrini@unibocconi.it