Navier-Stokes Announcement
Date: 11 September 2026
The Millennium Prize Problems were unveiled by the Clay Mathematics Institute (CMI) at a meeting in Paris in 2000 to celebrate “The Universality of Mathematical Thought”.
These problems encapsulate some of the most difficult challenges that mathematicians were grappling with at the turn of the millennium. CMI’s purpose in articulating these problems and attaching a $1M prize to each of them was threefold: to elevate in the consciousness of the general public the fact that in mathematics the frontier is open, close at hand, and abounds with important unsolved problems; to emphasize the abiding value of working towards a solution of the deepest, most difficult problems; and to recognize achievements in mathematics of historic magnitude.
Each of the Millennium Prize Problems concerns a classical question of compelling origin that had defied all attempts to resolve it over many years. These are not arbitrary puzzles akin to fiendish crosswords. Rather, they are fundamental challenges that mark the frontier of human knowledge and challenge us to develop new structures and methods. They provide foci for the continuing struggle, across generations and cultures, to deepen our human understanding of mathematics and the universe that it describes. The deep innovations that are required to make significant progress on these problems open new vistas of possibility that typically reach far beyond the domain of the problem.
The Millennium Problem concerning the motion of fluids has all these attributes. The problem asks about the existence and smoothness of Navier-Stokes solutions in 3-dimensional Euclidean space. In recent years there has been an increasing sense of anticipation as breakthroughs in the surrounding field (some recognised by the Clay Research Award) have raised hopes that the Navier-Stokes problem might soon be resolved. The increasing ability of new technologies to accelerate mathematical research has heightened this sense of anticipation.
Today, CMI shares in the excitement of the global mathematical community as we contemplate the announcement that the Navier-Stokes problem has apparently been settled. We hope to see waves of new human understanding unleashed as the innovations behind this work are analysed and interrogated.
The Clay Mathematics Institute is dedicated to furthering the beauty, power and universality of mathematical thought. Curating the Millennium Prize Problems is one of the most important ways in which it pursues this goal. The rules governing the prizes describe the process for evaluating what has been achieved and for assigning credit. The process is deliberately unhurried, but we will provide updates.
The Clay Mathematics Institute
September 11, 2026
Image: Wikimedia Commons, C. Fukushima and J. Westerweel, Technical University of Delft, The Netherlands
