Clay Mathematics Institute on the Navier-Stokes Problem

Recorded: Sept. 12, 2026, 5:09 a.m.

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Navier-Stokes Announcement - Clay Mathematics Institute

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Home — News — Navier-Stokes Announcement

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

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The Clay Mathematics Institute announced the status of the Millennium Prize Problems, which were introduced in 2000 to celebrate the universality of mathematical thought. These problems were designed to represent some of the most difficult challenges mathematicians faced at the turn of the millennium and serve the threefold purpose of raising public awareness about the open frontiers of mathematics, emphasizing the value of pursuing solutions to the deepest problems, and recognizing significant mathematical achievements. These challenges are presented not as arbitrary puzzles but as fundamental questions that demand novel structures and methods, driving the continuous effort to deepen the understanding of mathematics and the universe it describes.

The Millennium Problem concerning the motion of fluids is specifically highlighted as one of these significant challenges. This problem centers on determining the existence and smoothness of solutions for the Navier-Stokes equations within three-dimensional Euclidean space. There is a growing sense of anticipation within the mathematical community that progress in related fields, often recognized by the Clay Research Award, and advancements in mathematical research technologies suggest that this problem may soon be resolved. The Clay Mathematics Institute remains dedicated to advancing the beauty, power, and universality of mathematical thought, and curating the Millennium Prize Problems is a crucial aspect of this mission, with established rules governing the evaluation and recognition of progress.

Beyond the specific problem announcement, the institution actively engages in recognizing mathematical achievement through various awards and news updates. Recent announcements include honors extended to former Clay Research Fellows, such as the 2026 Fields Medals and the 2026 Frontiers of Science Prizes, and recognition for significant contributions to fields like geometric measure theory, as exemplified by the 2026 Maryam Mirzakhani New Frontiers Prize awarded to Anna Skorobogatova for her work in finding surfaces of minimal area. Furthermore, the Clay Mathematics Institute recognizes ongoing contributions through the distribution of the 2026 Clay Research Awards to various mathematicians.