The Clay Mathematics Institute (CMI) announced on September 11, 2026, that the Navier-Stokes Millennium Prize Problem has apparently been settled, according to a statement on the institute’s website.
The Millennium Prize Problems were unveiled by CMI at a meeting in Paris in 2000 to celebrate “The Universality of Mathematical Thought.” The institute established seven such problems, each carrying a $1 million prize, with three stated purposes: to elevate public awareness that mathematics has an open frontier with important unsolved problems; to emphasize the value of working toward solutions of deep, difficult problems; and to recognize historic mathematical achievements.
Each Millennium Problem concerns a classical question that had resisted resolution for many years. According to CMI, these are not arbitrary puzzles but fundamental challenges marking the frontier of human knowledge that require development of new structures and methods.
The Navier-Stokes problem specifically concerns the existence and smoothness of solutions to equations describing fluid motion in three-dimensional Euclidean space. CMI notes that the problem has “all these attributes” of a genuine frontier challenge with broad implications.
In recent years, according to CMI’s statement, there has been growing anticipation that the Navier-Stokes problem might be resolved. This optimism was fueled by breakthroughs in surrounding fields—some of which received Clay Research Awards—and by advances in computational technology that have accelerated mathematical research.
CMI stated: “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 institute emphasized that the rules governing the prizes describe a deliberate process for evaluating achievements and assigning credit. CMI indicated it will provide updates as evaluation proceeds, noting the process is “deliberately unhurried.”
Key facts
- The Clay Mathematics Institute announced the Navier-Stokes problem has apparently been settled
- The Navier-Stokes problem is one of seven Millennium Prize Problems, each with a $1 million prize
- The problems were unveiled in Paris in 2000 to celebrate mathematical thought
- The Navier-Stokes problem concerns existence and smoothness of fluid motion solutions in 3D space
- Recent breakthroughs in related fields raised hopes for resolution
- CMI will follow a deliberate evaluation process before formally assigning the prize