# Clay Institute says Navier-Stokes Millennium Prize problem apparently settled

_Thursday, September 10, 2026 at 8:00 PM EDT · Science · Latest · Tier 2 — Notable_

![Clay Institute says Navier-Stokes Millennium Prize problem apparently settled — Primary](https://www.claymath.org/wp-content/uploads/2026/09/False_color_image_of_the_far_field_of_a_submerged_turbulent_jet.jpg)

The Clay Mathematics Institute said on September 11 that the Navier-Stokes Millennium Prize problem has apparently been settled, while noting its prize rules require a deliberately unhurried evaluation process before credit is assigned.

The problem asks whether smooth solutions to the Navier-Stokes equations exist in three-dimensional Euclidean space. CMI said recent breakthroughs in surrounding fields, some recognized by the Clay Research Award, had raised hopes of a resolution, and that the increasing ability of new technologies to accelerate mathematical research heightened that anticipation.

The institute did not name the authors or describe the proof, and said it would provide updates as the work is analyzed and interrogated.

## Sources

- [claymath.org](https://www.claymath.org/news/navier-stokes-announcement/)

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