The London Mathematical Society welcomes the announcement of a major advance in the study of the Navier–Stokes equations, one of the most important and challenging problems in modern mathematics. The so-called Navier–Stokes problem is one of the seven Millennium Prize Problems identified by the Clay Mathematics Institute in 2000 as among the most significant unsolved questions in mathematics, and relates to the smoothness of the solution to the equations evolving from given smooth initial data. These equations describe how fluids such as air and water move and underpin countless applications across science, engineering, meteorology, and industry. Any significant progress towards understanding their behaviour represents a major milestone for the mathematical sciences and highlights the continuing power of mathematical research to deepen our understanding of the world.
Professor Mark Chaplain, President of the London Mathematical Society, said:
“The Navier–Stokes equations lie at the heart of our understanding of fluid motion, describing phenomena ranging from airflow over an aircraft wing to the dynamics of oceans and weather systems. For decades, mathematicians have sought a deeper understanding of the behaviour of these equations, making this breakthrough a remarkable achievement.
At a moment like this, it is important to recognise the enduring importance of human creativity, insight, innovation and perseverance in mathematics. While new AI tools can greatly accelerate exploration and discovery, the goal remains human understanding. This result is a powerful reminder that mathematics advances through people asking profound questions, developing new ideas, creating new mathematical tools, risking new avenues of exploration and building knowledge collectively across generations.
What makes this achievement so exciting is that it demonstrates both the extraordinary capacity of human intellect and the remarkable potential of new technologies when used to support that endeavour. This is, above all, a great human achievement, enabled by a powerful new tool. It shows what we can accomplish when mathematical insight and technological innovation work hand in hand."
Last updated: 9 September 2026