Clay Institute says the Navier-Stokes problem appears to be settled

The Clay Mathematics Institute (CMI) says it is contemplating an announcement that the Navier-Stokes problem "has apparently been settled", and that it shares the excitement of the global mathematical community over the claim.

Navier-Stokes is one of the Millennium Prize Problems unveiled by CMI at a meeting in Paris in 2000, each carrying a prize of $1 million. The problem asks about the existence and smoothness of Navier-Stokes solutions in 3-dimensional Euclidean space, describing the motion of fluids.

Why expectations had been rising

According to the institute, recent breakthroughs in the surrounding field, some of them recognised by the Clay Research Award, had raised hopes that the problem might soon be resolved. CMI adds that the increasing ability of new technologies to accelerate mathematical research heightened that sense of anticipation.

What happens next

CMI notes that the rules governing the prizes describe a process for evaluating what has been achieved and for assigning credit. That process is, in the institute's words, deliberately unhurried, and CMI says it will provide updates.

The institute restates the purpose behind articulating the problems: to show the public that the mathematical frontier is open and full of important unsolved questions, to emphasise the value of working on the deepest problems, and to recognise achievements of historic magnitude. It also says it hopes to see new human understanding emerge as the innovations behind the work are analysed and interrogated.

The full statement is available on the Clay Mathematics Institute website.