Penny Smith, a mathematician at Lehigh University, has posted a paper on the arXiv that purports to solve one of the Clay Foundation Millenium problems, the one about the Navier-Stokes Equation. The paper is here, and Christina Sormani has set up a web-page giving some background and exposition of Smith’s work. I should emphasize that I know just about nothing about this kind of mathematics, but I’m reporting on this here for two reasons:
1. It looks plausible that this really is important.
2. Penny Smith tells me that she is a regular reader of this weblog.
Update: There’s an informative news article about this on the Nature web-site.