Adam Larios and Kazuo Yamazaki, University of Nebraska

The equations of fluid dynamics are vital to our ability to understand the weather, solar storms, cardiovascular health, ocean dynamics, power generation, and many other pressing issues. They are thought to be accurately given by a system of partial differential equations (PDEs) known as the Navier-Stokes equations that are so notoriously difficult that we have been stuck on proving basic facts about them since 1934, namely the existence and uniqueness of smooth solutions for all time starting from smooth initial data. In the year 2000, the Clay Mathematics Institute announced a $1,000,000 prize for 7 challenging mathematical problems, and the Navier-Stokes problem was one of them. This week, OpenAI claimed to have solved one version of the problem. We will discuss what the Navier-Stokes problem is, get an understanding of the issues, sketch recent breakthroughs, and discuss what OpenAI claims to have done, and discuss possible future outcomes and directions.