A $1 million prize awaits anyone who can show where the math of fluid flow breaks down. With specially trained AI systems, ...

The study of free boundary problems in the Navier-Stokes equations addresses the subtle interplay between the dynamics of viscous, incompressible fluids and the evolution of interfaces whose locations ...

As we celebrate the International Year of Quantum Science and Technology (IYQ) in 2025, we look back on a century of quantum mechanics—a field that has fundamentally changed the way we understand ...

The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations. For nearly two centuries, all kinds of researchers ...

Contour plots (A, C, E, G) compare the input conditions, traditional finite difference method solutions, and the solutions generated by model B3, the most advanced model in the study. Velocity ...

When the greatest mathematician alive unveils a vision for the next century of research, the math world takes note. That’s exactly what happened in 1900 at the International Congress of Mathematicians ...