“Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don’t know what it means. But we have proved it, and therefore we know it must be the truth.” —Benjamin ...

The compressible Euler equations form the cornerstone of fluid dynamics, describing the conservation of mass, momentum and energy in a compressible fluid. When augmented by damping effects, these ...

This article describes a method for computing approximate equilibria for stochastic dynamic economies. The method is of general interest because it allows straightforward computation of equilibria in ...

Researchers have spent centuries looking for a scenario in which the Euler fluid equations fail. Now a mathematician has finally found one. Mathematicians have suspected for years that under specific ...

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near. For ...