For more than 250 years, mathematicians have wondered if the Euler equations might sometimes fail to describe a fluid’s flow. Now there’s a breakthrough.

Under the hood, mathematical problems called partial differential equations (PDEs) model these natural processes. Among the many PDEs used in physics and computer graphics, a class called second ...

In math and computer science, researchers have long understood that some questions are fundamentally unanswerable. ... For more than 250 years, mathematicians have wondered if the Euler equations ...