Explainers

A simple, step-by-step breakdown of two “perfect” math proofs.

The Navier-Stokes equations describe simple, everyday phenomena, like water flowing from a garden hose, yet they provide a million-dollar mathematical challenge.

It’s “a definitive study for all time, like writing the final book,” says one researcher who’s mapping out new classes of geometric structures.

Big advances in math can happen when mathematicians move ideas into areas where they seem like they shouldn’t belong.