Explainers

When pigeons outnumber pigeonholes, some birds must double up. This obvious statement — and its inverse — have deep connections to many areas of math and computer science.

A popular hypothesis for how the brain clears molecular waste, which may help explain why sleep feels refreshing, is a subject of debate.

Ten years ago, researchers proved that adding full memory can theoretically aid computation. They’re just now beginning to understand the implications.

Emmy Noether showed that fundamental physical laws are just a consequence of simple symmetries. A century later, her insights continue to shape physics.

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

Hypothetical devices that can quickly and accurately answer questions have become a powerful tool in computational complexity theory.

Our computers can get a lot more done when they share the load with other machines.

The security system that underlies the internet makes use of a curious fact: You can broadcast part of your encryption to make your information much more secure.

All modern multicellular life — all life that any of us regularly see — is made of cells with a knack for compartmentalization. Recent discoveries are revealing how the first eukaryote got its start.