When he invented Turing machines in 1936, Alan Turing also invented modern computing.

Four mathematicians have found a new upper limit to the “Ramsey number,” a crucial property describing unavoidable structure in graphs.

After decades of frustration, researchers have determined how an airborne scent molecule links to a human smell receptor.

Cynthia Rudin wants machine learning models, responsible for increasingly important decisions, to show their work.

It’s been known for thousands of years that the primes go on forever, but new proofs give fresh insights into how theorems depend on one another.

A new, deeper understanding of how the breeding structure of species affects their genetic diversity is giving conservationists better tools for saving animals.

A new analysis argues that ubiquitous eruptions in the sun’s corona explain the vast flow of charged particles seen streaming out through the solar system.

The “packing coloring” problem asks how many numbers are needed to fill an infinite grid so that identical numbers never get too close to one another. A new computer-assisted proof finds a surprisingly straightforward answer.

In all bilaterally symmetrical animals, from humans down to simple worms, nerves cross from one side of the body to the opposite side of the brain. Geometry may explain why.