Several years ago one of us, Toni, asked another of us, Marco, to come to his office at the Institute of Photonic Sciences, a large research center in Castelldefels near Barcelona. “There is a problem ...

A century ago, the strange behavior of atoms and elementary particles led physicists to formulate a new theory of nature. That theory, quantum mechanics, found immediate success, proving its worth ...

Imagine winding the hour hand of a clock back from 3 o’clock to noon. Mathematicians have long known how to describe this rotation as a simple multiplication: A number representing the initial ...

Imaginary numbers might seem like unicorns and goblins — interesting but irrelevant to reality. But for describing matter at its roots, imaginary numbers turn out to be essential. They seem to be ...

A forgotten number system invented in the 19th century may provide the simplest explanation for why our universe could have 10 dimensions As children, we all learn about numbers. We start with ...