Physicists construct theories to describe nature. Let us explain it through an analogy with something that we can do in our everyday life, like going on a hike in the mountains. To avoid getting lost, ...

Scientists have found what they say is a link between complex number theory and string theory. A mathematician and physicist working together found the connection, which they say is part of plotting ...

The square root of a negative number could easily be regarded as a curious mathematical construction that has little bearing on real life. Indeed, the French polymath René Descartes gave such numbers ...

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 ...

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 ...

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 ...

Have you ever sat in a math classroom and wondered, “When will I ever use this?” You might have asked yourself this question when you first encountered “imaginary” numbers, and with good reason: What ...

String theory and number theory have common ground in a specific kind of elliptic curve, called a torus. Toruses aren't just for compressing atoms: these curves represent torus cross-sections. The ...