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 ...

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, ...

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 ...

In this video playlist, you will learn how to simplify complex numbers under a radical as well as raised to a higher power. You will learn to add, subtract, multiply, and divide complex numbers to ...

Mathematics often feels like a collection of isolated islands. Each one operates with its own rules, and building bridges ...

Gerd Faltings shocked mathematicians around the world for his 1983 proof of the Mordell conjecture, which brought together ...