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 ...

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 ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

From machine learning to voting, the workings of the world demand randomisation, but true sources of randomness are ...

Quantum physics has a reputation for needing exotic hardware, from liquid-helium-cooled qubits to sprawling AI clusters, just ...

As far as we know, our physical world is governed by four fundamental forces: electromagnetism, weak and strong nuclear forces, and gravity. Apart from playing with bar magnets or marveling at the ...

Scientists are like prospectors, excavating the natural world seeking gems of knowledge about physical reality. And in the century just past, scientists have dug deep enough to discover that reality’s ...

Imagine a physicist observing a quantum system whose behavior is akin to a coin toss: it could come up heads or tails. They perform the quantum coin toss and see heads. Could they be certain that ...

The original version of this story appeared in Quanta Magazine. In 1974, five years before he wrote his Pulitzer Prize–winning book Gödel, Escher, Bach: An Eternal Golden Braid, Douglas Hofstadter was ...