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 ...

Like physics, math has its own set of “fundamental particles”—the prime numbers, which can’t be broken down into smaller natural numbers. They can only be divided by themselves and 1. And in a new ...

The Mandelbrot set, according to Wikipedia, is “the set of complex numbers for which the function does not diverge.” Even if you don’t understand the mathematics behind it, you’ve likely seen the ...

In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides ...

The techniques he developed in the field of complex numbers have found use in tackling a wide range of fundamental equations in physics. By Kenneth Chang Joseph J. Kohn, who played a key role in ...

A basic feature of number theory, prime numbers are also a fundamental building block of computer science, from hashtables to cryptography. Everyone knows that a prime number is one that cannot be ...

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, ...

An international team of researchers shows through a concrete theoretical experiment that the prediction by standard complex quantum theory cannot be expressed by its real counterpart and ratifies its ...

For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise. In October 2018, David Asperó was on holiday in Italy, gazing out a car ...