Real and complex functions both arise from the fundamental idea of mapping points in a domain to real or complex values, yet their theories display distinctive features. Real functions—mappings ...

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 ...

For almost a century, physicists have been intrigued by the fundamental question: why are complex numbers so important in quantum mechanics, that is, numbers containing a component with the imaginary ...

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 ...

Mathematicians were disturbed, centuries ago, to find that calculating the properties of certain curves demanded the seemingly impossible: numbers that, when multiplied by themselves, turn negative.

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 ...

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, ...

It’s been 162 years since Bernhard Riemann posed a seminal question about the distribution of prime numbers. Despite their best efforts, mathematicians have made very little progress on the Riemann ...

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 ...