It’s not often that 5-year-olds can grasp questions at the frontiers of computer science, but it can happen. Suppose, for instance, that a kindergartner named Alice has two apples, but she prefers ...

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.

To a nonmathematician, having the letter "i" represent a number that does not quite exist and is "imaginary" can be hard to wrap your head around. If you open your mind to this way of thinking, ...

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 ...

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 ...

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 ...