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 ...

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 a previous post, I argued that concepts and concerns, such as free will and determinism, can be complex in the same sense in which numbers can be: in other words, in combining a real with an ...

A century ago, the strange behavior of atoms and elementary particles led physicists to formulate a new theory of nature. That theory, quantum mechanics, found immediate success, proving its worth ...

Repetition doesn’t always have to be humdrum. In mathematics, it is a powerful force, capable of generating bewildering complexity. Even after decades of study, mathematicians find themselves unable ...