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 ...

The Markov numbers reveal the secrets of irrational numbers and the patterns of the Fibonacci sequence. But there’s one question about them that has resisted proof for over a century. Most people are ...

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 ...

§CQ.1 THE FIRST GREAT ADVANCE in algebra after the Middle Ages was the general solution of the cubic equation, immediately followed by a solution for the quartic. I tell the full story in the next ...

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, ...