Real and imaginary: The time-dependent Schrödinger equation formulated using complex numbers. (Courtesy: iStock/piranka) Complex numbers are essential to achieve the most accurate quantum-mechanical ...

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, ...

New findings are fueling an old suspicion that fundamental particles and forces spring from strange eight-part numbers called “octonions.” In 2014, a graduate student at the University of Waterloo, ...

In spite of their name, “imaginary” numbers are as real as any other numbers, especially when it comes to hunting for lost treasure. For our first Insights puzzle of 2019, let’s go on a treasure hunt.

William Ross does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their ...

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 ...

Mathematics has always stood quietly behind great changes, and the rise of AI is no different. As machines learn through ...

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 ...