The (Imaginary) Numbers at the Edge of Reality — Quanta Magazine

My latest column for Quanta Magazine connects the complex numbers from high school math classrooms to the quaternions and octonions, numbers systems currently being used in cutting-edge math and science research.

Have you ever sat in a math classroom and wondered, “When will I ever use this?” You might have asked yourself this question when you first encountered “imaginary” numbers, and with good reason: What could be less practical than a number described as imaginary?

But imaginary numbers, and the complex numbers they help define, turn out to be incredibly useful. They have a far-reaching impact in physics, engineering, number theory and geometry. And they are the first step into a world of strange number systems, some of which are being proposed as models of the mysterious relationships underlying our physical world.

Some physicists currently believe that the octonions, an eight-dimensional number system with non-commutative, non-associative multiplication and seven square roots of -1, may be the key to understanding the fundamental interactions between particles and forces. Learn more about their connections to “imaginary” numbers in the full article, which is freely available here.