A forgotten number system invented in the 19th century may provide the simplest explanation for why our universe could have 10 dimensions As children, we all learn about numbers. We start with ...

A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems. Joseph Silverman remembers when he began connecting ...

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.

Imaginary numbers are necessary to accurately describe reality, two new studies have suggested. Imaginary numbers are what you get when you take the square root of a negative number, and they have ...

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 ...

Complex numbers seem to have an almost mystical aura surrounding them. Perhaps it’s because of the terminology used for them – for example, they have a ‘real part’ and an ‘imaginary part’, and they ...

This course will introduce you to the theory of functions of complex variables, which is a core area of mathematics. It is a basic tool in many mathematical theories. We will cover complex numbers and ...

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, ...

AN editorial preface by Mr. H. P. Young, an appreciative foreword by Dr. Alexander Russell, the usual author's preface, four chapters of elementary ‘pure’ mathematics (complex numbers and calculus), a ...