Areas of pure math such as algebra, analysis, combinatorics and many others can be used—in some cases combined—to solve the complex math problems arising from applications of math to the real world.

Forbes contributors publish independent expert analyses and insights. Anisha Sircar is a journalist covering tech, finance and society. This voice experience is generated by AI. Learn more. This voice ...

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, ...

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 ...

The original version of this story appeared in Quanta Magazine. Sometimes mathematicians try to tackle a problem head on, and sometimes they come at it sideways. That’s especially true when the ...

In the mid-noughties, when music by the Killers and Franz Ferdinand blared out of every pub and nightclub I passed, I spent ...

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 ...

On October 16 1843, the Irish mathematician William Rowan Hamilton had an epiphany during a walk alongside Dublin’s Royal Canal. He was so excited he took out his penknife and carved his discovery ...

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 ...

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, ...