For centuries, the concept of infinity has captivated mathematicians and philosophers alike, stretching far beyond the simple idea of endless counting. Recent groundbreaking discoveries, however, have ...

One question has preoccupied humankind for thousands of years: Do infinities exist? More than 2,300 years ago Aristotle distinguished between two types of infinity: potential and actual. The former ...

When mathematician Georg Cantor first glimpsed the true nature of infinity, it changed mathematics forever. He demonstrated that infinity isn’t just endless; it exists in different sizes, each opening ...

A new kind of infinity appears to break the rules of how extremely large numbers behave, and could redraw the way the mathematical universe is ordered. It may come as a surprise, but mathematicians ...

The original version of this story appeared in Quanta Magazine. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in ...

It’s a complaint many algebra teachers are familiar with, as more letters and symbols are introduced with progressively harder courses in mathematics. But why did the plus symbol emerge as the ...

Infinity used to be the place where mathematics ran out of road, a hazy horizon rather than a mapped landscape. Now a pair of new, exotic infinities is forcing researchers to redraw that map and ...

Researchers from the Complutense University of Madrid (UCM, Spain) have mathematically shown that particles charged in a magnetic field can escape into infinity without ever stopping. One of the ...

A set of the six sides of a die matches up one-to-one with a set of red shoes, helping illustrate Georg Cantor's set theorem. Image courtesy of GBH/NOVA It can be easy to take math for granted. But ...