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 ...

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 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 ...

At the University of Vaasa in Finland, mathematician Yosra Barkaoui has successfully generalized a fundamental theorem that had remained confined to “bounded” systems for more than 40 years.

For four decades, a quiet boundary in pure mathematics kept a powerful theorem locked inside the safe world of finite quantities. Now a new result known as Sebestyen’s theorem has pushed that boundary ...