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 ...

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 ...

Is there an infinity of infinities? The question sounds almost absurd, like a child’s riddle meant to twist your brain into knots. But for mathematicians, it’s a serious (and endlessly fascinating) ...

For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise. In October 2018, David Asperó was on holiday in Italy, gazing out a car ...