Important update, Jan. 17 at 18:00 UTC: There have been a lot of objections raised about the video mentioned below and the way I describe the math therein. It’s more than I can simply add or update ...

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 ...

Mathematics is often about uncovering patterns. For example, certain areas of topology revolve around categorizing knots or geometric shapes, and number theory explores properties such as 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 ...

Several years ago, I tried to explain infinity to a class of fifth graders. In the story that I told them, I was preparing to eat a piece of cake when a friend walked in on me. Being polite, I gave ...

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 ...