The Poincaré conjecture can be understood by analogy with the case in two dimensions. A two-dimensional space, or surface, is like a bubble made from an infinitely thin film of soap. If the bubble is ...

In early 20th-century Paris, there was a boy so mesmerized by math that when his parents took his paper and pencil away, urging him to play, he found a rock and scribbled algebra equations on the ...

When Austin writer Karen Olsson was a teenager, she did a lot of reading. A lot. And not light fiction (though maybe there was some of that) or novels for school (of course), but heavy thinkers from ...

In mathematics, a simple problem is often not what it seems. Earlier this summer, Quanta reported on one such problem: What is the smallest area that you can sweep out while rotating an infinitely ...

It is well-known that our intuition is not perfect. We are predictably irrational in a huge number of ways in our everyday lives. But what about something a bit more sophisticated? Are there times ...

In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation ...