With a surprising new proof, two young mathematicians have found a bridge across the finite-infinite divide, helping at the same time to map this strange boundary. The boundary does not pass between ...

You can’t always solve a mathematical problem by reducing it to something you’ve already solved. Sometimes, you need to rethink and reform the original statements. Prof. Justin Moore, mathematics, ...

Descriptive set theorists study the niche mathematics of infinity. Now, they’ve shown that their problems can be rewritten in the concrete language of algorithms. All of modern mathematics is built on ...

Receive emails about upcoming NOVA programs and related content, as well as featured reporting about current events through a science lens. Reviel Netz: Something which is equal to some of its parts.

Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a set of real numbers especially intervals (with notations). Power set. Universal set. Venn ...

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 ...

In mathematics, real numbers are everywhere; but are they so real? Let me propose the following hypothetical game. The host has several point objects that can move with constant speeds; I like to ...

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 ...