Set theory

Two new notions of infinity challenge a long-standing plan to define the mathematical universe.

A new proof illuminates the hidden patterns that emerge when addition becomes impossible.

A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.”

The numbers count a variety of seemingly unrelated mathematical structures.

Can mathematics handle things that are essentially the same without being exactly equal? Category theorist Eugenia Cheng and host Steven Strogatz discuss the power and pleasures of abstraction.

On nights and weekends, Justin Gilmer attacked an old question in pure math using the tools of information theory.

Two young mathematicians have astonished their colleagues with a full proof of the Kahn-Kalai conjecture — a sweeping statement about how structure emerges in random sets and graphs.

One of the strangest results in mathematics explains how it’s possible to turn one sphere into two identical copies, simply by rearranging its pieces.

A pair of researchers has shown that trying to classify groups of numbers called “torsion-free abelian groups” is as hard as it can possibly be.