Mathematics

The surprisingly simple tile is the first single, connected tile that can fill the entire plane in a pattern that never repeats — and can’t be made to fill it in a repeating way.

The four-color problem is simple to explain, but its complex proof continues to be both celebrated and despised.

The prize-winning geometer feels most fulfilled when exploring the fertile ground where constraint meets creation.

Learn why the quadratic formula works and why quadratics are easier to solve than cubics.

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.

For decades, mathematicians have been inching forward on a problem about which sets contain evenly spaced patterns of three numbers. Last month, two computer scientists blew past all of those results.

In a recent paper, two mathematicians showed that a particular pattern is unavoidable when fractions are categorized.

Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical physics.

Lek-Heng Lim uses tools from algebra, geometry and topology to answer questions in machine learning.