Mathematics

A new proof marks the first progress in decades on important cases of the so-called kissing problem. Getting there meant doing away with traditional approaches.

It’s surprisingly difficult to prove one of the most basic properties of a number: whether it can be written as a fraction. A broad new method can help settle this ancient question.

Landmark results in geometry and number theory marked an exciting year for mathematics, at a time when advances in artificial intelligence are starting to transform the subject’s future.

To make progress on one of number theory’s most elementary questions, two mathematicians turned to an unlikely source.

Three high schoolers and their mentor revisited a century-old theorem to prove that all knots can be found in a fractal called the Menger sponge.

The mathematician David Bessis claims that everyone is capable of, and can benefit greatly from, mathematical thinking.

The security system that underlies the internet makes use of a curious fact: You can broadcast part of your encryption to make your information much more secure.

Two mathematicians have renewed a debate about the fundamental nature of some of math’s most important equations.

With lots of data, a strong model and statistical thinking, scientists can make predictions about all sorts of complex phenomena. Today, this practice is evolving to harness the power of machine learning and massive datasets. In this episode, co-host Steven Strogatz speaks with statistician Emmanuel Candès about black boxes, uncertainty and the power of inductive reasoning.