Mathematics

Useful mathematical concepts, like the number line, can linger for millennia before they are rigorously defined.

How are scientists able to crack fundamental questions about nature and life? How does math make the complex cosmos understandable? In this episode, the physicist Nigel Goldenfeld and co-host Steven Strogatz explore the deep foundations of the scientific process.

Mathematicians show that graphs of a certain common type must contain a route that visits each point exactly once.

By studying the geometry of model space-times, researchers offer alternative views of the universe’s first moments.

The topologist Danny Calegari discusses the inevitability of disappointment in math, and how to learn from it.

Mathematicians have disproved a major conjecture about the relationship between curvature and shape.

In 1940 André Weil wrote a letter to his sister, Simone, outlining his vision for translating between three distinct areas of mathematics. Eighty years later, it still animates many of the most exciting developments in the field.

Four mathematicians broke a 75-year-old record by finding a denser way to pack high-dimensional spheres.

Topologists prove two new results that bring some order to the confoundingly difficult study of four-dimensional shapes.