Mathematics

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.

Mathematicians think abstract tools from a field called symplectic geometry might help with planning missions to far-off moons and planets.

Mathematicians have struggled to prove Falconer’s Conjecture, a simple, but far-reaching, hypothesis about the distances between points. They’re finally getting close.

Mathematicians have illuminated what sets of points can look like if the distances between them are all whole numbers.

Mathematicians are using topological abstractions to find places where it’s hard to vote.