Topology

Jordan Ellenberg enjoys studying — and writing about — the mathematics underlying everyday phenomena.

Originally devised as a rigorous means of counting holes, homology provides a scaffolding for mathematical ideas, allowing for a new way to analyze the shapes within data.

The relationships among the properties of flexible shapes have fascinated mathematicians for centuries.

Long considered solved, David Hilbert’s question about seventh-degree polynomials is leading researchers to a new web of mathematical connections.

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

From crumpled paper to termite mounds to three-sided coins, L. Mahadevan has turned the whole world into his laboratory.

A small community of mathematicians is using a software program called Lean to build a new digital repository. They hope it represents the future of their field.

Mathematicians have long grappled with the reality that some problems just don’t have solutions.

Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.