Geometry

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.

Three mathematicians have resolved a fundamental question about straight paths on the 12-sided Platonic solid.

A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot.

By translating Keller’s conjecture into a computer-friendly search for a type of graph, researchers have finally resolved a problem about covering spaces with tiles.

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about.

How to safely reopen offices, schools and other public spaces while keeping people six feet apart comes down to a question mathematicians have been studying for centuries.

While locked down due to COVID-19, Joshua Greene and Andrew Lobb figured out how to prove a version of the “rectangular peg problem.”

Mathematicians typically appreciate either generic or exceptional beauty in their work, but one type is more useful in describing the universe.