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An exercise in pure mathematics has led to a wide-ranging theory of how the world comes together.

Struggling with math problems that can’t be solved helps us better understand the ones we can.

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

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.

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