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Physicists have identified an algebraic structure underlying the messy mathematics of particle collisions. Some hope it will lead to a more elegant theory of the natural world.

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.

Emperor penguins display rigorously geometric spacing and mathematical efficiency when they huddle together for warmth, which may reveal secrets to their overall health.

Two mathematicians have proved the first leg of Paul Erdős’ all-time favorite problem about number patterns.

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

Why do mathematicians enjoy proving the same results in different ways?

Can we test speculations about how quantum physics affects black holes and the Big Bang?

His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences.

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.