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In mathematics, where proofs are everything, evidence is important too. But evidence is only as good as the model, and modeling can be dangerous business. So how much evidence is enough?

A science fiction novelist and an internet commenter made breakthroughs on a longstanding problem about the number of ways you can arrange a set of items. What did they discover?

Odd enough to potentially model the strangeness of the physical world, complex numbers with “imaginary” components are rooted in the familiar.

Studying the structure of existing friendships in your community can help you forge the best connections when forming a new circle of friends.

How many colors do you need to color an infinite plane so that no points 1 unit apart are the same color?

What does John Nash’s game theory equilibrium concept look like in Rock-Paper-Scissors?

Simple math shows how widespread vaccination can disrupt the exponential spread of disease and prevent epidemics.

Triangles fit effortlessly together, as do squares. When it comes to pentagons, what gives?

Simple math can help scheming politicians manipulate district maps and cruise to victory. But it can also help identify and fix the problem.