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Perfect black holes are versatile mathematical tools. Just don’t mistake them for the real thing.

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.

Computer simulations and custom-built quantum analogues are changing what it means to search for the laws of nature.

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?

Scientists seek a single description of reality. But modern physics allows for many different descriptions, many equivalent to one another, connected through a vast landscape of mathematical possibility.

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

Gravitational waves have opened up new ways to test the properties of black holes — and Einstein’s theory of gravity along with them.