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It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown.

The astrophysicist Janna Levin reflects on the newly unveiled, first-ever photograph of a black hole.

Just how fast can the fastest human run? This adapted book excerpt from Infinite Powers reveals how calculus helps us investigate the nature of motion and change.

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?

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.