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Sizing up patternless sets is hard, so mathematicians rely on simple bounds to help answer their questions.

Finding the best way to approximate the ever-elusive irrational numbers pits the infinitely large against the infinitely small.

No one knows how to find the smallest shape that can cover all other shapes of a certain width. But high school geometry is getting us closer to an answer.

Looking for answers in infinite space is hard. High school math can help narrow your search.

The way you learned to multiply works, but computers employ a faster algorithm.

Polynomials aren’t just exercises in abstraction. They’re good at illuminating structure in surprising places.

A little high school geometry can help you understand the basic math behind movie recommendation engines.

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?

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