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Vesselin Dimitrov’s proof of the Schinzel-Zassenhaus conjecture quantifies the way special values of polynomials push each other apart.

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

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”

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

Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work.

Equations, like numbers, cannot always be split into simpler elements.

The 30-year-old math sensation Peter Scholze is now one of the youngest Fields medalists for “the revolution that he launched in arithmetic geometry.”

A century ago, the great mathematician David Hilbert posed a probing question in pure mathematics. A recent advance in optimization theory is bringing Hilbert’s work into a world of self-driving cars.

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