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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.

June Huh thought he had no talent for math until a chance meeting with a legendary mind. A decade later, his unorthodox approach to mathematical thinking has led to major breakthroughs.

Just five days after posting a retraction, László Babai announced that he had fixed the error in his landmark graph isomorphism algorithm.