Polynomials

The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory.

After 44 years, there’s finally a better way to find approximate solutions to the notoriously difficult traveling salesperson problem.

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.