number theory

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

The legendary mathematician, who died on April 11, was curious, colorful and one of the greatest problem-solvers of his generation.

Mathematicians have figured out how to expand the reach of a mysterious bridge connecting two distant continents in the mathematical world.

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

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

Mathematicians and computer scientists made big progress in number theory, graph theory, machine learning and quantum computing, even as they reexamined our fundamental understanding of mathematics and neural networks.

Mathematicians regard the Collatz conjecture as a quagmire and warn each other to stay away. But now Terence Tao has made more progress than anyone in decades.

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

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