Number theory

In his rapid ascent to the top of his field, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

Representation theory was initially dismissed. Today, it’s central to much of mathematics.

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.

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.