Number theory

A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot.

Two mathematicians have proved the first leg of Paul Erdős’ all-time favorite problem about number patterns.

Why do mathematicians enjoy proving the same results in different ways?

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.