Mathematics

A new proof identifies precisely how large a mathematical graph must be before it contains a regular substructure.

For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them.

Jared Duker Lichtman, 26, has proved a longstanding conjecture relating prime numbers to a broad class of “primitive” sets. To his adviser, it came as a “complete shock.”

Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.

The Langlands program provides a beautifully intricate set of connections between various areas of mathematics, pointing the way toward novel solutions for old problems.

Four puzzle solutions reveal different ways to divine someone’s hidden number with impossibly little information.

A bit of information theory can help you analyze — and improve — your Wordle game.

“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.

Mathematical magic can seem like mind reading. Your job is to reveal the secret behind these four tricks.