Number theory

A famously difficult mathematical problem resisted solution for over 40 years. Mathematicians have finally resolved it by following an intuition that links number theory to physics.

An eminent mathematician reveals that his advances in the study of millennia-old mathematical questions owe to concepts derived from physics.

A type of symmetry so unusual that it was called a “pariah” turns out to have deep connections to number theory.

Kaisa Matomäki has proved that properties of prime numbers over long intervals hold over short intervals as well. The techniques she uses have transformed the study of these elusive numbers.

An obscure number theorist who became an overnight sensation with a major proof about the gaps between prime numbers now finds quiet inspiration walking along the Pacific Coast.

19th-century mathematicians thought the “roots of unity” were the key to solving Fermat’s Last Theorem. Then they discovered a fatal flaw.

For centuries, mathematicians tried to solve problems by adding new values to the usual numbers. Now they’re investigating the unintended consequences of that tinkering.

Peter Scholze is a favorite to win one of the highest honors in mathematics for his contributions in number theory and geometry.

At 28, Peter Scholze is uncovering deep connections between number theory and geometry.