Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.

The color of LED lights is controlled by a clumsy process. A new mathematical discovery may make it easier for us to get the hues we want.

The mathematician Svitlana Mayboroda and collaborators have figured out how to predict the behavior of electrons — a mathematical discovery that could have immediate practical effects.

It’s “a definitive study for all time, like writing the final book,” says one researcher who’s mapping out new classes of geometric structures.

Two “rare jewels” have illuminated a mysterious multidimensional object that connects a huge variety of mathematical work.

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.

Big advances in math can happen when mathematicians move ideas into areas where they seem like they shouldn’t belong.

June Huh thought he had no talent for math until a chance meeting with a legendary mind. A decade later, his unorthodox approach to mathematical thinking has led to major breakthroughs.

Paul Erdős placed small bounties on hundreds of unsolved math problems. Over the past 20 years, only a handful have been claimed.