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

A new series of papers has settled a long-standing question related to the popular game in which players seek patterned sets of three cards.

The Ukrainian mathematician Maryna Viazovska has solved the centuries-old sphere-packing problem in dimensions eight and 24.

A previously unnoticed property of prime numbers seems to violate a long-standing assumption about how they behave.

Computer scientists are abuzz over a fast new algorithm for solving one of the central problems in the field.

Three computer scientists have solved a problem central to a dozen far-flung mathematical fields.

Using crowd-sourced and traditional mathematics research, Terence Tao has devised a solution to a long-standing problem posed by the legendary Paul Erdős.

For more than 50 years, the mathematician Neil Sloane has curated the authoritative collection of interesting and important integer sequences.

A 150-year-old conundrum about how to group people has been solved, but many puzzles remain.