Elliptic curves

Mathematicians are working to fully explain unusual behaviors uncovered using artificial intelligence.

Landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.

Some strange mathematical sequences are always whole numbers — until they’re not. The puzzling patterns have revealed ties to graph theory and prime numbers, awing mathematicians.

Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?

Ana Caraiani and James Newton have extended an important result in number theory to the imaginary realm.

The work — the first-ever limit on how many whole numbers can be written as the sum of two cubed fractions — makes significant headway on “a recurring embarrassment for number theorists.”

Wei Ho, the first director of the Women and Mathematics program at the Institute for Advanced Study, combines algebra and geometry in her work on an ancient class of curves.

Two researchers have broken an encryption protocol that many saw as a promising defense against the power of quantum computing.

A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.