Modular forms

By extending the scope of the key insight behind Fermat’s Last Theorem, four mathematicians have made great strides toward building a “grand unified theory” of math.

It’s surprisingly difficult to prove one of the most basic properties of a number: whether it can be written as a fraction. A broad new method can help settle this ancient question.

Born poor in colonial India and dead at 32, Ramanujan had fantastical, out-of-nowhere visions that continue to shape the field today.

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

Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical physics.

With her homeland mired in war, the sphere-packing number theorist Maryna Viazovska has become the second woman to win a Fields Medal in the award’s 86-year history.

The legendary mathematician, who died on April 11, was curious, colorful and one of the greatest problem-solvers of his generation.

Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space.

The 30-year-old math sensation Peter Scholze is now one of the youngest Fields medalists for “the revolution that he launched in arithmetic geometry.”