Modular forms

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.”

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

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

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

Researchers are on the trail of a mysterious connection between number theory, algebra and string theory.