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modular forms

Art for "How Feynman Diagrams Revolutionized Physics"
sphere packing

Out of a Magic Math Function, One Solution to Rule Them All

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

Photo of Dr. Peter Scholze
2018 Fields Medal and Nevanlinna Prize Winners

A Master of Numbers and Shapes Who Is Rewriting Arithmetic

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.”

Pariah moonshine
number theory

Mathematicians Find Moonshine Link for Pariah Symmetries

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

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The Oracle of Arithmetic

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

geometry

Sphere Packing Solved in Higher Dimensions

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

number theory

Mathematicians Chase Moonshine’s Shadow

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