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# Modular forms

## Latest Articles

### Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math

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

### New Proof Distinguishes Mysterious and Powerful ‘Modular Forms’

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.

### In Times of Scarcity, War and Peace, a Ukrainian Finds the Magic in Math

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.

### John Conway Solved Mathematical Problems With His Bare Hands

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

### 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.

### 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.”

### Moonshine Link Discovered for Pariah Symmetries

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

### The Oracle of Arithmetic

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