## Latest Articles

### How Failure Has Made Mathematics Stronger

The topologist Danny Calegari discusses the inevitability of disappointment in math, and how to learn from it.

### Strangely Curved Shapes Break 50-Year-Old Geometry Conjecture

Mathematicians have disproved a major conjecture about the relationship between curvature and shape.

### Mathematicians Marvel at ‘Crazy’ Cuts Through Four Dimensions

Topologists prove two new results that bring some order to the confoundingly difficult study of four-dimensional shapes.

### Michel Talagrand Wins Abel Prize for Work Wrangling Randomness

The French mathematician spent decades developing a set of tools now widely used for taming random processes.

### ‘The Rest of the World Disappears’: Claire Voisin on Mathematical Creativity

The recipient of the 2024 Crafoord Prize in Mathematics discusses math as art, math as language, and math as abstract thought.

### Complex Structures Like ‘Entropy Bagels’ Emerge From Simple Rules

Simple rules in simple settings continue to puzzle mathematicians, even as they devise intricate tools to analyze them.

### How to Build an Origami Computer

Two mathematicians have shown that origami can, in principle, be used to perform any possible computation.

### The Quest to Decode the Mandelbrot Set, Math’s Most Famous Fractal

For decades, a small group of mathematicians has patiently unraveled the mystery of what was once math’s most popular picture. Their story shows how technology transforms even the most abstract mathematical landscapes.

### 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?