Fractals

Focus, commitment, and insight resulted in a “once in a century” proof. Hong Wang is now just the third woman to win a Fields Medal.

By replacing the most fundamental concept in topology, Peter Scholze and Dustin Clausen are taking the first step in a far bigger program to understand why numbers behave the way they do.

The proof, known to be so hard that a mathematician once offered 10 martinis to whoever could figure it out, connects quantum mechanics to infinitely intricate mathematical structures.

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

Mathematicians have struggled to prove Falconer’s Conjecture, a simple, but far-reaching, hypothesis about the distances between points. They’re finally getting close.

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

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.

A new paper establishes a long-conjectured bound about the size of the overlap between sets of lines and points.

A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures.