## Latest Articles

### Monumental Proof Settles Geometric Langlands Conjecture

In work that has been 30 years in the making, mathematicians have proved a major part of a profound mathematical vision called the Langlands program.

### Merging Fields, Mathematicians Go the Distance on Old Problem

Mathematicians have illuminated what sets of points can look like if the distances between them are all whole numbers.

### A New Generation of Mathematicians Pushes Prime Number Barriers

New work attacks a long-standing barrier to understanding how prime numbers are distributed.

### Hobbyist Finds Math’s Elusive ‘Einstein’ Tile

The surprisingly simple tile is the first single, connected tile that can fill the entire plane in a pattern that never repeats — and can’t be made to fill it in a repeating way.

### Emmy Murphy Is a Mathematician Who Finds Beauty in Flexibility

The prize-winning geometer feels most fulfilled when exploring the fertile ground where constraint meets creation.

### Mathematicians Roll Dice and Get Rock-Paper-Scissors

Mathematicians have uncovered a surprising wealth of rock-paper-scissors-like patterns in randomly chosen dice.

### Mathematical Trio Advances Centuries-Old Number Theory Problem

The work — the first-ever limit on how many whole numbers can be written as the sum of two cubed fractions — makes significant headway on “a recurring embarrassment for number theorists.”

### ‘Monumental’ Math Proof Solves Triple Bubble Problem and More

The decades-old Sullivan’s conjecture, about the best way to minimize the surface area of a bubble cluster, was thought to be out of reach for three bubbles and up — until a new breakthrough result.

### The Math Evangelist Who Preaches Problem-Solving

Richard Rusczyk, founder of Art of Problem Solving, has a vision for bringing “joyous, beautiful math” — and problem-solving — to classrooms everywhere.