What's up in

# Combinatorics

## Latest Articles

### A 53-Year-Old Network Coloring Conjecture Is Disproved

In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible.

### How a Strange Grid Reveals Hidden Connections Between Simple Numbers

A graduate student has helped illuminate a long-suspected connection between addition and multiplication.

### A Child’s Puzzle Has Helped Unlock the Secrets of Magnetism

People have known about magnets since ancient times, but the physics of ferromagnetism remains a mystery. Now a familiar puzzle is getting physicists closer to the answer.

### Unscrambling the Hidden Secrets of Superpermutations

A science fiction novelist and an internet commenter made breakthroughs on a longstanding problem about the number of ways you can arrange a set of items. What did they discover?

### Mystery Math Whiz and Novelist Advance Permutation Problem

A new proof from the Australian science fiction writer Greg Egan and a 2011 proof anonymously posted online are now being hailed as significant advances on a puzzle mathematicians have been studying for at least 25 years.

### Four Is Not Enough

How many colors do you need to color an infinite plane so that no points 1 unit apart are the same color?

### Decades-Old Graph Problem Yields to Amateur Mathematician

By making the first progress on the “chromatic number of the plane” problem in over 60 years, an anti-aging pundit has achieved mathematical immortality.

### The (Math) Problem With Pentagons

Triangles fit effortlessly together, as do squares. When it comes to pentagons, what gives?

### A Mathematician Who Dances to the Joys and Sorrows of Discovery

Federico Ardila opens up about his journey as a mathematician, teacher, Colombian transplant, DJ and creator of mathematical spaces.