combinatorics

“Rainbow colorings” recently led to a new proof. It’s not the first time they’ve come in handy.

Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones.

A major advance toward solving the 60-year-old sunflower conjecture is shedding light on how order begins to appear as random systems grow in size.

Polynomials aren’t just exercises in abstraction. They’re good at illuminating structure in surprising places.

The “sensitivity” conjecture stumped many top computer scientists, yet the new proof is so simple that one researcher summed it up in a single tweet.

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

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

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.

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?