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combinatorics

An animation showing a 3-by-3 Latin square, with numbers color coded, and the equivalent graph.
Abstractions blog

‘Rainbows’ Are a Mathematician’s Best Friend

March 18, 2020

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

Animated demonstration of a colorful complete graph being tiled by a smaller tree
combinatorics

Rainbow Proof Shows Graphs Have Uniform Parts

February 19, 2020

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

Photo of a yellow sunflower against a yellow background.
Abstractions blog

Mathematicians Begin to Tame Wild ‘Sunflower’ Problem

October 21, 2019

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.

Art for "Color Me Polynomial"
Quantized Academy

Color Me Polynomial

August 13, 2019

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

combinatorics

Decades-Old Computer Science Conjecture Solved in Two Pages

July 25, 2019

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.

Art for "A 53-Year-Old Network Coloring Conjecture Is Disproved"
graph theory

A 53-Year-Old Network Coloring Conjecture Is Disproved

June 17, 2019

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

number theory

How a Strange Grid Reveals Hidden Connections Between Simple Numbers

February 6, 2019

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

mathematical physics

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

January 24, 2019

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.

Art for "Unscrambling the Hidden Secrets of Superpermutations"
Quantized Academy

Unscrambling the Hidden Secrets of Superpermutations

January 16, 2019

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?