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combinatorics

Art for "Color Me Polynomial"
Quantized Academy

Color Me Polynomial

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

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

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

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

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

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?

combinatorics

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.

Illustration for "Four Is Not Enough"
Quantized Academy

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?

Illustration of 826-vertex graph for "Decades-Old Graph Problem Yields to Amateur Mathematician"
graph theory

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.