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combinatorics
Abstractions blog
Mathematicians Begin to Tame Wild ‘Sunflower’ Problem
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.
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.
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.
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.
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?