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combinatorics
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From Systems in Motion, Infinite Patterns Appear
Mathematicians are finding inevitable structures in sufficiently large sets of integers.
Hypergraphs Reveal Solution to 50-Year-Old Problem
In 1973, Paul Erdős asked if it was possible to assemble sets of “triples” — three points on a graph — so that they abide by two seemingly incompatible rules. A new proof shows it can always be done.
For His Sporting Approach to Math, a Fields Medal
With Hugo Duminil-Copin, thinking rarely happens without moving. His insights into the flow-related properties of complex networks have earned him the Fields Medal.
He Dropped Out to Become a Poet. Now He’s Won a Fields Medal.
June Huh wasn’t interested in mathematics until a chance encounter during his sixth year of college. Now his profound insights connecting combinatorics and geometry have led to math’s highest honor.
In Times of Scarcity, War and Peace, a Ukrainian Finds the Magic in Math
With her homeland mired in war, the sphere-packing number theorist Maryna Viazovska has become the second woman to win a Fields Medal in the award’s 86-year history.
What a Math Party Game Tells Us About Graph Theory
Play this simple math game with your friends to gain insights into fundamental principles of graph theory.
Euler’s 243-Year-Old ‘Impossible’ Puzzle Gets a Quantum Solution
A surprising new solution to Leonhard Euler’s famous “36 officers puzzle” offers a novel way of encoding quantum information.
Mathematician Hurls Structure and Disorder Into Century-Old Problem
A new paper shows how to create longer disordered strings than mathematicians had thought possible, proving that a well-known recent conjecture is “spectacularly wrong.”
Mathematicians Find Structure in Biased Polynomials
New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs.