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graph theory
combinatorics
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.
2022 Fields and Abacus Medals
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.
graph theory
Mathematical Connect-the-Dots Reveals How Structure Emerges
A new proof identifies precisely how large a mathematical graph must be before it contains a regular substructure.
networks
Researchers Achieve ‘Absurdly Fast’ Algorithm for Network Flow
Computer scientists can now solve a decades-old problem in practically the time it takes to write it down.
topology
Unimaginable Surfaces Discovered After Decades-Long Search
Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.
graph theory
Elegant Six-Page Proof Reveals the Emergence of Random Structure
Two young mathematicians have astonished their colleagues with a full proof of the Kahn-Kalai conjecture — a sweeping statement about how structure emerges in random sets and graphs.
Quantized Academy
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.
geometry
An Ancient Geometry Problem Falls to New Mathematical Techniques
Three mathematicians show, for the first time, how to form a square with the same area as a circle by cutting them into interchangeable pieces that can be visualized.
information theory
Qubits Can Be as Safe as Bits, Researchers Show
A new result shows that quantum information can theoretically be protected from errors just as well as classical information can.