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# combinatorics

## Latest Articles

### Mathematicians Settle Erdős Coloring Conjecture

Fifty years ago, Paul Erdős and two other mathematicians came up with a graph theory problem that they thought they might solve on the spot. A team of mathematicians has finally settled it.

### Pioneers Linking Math and Computer Science Win the Abel Prize

Avi Wigderson and László Lovász won for their work developing complexity theory and graph theory, respectively, and for connecting the two fields.

### The Coach Who Led the U.S. Math Team Back to the Top

Po-Shen Loh has harnessed his competitive impulses and iconoclastic tendencies to reinvigorate the U.S. Math Olympiad program.

### A Mathematician’s Unanticipated Journey Through the Physical World

Lauren Williams has charted an adventurous mathematical career out of the pieces of a fundamental object called the positive Grassmannian.

### Disorder Persists in Larger Graphs, New Math Proof Finds

David Conlon and Asaf Ferber have raised the lower bound for multicolor “Ramsey numbers,” which quantify how big graphs can get before patterns inevitably emerge.

### A New Algorithm for Graph Crossings, Hiding in Plain Sight

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory.

### Computer Scientists Attempt to Corner the Collatz Conjecture

A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot.

### Computer Search Settles 90-Year-Old Math Problem

By translating Keller’s conjecture into a computer-friendly search for a type of graph, researchers have finally resolved a problem about covering spaces with tiles.

### Landmark Math Proof Clears Hurdle in Top Erdős Conjecture

Two mathematicians have proved the first leg of Paul Erdős’ all-time favorite problem about number patterns.