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combinatorics

Side-by-side illustrations of the same linear hypergraph. The edges of the hypergraph are colored in the illustration on the right, but not in the illustration on the left.
combinatorics

Mathematicians Settle Erdős Coloring Conjecture

April 5, 2021

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.

Abel Prize

Pioneers Linking Math and Computer Science Win the Abel Prize

March 17, 2021

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

Po-Shen Loh standing on a stairway in front of a colored wall outside of his office in Pittsburgh.
Q&A

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

February 16, 2021

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

Mathematician Lauren Williams standing in front of a whiteboard that has mathematics written on it.
combinatorics

A Mathematician’s Unanticipated Journey Through the Physical World

December 16, 2020

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

Illustration showing a large multicolored graph on top and a smaller one below, which is rising and growing bigger
combinatorics

Disorder Persists in Larger Graphs, New Math Proof Finds

November 4, 2020

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.

Aerial image of a complicated road network.
Abstractions blog

A New Algorithm for Graph Crossings, Hiding in Plain Sight

September 15, 2020

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

Photo of Marijn Heule walking among computer processors
Abstractions blog

Computer Scientists Attempt to Corner the Collatz Conjecture

August 26, 2020

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

Illustration of floating metal cubes joining together, some of their faces yellow
geometry

Computer Search Settles 90-Year-Old Math Problem

August 19, 2020

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.

number theory

Landmark Math Proof Clears Hurdle in Top Erdős Conjecture

August 3, 2020

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