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combinatorics

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

By Max G. Levy
February 16, 2021
Read Later

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

By Kevin Hartnett
December 16, 2020
Read Later

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

By Kevin Hartnett
November 4, 2020
Read Later

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

By Stephanie DeMarco
September 15, 2020
Read Later

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

By Kevin Hartnett
August 26, 2020
Read Later

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

By Kevin Hartnett
August 19, 2020
Read Later

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

By Erica Klarreich
August 3, 2020
Read Later

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

An animation showing a 3-by-3 Latin square, with numbers color coded, and the equivalent graph.
Abstractions blog

‘Rainbows’ Are a Mathematician’s Best Friend

By Kevin Hartnett
March 18, 2020
Read Later

“Rainbow colorings” recently led to a new proof. It’s not the first time they’ve come in handy.

Animated demonstration of a colorful complete graph being tiled by a smaller tree
combinatorics

Rainbow Proof Shows Graphs Have Uniform Parts

By Kevin Hartnett
February 19, 2020
Read Later

Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones.


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