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graph theory

Photo of Ashwin Sah standing in front of a sculpture in a park
Abstractions blog

Undergraduate Math Student Pushes Frontier of Graph Theory

November 30, 2020

At 21, Ashwin Sah has produced a body of work that senior mathematicians say is nearly unprecedented for a college student.

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.

An abstract illustration showing broken tools, cubes, numbers and other abstract representations of impossible math
Quantized Columns

When Math Gets Impossibly Hard

September 14, 2020

Mathematicians have long grappled with the reality that some problems just don’t have solutions.

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

March 18, 2020

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

Animation showing toy-like depictions of computer science, quantum mechanics and pure math affecting each other.
computational complexity

Landmark Computer Science Proof Cascades Through Physics and Math

March 4, 2020

Computer scientists established a new boundary on computationally verifiable knowledge. In doing so, they solved major open problems in quantum mechanics and pure mathematics.

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

Rainbow Proof Shows Graphs Have Uniform Parts

February 19, 2020

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

Multimedia

The Map of Mathematics

February 13, 2020

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

A dartboard with pi at its center.
number theory

New Proof Settles How to Approximate Numbers Like Pi

August 14, 2019

The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer.