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graph theory

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.

Art for "A 53-Year-Old Network Coloring Conjecture Is Disproved"
graph theory

A 53-Year-Old Network Coloring Conjecture Is Disproved

June 17, 2019

In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible.

Art for "Computer Scientists Expand the Frontier of Verifiable Knowledge"
quantum information theory

Computer Scientists Expand the Frontier of Verifiable Knowledge

May 23, 2019

The universe of problems that a computer can check has grown. The researchers’ secret ingredient? Quantum entanglement.