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graph theory
combinatorics
Rainbow Proof Shows Graphs Have Uniform Parts
Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones.
Multimedia
The Map of Mathematics
Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.
number theory
New Proof Settles How to Approximate Numbers Like Pi
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.
graph theory
A 53-Year-Old Network Coloring Conjecture Is Disproved
In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible.
quantum information theory
Computer Scientists Expand the Frontier of Verifiable Knowledge
The universe of problems that a computer can check has grown. The researchers’ secret ingredient? Quantum entanglement.
Abstractions blog
Why Mathematicians Can’t Find the Hay in a Haystack
In math, sometimes the most common things are the hardest to find.
geometry
Tinkertoy Models Produce New Geometric Insights
An upstart field that simplifies complex shapes is letting mathematicians understand how those shapes depend on the space in which you visualize them.
algorithms
Universal Method to Sort Complex Information Found
The nearest neighbor problem asks where a new point fits into an existing data set. A few researchers set out to prove that there was no universal way to solve it. Instead, they found such a way.
Quantized Academy
Four Is Not Enough
How many colors do you need to color an infinite plane so that no points 1 unit apart are the same color?