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graph theory

A dartboard with pi at its center.
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.

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

Art for "Computer Scientists Expand the Frontier of Verifiable Knowledge"
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.

Art for "Why Mathematicians Can’t Find the Hay in a Haystack"
Abstractions blog

Why Mathematicians Can’t Find the Hay in a Haystack

In math, sometimes the most common things are the hardest to find.

Illustration of a complex shape casting a shadow
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.

Illustration for "Four Is Not Enough"
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?

Lede art for "First Big Steps Toward Proving the Unique Games Conjecture"
computational complexity

First Big Steps Toward Proving the Unique Games Conjecture

The latest in a new series of proofs brings theoretical computer scientists within striking distance of one of the great conjectures of their discipline.

Illustration of 826-vertex graph for "Decades-Old Graph Problem Yields to Amateur Mathematician"
graph theory

Decades-Old Graph Problem Yields to Amateur Mathematician

By making the first progress on the “chromatic number of the plane” problem in over 60 years, an anti-aging pundit has achieved mathematical immortality.