## ‘Nasty’ Geometry Breaks a Decades-Old Tiling Conjecture

Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. They ..

1 week ago
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## Hypergraphs Reveal a Solution to a 50-Year-Old Problem

In 1973, Paul Erdős asked if it was possible to assemble sets of “triples”—three points on a graph—so that they abide by two seemingly incompatible ..

6 months ago
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## A Grad Student’s Side Project Proves a Prime Number Conjecture

Jared Duker Lichtman proved a long-standing conjecture relating prime numbers to a broad class of “primitive” sets. To his adviser, it was a “complete ..

8 months ago
99
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## A Father-Son Team Solves a Geometry Problem With Infinite Folds

The result could help researchers answer a larger question about flattening objects from the fourth dimension to the third dimension. ..

8 months ago
95
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## Math’s ‘Oldest Problem Ever’ Gets a New Answer

A new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of fractions. ..

11 months ago
155
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## Mathematicians Outwit a Hidden Number ‘Conspiracy’

Decades ago, a mathematician posed a warmup problem for difficult questions about prime numbers. It turned out to be just as difficult to solve—until ..

1 year ago
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## Euler’s 243-Year-Old ‘Impossible’ Puzzle Gets a Quantum Solution

A surprising new solution to the famous “36 officers puzzle” offers a novel way of encoding quantum information. ..

1 year ago
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## A Mathematician Answers a 150-Year-Old Chess Problem

The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. ..

1 year ago
312
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## Pigeons, Curves, and the Traveling Salesperson Problem

Mathematician Ian Stewart explains the twisty history of combinatorial optimization. ..

1 year ago
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## Mathematicians Settle the Erdős Coloring Conjecture

Fifty years ago, three mathematicians came up with a graph theory problem that they thought they might solve on the spot. A team has finally settled it. ..

2 years ago
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