‘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 ..
Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. They ..
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 ..
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 ..
The result could help researchers answer a larger question about flattening objects from the fourth dimension to the third dimension. ..
A new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of fractions. ..
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 ..
A surprising new solution to the famous “36 officers puzzle” offers a novel way of encoding quantum information. ..
The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. ..
Mathematician Ian Stewart explains the twisty history of combinatorial optimization. ..
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. ..