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 ..
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 ..
With her homeland mired in war, the sphere-packing number theorist Maryna Viazovska has become the second woman to win a Fields Medal in the award’s ..
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 ..
More than 30 years ago, Andreas Floer changed geometry. Now, two mathematicians have finally figured out how to extend his revolutionary perspective. ..
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. ..
The same phenomenon by which an opera singer can shatter a wineglass also underlies the very existence of subatomic particles. ..
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 ..
Researchers find that densely packed neurons play an outsize role in quantitative skill—calling into question old assumptions about evolution. ..
A surprising new solution to the famous “36 officers puzzle” offers a novel way of encoding quantum information. ..