Math

Math provokes dread in so many people—yet we are all born with a sense for numbers.

Two mathematicians have proven Patterson’s conjecture, which was designed to explain a strange pattern in sums involving prime numbers.

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

How the modern world arose from imaginary numbers.

Three mathematicians show, for the first time, how to form a square with the same area as a circle by cutting them into interchangeable pieces that can be visualized.

New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs.

To understand self-organization in nature, behold the sandpile.

As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent.

The most widely used technique for finding the largest or smallest values of a math function turns out to be a fundamentally difficult computational problem.

There’s a rude charm to the title, “Why Your Friends Have More Friends Than You.” It’s catchy, like the title of an antagonistic explainer: Here are the causes of your lackluster social life. It sounds more like a New York Times op-ed than an academic paper. But in fact, “Why Your Friends Have More Friends […]

Mathematical tools that proved essential during the pandemic were in many cases invented by mathematicians who had no particular goal in mind.

A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections.

Originally devised as a rigorous means of counting holes, homology provides a scaffolding for mathematical ideas, allowing for a new way to analyze the shapes within data.