Mathematics

In a recent paper, two mathematicians showed that a particular pattern is unavoidable when fractions are categorized.

Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical physics.

Lek-Heng Lim uses tools from algebra, geometry and topology to answer questions in machine learning.

Mathematicians have struggled to understand the moduli space of graphs. A new paper uses tools from physics to peek inside.

Large language models still struggle with basic reasoning tasks. Two new papers that apply machine learning to math provide a blueprint for how that could change.

Is it possible to fill space “cubically” with shapes that act like spheres? A proof at the intersection of geometry and theoretical computer science says yes.

As The Joy of Why podcast returns for a second season, producer Polly Stryker and host Steven Strogatz invite listeners to join them and their brilliant new guests on another voyage of discovery.

A new proof shows that a knot some thought would contradict the famed slice-ribbon conjecture doesn’t.

In three-dimensional space, the surface of a black hole must be a sphere. But a new result shows that in higher dimensions, an infinite number of configurations are possible.