Mathematics

Learn why the quadratic formula works and why quadratics are easier to solve than cubics.

Can mathematics handle things that are essentially the same without being exactly equal? Category theorist Eugenia Cheng and host Steven Strogatz discuss the power and pleasures of abstraction.

For decades, mathematicians have been inching forward on a problem about which sets contain evenly spaced patterns of three numbers. Last month, two computer scientists blew past all of those results.

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.