Mathematics

Crows recently demonstrated an understanding of the concept of zero. It’s only the latest evidence of animals’ talents for numerical abstraction — which may still differ from our own grasp of numbers.

A pair of researchers has shown that trying to classify groups of numbers called “torsion-free abelian groups” is as hard as it can possibly be.

By focusing on relationships between solutions to polynomial equations, rather than the exact solutions themselves, Évariste Galois changed the course of modern mathematics.

Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics.

Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.

Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program.

The Standard Model is a sweeping equation that has correctly predicted the results of virtually every experiment ever conducted, as Quanta explores in a new video.

For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.

A group of mathematicians has shown that at critical moments, a symmetry called rotational invariance is a universal property across many physical systems.