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# Mathematics

## Latest Articles

### How Big Data Carried Graph Theory Into New Dimensions

Researchers are turning to the mathematics of higher-order interactions to better model the complex connections within their data.

### Turing Patterns Turn Up in a Tiny Crystal

The mechanism behind leopard spots and zebra stripes also appears to explain the patterned growth of a bismuth crystal, extending Alan Turing’s 1952 idea to the atomic scale.

### Mathematicians Solve Decades-Old Classification Problem

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.

### Galois Groups and the Symmetries of Polynomials

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

### Proof Assistant Makes Jump to Big-League Math

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

### How to Find Rational Points Like Your Job Depends on It

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

### New Shape Opens ‘Wormhole’ Between Numbers and Geometry

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.

### How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer.

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

### Mathematicians Prove Symmetry of Phase Transitions

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