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# Mathematics

## Latest Articles

### The Journey to Define Dimension

The concept of dimension seems simple enough, but mathematicians struggled for centuries to precisely define and understand it.

### New Math Book Rescues Landmark Topology Proof

Michael Freedman’s momentous 1981 proof of the four-dimensional Poincaré conjecture was on the verge of being lost. The editors of a new book are trying to save it.

### Banach-Tarski and the Paradox of Infinite Cloning

One of the strangest results in mathematics explains how it’s possible to turn one sphere into two identical copies, simply by rearranging its pieces.

### Math Can, in Theory, Help You Escape a Hungry Bear

How readers used their geometry skills to survive a dangerous puzzle.

### 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.