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# geometry

## Latest Articles

### A Unified Theory of Randomness

Researchers have uncovered deep connections among different types of random objects, illuminating hidden geometric structures.

### Handicapping the 2018 Fields Medal

Peter Scholze is a favorite to win one of the highest honors in mathematics for his contributions in number theory and geometry.

### The Oracle of Arithmetic

At 28, Peter Scholze is uncovering deep connections between number theory and geometry.

### Sphere Packing Solved in Higher Dimensions

The Ukrainian mathematician Maryna Viazovska has solved the centuries-old sphere-packing problem in dimensions eight and 24.

### Solution: ‘The Problem With Dancing Shapes’

Assigning elements from a large collection to one of two categories can yield almost “magical” predictions about highly complicated problems without actually solving them.

### The Problem With Dancing Shapes

In a geometrically designed social club, how do dancing, triangles and hexagons mix?

### A Life in Games

The mathematician John Horton Conway’s myriad accomplishments — including the Game of Life, sprouts and the surreal numbers — are the product of a mind at play.

### A Proof That Some Spaces Can’t Be Cut

Mathematicians have solved the century-old triangulation conjecture, a major problem in topology that asks whether all spaces can be subdivided into smaller units.

### Scientists Conjure Curves From Flatness

Researchers have found a set of rules for imbuing flat surfaces with curvature, enabling them to form a virtually unlimited range of three-dimensional structures.