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# mathematics

## Latest Articles

### 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: A Hat Trick + 1 of Hat Puzzles

For four game show variations of the hat puzzle, four clever ways to earn a better payoff than you might expect.

### Mathematicians Discover Prime Conspiracy

A previously unnoticed property of prime numbers seems to violate a long-standing assumption about how they behave.

### A Hat Trick of Hat Puzzles

In three new variations of a famous logic puzzle, what are the best strategies for guessing the color of the hat on your head?

### Michael Atiyah’s Imaginative State of Mind

At 86, Britain’s preeminent mathematical matchmaker is still tackling the big questions and dreaming of a union between the quantum and the gravitational forces.

### 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?

### Solution: ‘Sleeping Beauty’s Dilemma’

The solution to this month’s puzzle gets to the bottom of the famously ambiguous Sleeping Beauty probability problem.

### Sleeping Beauty’s Necker Cube Dilemma

Like a visually ambiguous Necker cube, the famous Sleeping Beauty problem can be perceived in two seemingly valid ways.