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# mathematics

## Latest Articles

### Why Sleeping Beauty Is Lost in Time

The famous Sleeping Beauty problem has divided probability theorists, decision theorists and philosophers for over 15 years. Puzzle columnist Pradeep Mutalik claims to have discovered the source of confusion.

### 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.