The golden ratio has many amazing properties. But is it really a secret of nature and the epitome of beauty?

We take the real numbers for granted, but what are they really?

Here's one of the most elegant proofs in all of maths. Rejoice in its simplicity!

The Plus anniversary year — A word from the editors

Nineteenth-century German mathematician Leopold Kronecker once said

God created the integers, all the rest is the work of man.

For millennia, puzzles and paradoxes have forced mathematicians to continually rethink their ideas of what proofs actually are. Jon Walthoe explains the tricks involved and how great thinkers like Pythagoras, Newton and Gödel tackled the problems.