The concept of homotopy is a great example of how the language of maths can make intuition precise.

How would you explain the natural numbers to an alien devoid of a number instinct? You could try Peano arithmetic...

Tea gone cold? Don't worry, you can cheer yourself up with the theory of thermodynamics.

How does your phone know what the weather's going to be like?

Wet cats don't cause umbrellas and umbrellas don't cause wet cats.

How good is your estimate?

If you've ever marvelled at a rainbow, you have witnessed dispersion in action!

Whether you want to understand viruses, win at lotto or solve a rubik's cube – you'll need some help from combinatorics.

A hundred pounds is a lot more to someone who's poor than to a millionaire. But how do you measure such differences? Utility theory has the answer.

Curious about calculus? This accessible introduction is for you!

Find out about the beautifully intuitive concept that lies at the heart of calculus.

When you let go of the notions of distance, area, and angles, all you are left with is holes.