Want facts and want them fast? Our *Maths in a minute* series explores key mathematical concepts in just a few words. From symmetry to Euclid's axioms, and from binary numbers to the prosecutor's fallacy, learn some maths without too much effort.

Maths in a minute: Non-linearityNon-linear relationships are tricky relationships. Find out why here.

Maths in a minute: HomotopyThe concept of homotopy is a great example of how the language of maths can make intuition precise.

Maths in a minute: Peano arithmeticHow would you explain the natural numbers to an alien devoid of a number instinct? You could try Peano arithmetic...

Maths in a minute: ThermodynamicsTea gone cold? Don't worry, you can cheer yourself up with the theory of thermodynamics.

Maths in a minute: Numerical weather predictionHow does your phone know what the weather's going to be like?

Maths in a minute: Correlation versus causationWet cats don't cause umbrellas and umbrellas don't cause wet cats.

Maths in a minute: DispersionIf you've ever marvelled at a rainbow, you have witnessed dispersion in action!

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

Maths in a minute: Utility theoryA 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.

Maths in a minute: LimitsFind out about the beautifully intuitive concept that lies at the heart of calculus.