Think of it: of the infinity of real numbers, those that are most important to mathematics—0, 1, √2, e and π—are located within less than four units … - William Rowan Hamilton

The element of play, which makes recreational mathematics recreational, may take many forms: a puzzle to be solved, a competitive game, a magic trick, paradox, fallacy, or simply mathematics with any sort of curious or amusing fillip.

The nature of mathematical demonstration is totally different from all other, and the difference consists in this—that, instead of showing the contrary of the proposition asserted to be only improbable, it proves it at once to be absurd and impossible. This is done by showing that the contrary of the proposition which is asserted is in direct contradiction to some extremely evident fact, of the truth of which our eyes and hands convince us.

For many, maths is fundamentally beautiful; indeed many mathematicians won’t be entirely satisfied with their work until it has an elegance, simplicity and grace. Others are drawn by its ‘unreasonable effectiveness’ - its power to explain the world we live in.