The Four Colour Theorem - the statement that four colours suffice to fill in any map so that neighbouring countries are always coloured differently - has had a long and controversial history. It was first conjectured 150 years ago, and finally (and infamously) proved in 1976 with much of the work done by a computer. The published proof relied on checking 1432 special cases, which took more than 1,000 hours of computer time.
Many people, when they look back, can pinpoint the precise moment when their interest in mathematics was awakened - it was when they found a puzzle that intrigued them. Perhaps they now realise the puzzle was trivial or insignificant, but at the time something about it captured their imagination and started them on a path that may have led very far - perhaps even into fundamental mathematical research.
Ballet and mathematics - not a combination that you often come across, but one that works beautifully in Frederick Ashton's 1948 ballet, Scénes de ballet. From the geometric patterns on the men's tunics and the perpendicular angle of the ballerina's tutu, to the movements and positioning of the dancers themselves, this ballet is a celebration of mathematics. Ashton was inspired by mathematics, and, according to the programme notes, used a system of Euclidean geometry to choreograph the piece.
Not many books about maths have chapters that start "The dead man seemed to stare at me in a most disconcerting way." But maybe more should - this book is a highly entertaining read, crossing sound mathematical exposition with the classic Sherlock Holmes style of investigation.
This video, aimed at students aged 16+, opens with Professor Chris Budd holding the plastic yellow duck he is entering in the Annual Bath Plastic Duck Race. Competition is stiff - there are over 3,000 contestants - but how can we predict who will win? Very few competitors have form, and it's hard to tell much about their training regimens... so is the outcome totally unpredictable?