The Dark Ages are often painted as an era of scholarly decline. The Western Roman Empire was on its way out, books were few and far between, and, if you believe the stereotype, mud-splattered peasants ran around in rags.

However, it was far more intellectually vibrant than you might imagine. Out of this era emerged a set of ‘problems to sharpen the young,’ including the famous river crossing puzzle that’s still taught in maths today. The presumed author of these riddles is Alcuin of York – ‘the most learned man in the world.’ And it was this monk and his puzzles that laid the foundations for a branch of mathematics called combinatorics – the thinking behind today’s computer coding and cryptography.

Philip Ball speaks to historian Mary Garrison from the University of York to learn of Alcuin's character and how he encouraged his students to learn for the sake of learning, as opposed to salvation. And University College London mathematician Hannah Fry shows Philip just how much of a role combinatorics plays in today’s world.

Picture: White horned goat chewing a cabbage leaf, Credit: Oxana Medvedeva

Producer: Graihagh Jackson