Everything we buy, from books to baked beans, has a product code printed on it. More sophisticated check-digit codes exist on official documents, bank notes and air tickets. What are they for and what do they mean? We take a look at the mathematical structure of these codes and explain their purposes. And in this age of boundless surveillance, are there enough numbers for each of us to have a serial number of our own?

Talk given by Professor John D Barrow FRS