On a late September day in 1956, John Horton Conway left home with a trunk on his back. He was a skinny 18-year-old, with long, unkempt hair – a sort of proto-hippie – and although he generally preferred to go barefoot, on this occasion he wore strappy Jesus sandals. He travelled by steam train from Liverpool to Cambridge, where he was to start life as an undergraduate. During the five-hour journe