At the time, Dijkstra was working at the Mathematical Centre in Amsterdam. He had been asked to demonstrate the powers of the ARMAC [a scientific computer built at the Centre, occupying a classroom] for the forthcoming International Mathematical Conference of 1956.
He started to think about the problem of determining the shortest route between two points on a railroad map. A short time later, Dijkstra and his wife were sitting on the terrace of a cafe sipping coffee on a sunny Saturday morning. Suddenly he fell silent (``My wife knew such periods,'' he says.)
A short while later, he had the algorithm worked out.