The dream of the physicist and the mathematician

''Once upon a time a methodologist of science had a nightmare. He dreamt that some physicists, called 'quantum field theorists,' used an approximation scheme, some of the terms of which were infinite. But the quantum field theorists just threw out the infinite terms, kept the remaining finite expressions, and, to add methodological insult to mathematical injury, thereby obtained the best agreement between theory and experiment that existed anywhere in science. As the reader knows, the methodologist woke up to find that his dream was true.''

In Teller, “Infinite Renormalization,” p. 238.
.