The other day a friend posted the following old joke about the level of rigor that mathematicians usually require. (Disclaimer: if you take the joke as a serious claim about the standards of quality in the other fields referenced in the joke, it is an obviously unfair characterization of both astronomy and physics.)
A Mathematician, a Physicist, and an astronomer were travelling north by train. They had just crossed the border into Scotland, when the Astronomer looked out of the window and saw a single black sheep in the middle of a field. “All Scottish sheep are black,” he remarked. “No, my friend,” replied the Physicist, “Some Scottish sheep are black.” At which point the Mathematician looked up from his paper and glanced out the window. After a few second’s thought he said blandly: “In Scotland, there exists at least one field, in which there exists at least one sheep, at least one side of which is black.”
I thought the joke was particularly timely given the recent round of arguments in psychology about the field’s evidentiary standards. As a former psychologist, I am continually surprised that more people in the field won’t yet acknowledge that the field often behaves like the astronomer in the joke even though the empirical tradition in psychology can only justify very weak claims of the sort that the mathematician produces.