The phrase and the physicist
“Shut up and calculate” is shorthand for an attitude to quantum mechanics: the equations predict experiments superbly, so stop arguing about what they mean and use them. It gets pinned on Feynman constantly, probably because it sounds like him. He was famously impatient with philosophising.
But the person who went digging is the physicist who seems to have coined it. In April 1989, N. David Mermin wrote a column for Physics Today in which he counted himself among those who feel uncomfortable when asked what they really think about quantum theory. He added: “If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be ‘Shut up and calculate!’”
Mermin investigates
Years later Mermin came across a paper that spoke of “Feynman’s famous dictum” and the “shut up and calculate interpretation”. So he went looking, and reported the results in “Could Feynman have said this?” (Physics Today, May 2004).
He found the attribution all over the web, with lines like “When asked which interpretation of QM he favored, Feynman replied ‘Shut up and calculate.’” But: “not a single one of the Web sites attributing the phrase to Feynman cited a source or hinted at the circumstances under which he had said it.”
His own answer to the title question is blunt: “Does that mean that Feynman said it? No!” He is careful about his own claim, though. He puts it forward as a “hypothesis that I was the first to use ‘shut up and calculate’ in the context of quantum foundations.” His guess about how Feynman got the credit: “it is only Feynman’s habitual irreverence” that linked the two in people’s minds.
Our take
Misattributed. There’s no recording, book, lecture or letter in which Feynman says it, and the earliest known use belongs to Mermin. We say “earliest known” because a phrase this short could have been said in a corridor before 1989. But a corridor isn’t a source. If you want to use the line, credit David Mermin, Physics Today, 1989. It’s a better story anyway.