M. F. Burnyeat in the London Review of Books:
It is hard to let go of Pythagoras. He has meant so much to so many for so long. I can with confidence say to readers of this essay: most of what you believe, or think you know, about Pythagoras is fiction, much of it deliberately contrived. Did he discover the geometrical theorem that bears his name? No. Did he ponder the harmony of the spheres? Certainly not: celestial spheres were first excogitated decades or more after Pythagoras’ death. Does he even deserve credit for his most famous accomplishment, analysing the mathematical ratios that structure musical concordances? Possibly, but there is little reason to believe the stories about his being the first to discover them, and compelling reason not to believe the oft-told story about how he did it. Allegedly, as he was passing a smithy, he heard that the sounds made by the hammers exemplified the intervals of fourth, fifth and octave, so he measured their weights and found their ratios to be respectively 4:3, 3:2, 2:1. Unfortunately for this anecdote, recently rehashed in the article on Pythagoras in Grove Music Online, the sounds made by a blow do not vary proportionately with the weight of the instrument used.
My problem is that to convince you of such deflationary truths I have to give an account which inevitably is less exciting than, for example, the following extract from Bertrand Russell’s well-known History of Western Philosophy (1946):
Pythagoras . . . was intellectually one of the most important men that ever lived, both when he was wise and when he was unwise. Mathematics, in the sense of demonstrative deductive argument, begins with him, and in him is intimately connected with a peculiar form of mysticism. The influence of mathematics on philosophy, partly owing to him, has, ever since his time, been both profound and unfortunate.