The Cult of Pythagoras: Math and Myths

12. The Cult of Pythagoras

201 Mythology deals with gods and heroes, tales that are passed down especially in popular oral traditions. We began with Pythagoras, in a time when religion and science mixed. I don’t know if he really contributed anything to mathematics, but he became portrayed in the form of classic myths: a wise demigod who started a Golden Age, a hero who solved problems and knew the secret of immortality. In time, stories about him increasingly included science and mathematics, and teachers learned to ignore his older tales about gods, sacrifices, and magical powers. But still, other elements from the mythical tradition continued to spread. We should then return to the question of whether Pythagoras proved the hypotenuse theorem. Whether this claim was made by Galileo in a fictional dialogue, or whether it is voiced nowadays by a schoolteacher or painstakingly elaborated by qualified professors of ancient Greek mathematics, my impression is that all such claims suffer from a traditional urge to credit Pythagoras, to heap fame upon fame. Hence an imagined past shines like a light that might orient us. Against my impression, a common defense is to argue that whereas indeed there is no evidence that someone in fact did discover this or that, there is no evidence either that he did not, and therefore it is quite possible that he did. Humbug. Possibilities properly do not exist in the past: either events happened, or they did not; our historical conjectures are not “possible,” they are merely conceivable, products of the imagination, plausible fictions. They are welcome and useful, but they are scarcely history. 12 THE CULT OF PYTHAGORAS There was a serpent in the philosophic paradise, and his name was Pythagoras. —Bertrand Russell, “How to Read and Understand History” 202 T H E C U LT O F P Y T H AG O R A S A popular book relates these allegedly historical claims: Pythagoras developed the idea of numerical logic and was responsible for the first golden age of mathematics. . . . After twenty years of travel Pythagoras had assimilated all the mathematical rules in the known world. . . . Pythagoras had uncovered for the first time the mathematical rule that governs a physical phenomenon and demonstrated that there was a fundamental relationship between mathematics and science. . . . Pythagoras died confident in the knowledge that his theorem, which was true in 500 B.C., would remain true for eternity. . . . Pythagoras constructed a proof that shows that every possible right-angled triangle will obey his theorem. For Pythagoras the concept of mathematical proof was sacred, and it was proof that enabled the Brotherhood to discover so much.1 I find it astonishing that despite their familiarity and currency, all of these claims are fiction. Ancient peoples used to explain away puzzling phenomena by telling tales about gods, rather than with science. Likewise, throughout the centuries many writers have tried to explain the past by telling tales about Pythagoras. Instead, we can write accounts that piece together mosaics of extant evidence without masking guesswork as certainties. Historian David Fowler has worked to reconstruct the state of Greek mathematics during the early years of Plato’s Academy. To do so, he rightly begins by focusing on chronology: by first setting aside most of the later sources, the ones that, for example, attribute achievements to Pythagoras. Following Walter Burkert, Fowler explains that the habit of giving credit to Pythagoras comes not from early Greek mathematics, but from later educational tradition. Fowler gives an example from a secondcentury text that required students to work on the grammar of a sentence about Pythagoras, the philosopher. Subsequently, the image of Pythagoras continued to evolve in the minds of teachers and students. Fowler carried out an amusing survey, asking people to complete the sentence: “Pythagoras the _______ was born in Samos and later went to Croton.” From about 190 replies, “40% said mathematician or some variant (geometer, mystic geometer, triangle theorist . . . ), 28% said philosopher or some similar variant, 12% philosopher-mathematician, and the rest a very mixed bag of activities— number freak, bean-hater, vegetarian, polymath, new ager.”2 Having read the first chapters of the present book, readers who have not studied the many accounts of Pythagoras’s alleged achievements might T H E C U LT O F P Y T H AG O R A S 203 now imagine that it is fairly obvious that such stories are just legends...