Common Errors (31): Pythagoras

Pythagoras (Musei Capitolini, Rome)

One of the most famous anecdotes from Antiquity deals with the philosopher-mathematician Pythagoras (c.570-c.495), who discovered the theorem that is named after him, and sacrificed an ox – or even one hundred oxen – to celebrate this. The joke that ever since the oxen are afraid of scientific progress has been used a bit too often by scientists dismissing critical reviews.

For several reasons, this anecdote is problematic. In the first place, because it is probably one of those unhistorical tales attributed to Pythagoras. Another example is his legendary visit to the ancient Near East, which is referred to for the first time in the second century CE, when Apuleius says that the Samian sage was “believed by some to have been a pupil of Zoroaster” (Apology, 31). In his Refutation of All Heresies (1.2.12), Hippolytus of Rome (early third century CE) implies that he had read this story in a book by Aristoxenus of Tarentum, a contemporary of Alexander the Great. Yet, even if Hippolytus’ is right (which is doubtful), this means that Pythagoras’ eastern trip is unmentioned by earlier authors describing Pythagoras’ life and opinions, even though Herodotus, Plato, and Aristotle had many opportunities to discuss it. The story is almost certainly invented, just like Pythagoras’ visit to India.

The same applies to the theorem that in right-angled triangles the square on the hypothenuse is equal to the sum of the squares on the sides containing the right angle. Pythagoras and his pupils were interested in mathematical proof, certainly, but the first to attribute the theorem to the Samian sage is Proclus (412-485), who lived almost one thousand years after Pythagoras (On Euclid I, 426.6-14 [Friedlein]).

A second problem is that the principle was already well-known prior to Pythagoras. Several cuneiform texts from the twenty-first and twentieth century BCE prove the that the ancient Babylonians not only knew that a²+b²=c², but also knew that this principle was generally applicable. There is a difference in the way Babylonians and Greeks proved this rule, but it is possible to overstate Pythagoras’ importance.

Literature

J. Høyrup, ‘The Pythagorean “Rule” and “Theorem” – Mirror of the Relation between Babylonian and Greek Mathematics’ in: J. Renger (red.): Babylon. Focus mesopotamischer Geschichte, Wiege früher Gelehrsamkeit, Mythos in der Moderne (1999).

<Overview of Common Errors>

One Response to Common Errors (31): Pythagoras

  1. Bill says:

    To be extremely precise, in English: to speak of the squares “on” the sides sounds geometric, in which case we should speak of “the areas of the squares” (because geometric figures are never “equivalent”. Otherwise, we might speak (exponentially) of the arithmetic square, in which case we’d say “of” (not “on”). But now I’m just being picky. 😉

    I’m honestly curious though – is there a different convention in Dutch?

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