Pythagoras
/pᵻˈθæɡərəs/;
Greek: Πυθαγόρας ὁ Σάμιος
Pythagóras ho Sámios
“Pythagoras the Samian”,
or simply Πυθαγόρας;
Πυθαγόρης in Ionian Greek
570 – c. 495 BC
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Ionian Greek philosopher, mathematician, and putative founder of the Pythagoreanism movement. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem which bears his name.
Legend and obfuscation cloud his work, so it is uncertain whether he truly contributed much to mathematics or natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues or successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were important. It was said that he was the first man to call himself a philosopher, or lover of wisdom, and Pythagorean ideas exercised a marked influence on Plato, and through him, all of Western philosophy.
PYTHAGOREAN THEOREM:
Since the fourth century AD, Pythagoras has commonly been given credit for discovering the Pythagorean theorem that states that in a right-angled triangle the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of the other two sides—that is, a^2 + b^2 = c^2.
While the theorem that now bears his name was known and previously utilised by the Babylonians and Indians, he, or his students, are often said to have constructed the first proof. It must, however, be stressed that the way in which the Babylonians handled Pythagorean numbers implies that they knew that the principle was generally applicable, and knew some kind of proof, which has not yet been found in the (still largely unpublished) cuneiform sources. Because of the secretive nature of his school and the custom of its students to attribute everything to their teacher, there is no evidence that Pythagoras himself worked on or proved this theorem. For that matter, there is no evidence that he worked on any mathematical or meta-mathematical problems. Some attribute it as a carefully constructed myth by followers of Plato over two centuries after the death of Pythagoras, mainly to bolster the case for Platonic meta-physics, which resonate well with the ideas they attributed to Pythagoras. This attribution has stuck down the centuries up to modern times. The earliest known mention of Pythagoras’s name in connection with the theorem occurred five centuries after his death, in the writings of Cicero and Plutarch.
Musical theories and investigations
According to legend, the way Pythagoras discovered that musical notes could be translated into mathematical equations was when he passed blacksmiths at work one day and thought that the sounds emanating from their anvils were beautiful and harmonious and decided that whatever scientific law caused this to happen must be mathematical and could be applied to music. He went to the blacksmiths to learn how the sounds were produced by looking at their tools. He discovered that it was because the hammers were “simple ratios of each other, one was half the size of the first, another was 2/3 the size, and so on”.
This legend has since proven to be false by virtue of the fact that these ratios are only relevant to string length (such as the string of a monochord), and not to hammer weight. However, it may be that Pythagoras was indeed responsible for discovering the properties of string length.
Pythagoreans elaborated on a theory of numbers, the exact meaning of which is still debated among scholars. Another belief attributed to Pythagoras was that of the “harmony of the spheres”. Thus the planets and stars moved according to mathematical equations, which corresponded to musical notes and thus produced a symphony.
Tetractys
Pythagoras was also credited with devising the tetractys, the triangular figure of four rows which add up to the perfect number, ten. As a mystical symbol, it was very important to the worship of the Pythagoreans who would swear oaths by it.
Religion and science
Heraclides Ponticus reports the story that Pythagoras claimed that he had lived four previous lives that he could remember in detail. One of his past lives, as reported by Aulus Gellius, was as a beautiful courtesan. According to Xenophanes, Pythagoras heard the cry of his dead friend in the bark of a dog. Pythagoras maintained that the soul has three vehicles: (1) the ethereal, which is luminous and celestial, in which the soul resides in a state of bliss in the stars; (2) the luminous, which suffers the punishment of sin after death; and (3) the terrestrial, which is the vehicle it occupies on this earth.
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