Pythagoras is the mythical Greek founder of an ancient school of religion, philosophy, geometry, and astronomy. His life has been dated to 570BC – 490 BC. He was raised on the island of Samos off the coast of modern day Turkey. Some suggest he was the son of a stone-engraver. As he grew, Pythagoras emigrated to southern Italy where his philosophy flourished.
His school in Italy was something like an ascetic, religious commune. He is said to have been a teacher of many women, as well as men. In fact, years after his death, a cult arose regarding the divinity of Pythagoras. He preached a restrictive diet, perhaps of vegetarianism (as depicted by Ovid in his masterful Metamorphoses, and was later cited by Shakespeare and Montaigne), and he taught of the immortality and the transmigration (or metampsychosis) of the soul (much like Plato in Book X of the Republic – for which Pythagoras was later praised by Christian and Islamic writers) and he advanced a theory of planetary musical and mathematical harmony (an inquiry that continues with certain writings of Kepler and Copernicus – in fact both writers pay homage to Pythagoras in their writings). Newton, Einstein, Whitehead, and other modern giants of science and natural philosophy have all given a nod to the power and authority of Pythagoras. Plato’s Timaeus is one of the most vivid depictions of Pythagoreanism we have in our possession today. Platonism, and perhaps more potently Neo-Platonism, have been modeled rather closely on the mysteries of the Pythagoreans. Pythagoras’s esoteric numerology appears as an influence in Dante’s Paradiso, and also in the American Transcendentalists, such as Thoreau. Pythagoras taught the importance of early morning walks, the sacredness of music for the soul, the importance of physical exercise, Aristotle describes the Pythagoreans as the first to take up the cause of mathematics, and thus they believed mathematics was the root of all things (in contrast to other early natural philosophers pursued first principles through metaphysical claims, like Thales or Heraclitus).
Pythagoras and his school were referenced earliest by Plato and Aristotle, and then sayings attributed to him and his life are attested to in various fragments quoting older texts, until Diogenes Laertius’s “Life of Pythagoras” around 200-250 AD, Porphyry’s (the Neoplatonist) Life of Pythagoras in the 3rd century, and Iamblichus’s (the Arab Neoplatonist) On the Pythagorean Life from the 3rd or 4th century.
Nothing has survived if Pythagoras wrote anything at all. The only fragments were have are some fragments attributed to Heraclitus and a satirical poem attributed to Xenophanes. Much of our account of Pythagoras comes from the Romans, particularly Diogenes Laërtius’s, however by this time, hundreds of years had passed since the death of Pythagoras and his mystery cult was the subject of great fascination. Perhaps he was a contemporary of Anaximander and Anaximenes. Some have suggested Ptyhagoras studied among eastern mystics, like Zoroaster (or Zarathustra) and other Hebrew rabbis, even Plutarch has account of Pythagoras traveling to Egypt to study. Some say he was a student of Orpheus, and thus was inducted into the ancient Orphic mysteries. Perhaps his moral teaching came from a fabled meeting with Thales, or perhaps it came from the Delphic oracle. The anonymous Suda suggests Pythagoras had four children, despite his proclamations and restrictions regarding sexual activity. With regard to politics, he regularly advised the leaders of the city of Croton, where he resided in southern Italy, and he rejected democracy. Rumors about of Pythagoras as a “wonder-worker” with a golden thigh or as the human incarnation of Apollo.
At any rate, Pythagoras’s mythology has been significant, but perhaps nothing has lasted in the minds of men more than the fabled image of Pythagoras discovering the “Pythagorean Theorem” – a theory of right angles triangles, a subject addressed in Euclid’s Elements. As a modern equation, the theorem can be written as follows:
In other words, in right angled triangles, the square of the hypotenuse (c) is equal to the sum of the square of the other two sides.
In Euclid’s proof, each side of a right triangle is also the side of a square. As with most geometric shapes found in Euclidean space, the theorem rests on an assumption of proportionality of two similar triangles. Euclid’s proof (1.41) is presented as axiomatic, the oldest such surviving proof, outside of certain texts from India, Babylon, and even China in which the theorem is used.