Pythagoras

Pythagoras was an ancient Greek mathematician and philosopher, best known for the Pythagorean theorem. He founded the Pythagorean school of mathematics in Croton, where he taught his followers various principles of mathematics, music, and philosophy. Pythagoras believed in the concept of numbers as the foundation of the universe and contributed significantly to the development of mathematics. His teachings and theories had a profound influence on the subsequent development of Western mathematics and philosophy.No authentic writings of Pythagoras have survived,[6][7][8] and almost nothing is known for certain about his life.[9][10][11] The earliest sources on Pythagoras's life are brief, ambiguous, and often satirical.[8][12][13] The earliest source on Pythagoras's teachings is a satirical poem probably written after his death by Xenophanes of Colophon, who had been one of his contemporaries.[14][15] In the poem, Xenophanes describes Pythagoras interceding on behalf of a dog that is being beaten, professing to recognize in its cries the voice of a departed friend.[13][14][16][17] Alcmaeon of Croton, a doctor who lived in Croton at around the same time Pythagoras lived there,[14] incorporates many Pythagorean teachings into his writings[18] and alludes to having possibly known Pythagoras personally.[18] The poet Heraclitus of Ephesus, who was born across a few miles of sea away from Samos and may have lived within Pythagoras's lifetime,[19] mocked Pythagoras as a clever charlatan,[12][19] remarking that "Pythagoras, son of Mnesarchus, practiced inquiry more than any other man, and selecting from these writings he manufactured a wisdom for himself—much learning, artful knavery."[12][19] Fictionalized portrait of Pythagoras from a 17th-century engraving The Greek poets Ion of Chios (c. 480 – c. 421 BC) and Empedocles of Acragas (c. 493 – c. 432 BC) both express admiration for Pythagoras in their poems.[20] The first concise description of Pythagoras comes from the historian Herodotus of Halicarnassus (c. 484 – c. 420 BC),[21] who describes him as "not the most insignificant" of Greek sages[22] and states that Pythagoras taught his followers how to attain immortality.[21] The accuracy of the works of Herodotus is controversial.[23][24][25][26][27] The writings attributed to the Pythagorean philosopher Philolaus of Croton, who lived in the late fifth century BC, are the earliest texts to describe the numerological and musical theories that were later ascribed to Pythagoras.[28] The Athenian rhetorician Isocrates (436–338 BC) was the first to describe Pythagoras as having visited Egypt.[21] Aristotle wrote a treatise On the Pythagoreans, which no longer exists.[29] Some of it may be preserved in the Protrepticus. Aristotle's disciples Dicaearchus, Aristoxenus, and Heraclides Ponticus also wrote on the same subject.[30] Most of the major sources on Pythagoras's life are from the Roman period,[31] by which point, according to the German classicist Walter Burkert, "the history of Pythagoreanism was already... the laborious reconstruction of something lost and gone."[30] Three ancient biographies of Pythagoras have survived from late antiquity,[11][31] all of which are filled primarily with myths and legends.[11][31][32] The earliest and most respectable of these is the one from Diogenes Laërtius's Lives and Opinions of Eminent Philosophers.[31][32] The two later biographies were written by the Neoplatonist philosophers Porphyry and Iamblichus[31][32] and were partially intended as polemics against the rise of Christianity.[32] The later sources are much lengthier than the earlier ones,[31] and even more fantastic in their descriptions of Pythagoras's achievements.[31][32] Porphyry and Iamblichus used material from the lost writings of Aristotle's disciples[30] and material taken from these sources is generally considered to be the most reliable.