Pythagoras of Samos (b. about 570 – d. about 495 BC) was an Ionian Greek philosopher, mathematician and founder of the religious movement called Pythagoreanism. He was born on the island of Samos and might have travelled widely in his youth, visiting Egypt and other places seeking knowledge. He set up a religious sect around 530 BC in Croton.
Pythagoras was famous (1) as an expert on the fate of the soul after death, who thought that the soul was immortal and went through a series of reincarnations; (2) as an expert on religious ritual; (3) as a wonder-worker who had a thigh of gold and who could be two places at the same time; (4) as the founder of a strict way of life that emphasized dietary restrictions, religious ritual and rigorous self discipline.
Legend has it that upon completion of his famous theorem, Pythagoras sacrificed 100 oxen. Although he is credited with the discovery of the famous theorem, it is not possible to tell if Pythagoras is the actual author. The Pythagoreans wrote many geometric proofs, but it is difficult to ascertain who proved what, as the group wanted to keep their findings secret.
Pythagoras almost certainly learned his famous theorem about right-angled triangles from the Babylonians, but we owe to him a far greater idea: “All is number,” he declared, becoming the first person to say that the physical world could be described by the language of mathematics.
His immediate followers were strongly influenced by him, and even until today Pythagoras shines through the mist of ages as one of the brightest figures of early Greek antiquity. The Pythagorean theorem is often cited as the beginning of mathematics in Western culture
All things are numbers. Mathematics is the basis for everything, and geometry is the highest form of mathematical studies. The physical world can understood through mathematics.
The Pythagoreans, as a result of their religious beliefs and careful study of mathematics, developed a cosmology (dealing with the structures of the universe) which differed in some important respects from the world views at the time, the most important of which was their view of the Earth as a sphere which circled the center of the universe.
Pythagoras developed a modern theory of vision much simpler than that of Plato. This theory maintained that light is emitted from luminous bodies, can suffer reflections, and causes the sensation of sight when it enters the eyes. He was the first Greek to realize that the morning star and evening star were both the planet Venus.
After Pythagoras introduced the idea of eternal recurrence into Greek thought, which was apparently motivated by his studies of earlier Egyptian scriptures, the idea soon became popular in Greece. It was Pythagoras’ ambition to reveal in his philosophy the validity and structure of a higher order, the basis of the divine order, for which souls return in a constant cycle.
All evidence points to Pythagoras as the source of metempsychosis in the Greek world as a doctrine with moral implications.
His religious teachings were based on the doctrine (teaching) of metempsychosis, which teaches that the soul never dies and is destined to a cycle of rebirths until it is able to free itself from the cycle through the purity of its life.
Pythagoras also related music to mathematics. He had long played the seven string lyre, and learned how harmonious the vibrating strings sounded when the lengths of the strings were proportional to whole numbers, such as 2:1, 3:2, 4:3.
Pythagoras wrote nothing, nor were there any detailed accounts of his thought written by contemporaries. By the first centuries BCE, moreover, it became fashionable to present Pythagoras in a largely unhistorical fashion as a semi-divine figure, who originated all that was true in the Greek philosophical tradition, including many of Plato's and Aristotle's mature ideas.
By this time Thales was an old man and, although he created a strong impression on Pythagoras, he probably did not teach him a great deal. However he did contribute to Pythagoras's interest in mathematics and astronomy, and advised him to travel to Egypt to learn more of these subjects. Thales's pupil, Anaximander, lectured on Miletus and Pythagoras attended these lectures. Anaximander certainly was interested in geometry and cosmology and many of his ideas would influence Pythagoras's own views.
Born c. 570 BC on the cultured Aegean island of Samos, Pythagoras founded a school at Croton in Southern Italy where he and his followers began to unravel the deep truths behind such everyday tasks as tuning a lyre.