Pythagoras, Greek philosopher, mathematician, and founder of the Pythagorean brotherhood that, although religious in nature, formulated principles that influenced the thought of Plato and Aristotle and contributed to the development of mathematics and Western rational philosophy.
Pythagoras
Philosopher
Pythagoras, Greek philosopher, mathematician, and founder of the Pythagorean brotherhood that, although religious in nature, formulated principles that influenced the thought of Plato and Aristotle and contributed to the development of mathematics and Western rational philosophy.
Born: 570 BC, Samos, Greece
Died:497 BC, Metapontum Village, Italy

Pythagoras of Samos was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia. Pythagoreans believed that everything could be reduced to numbers: the whole universe had been built using mathematics. Modern physicists seeking the ‘theory of everything’ or the ‘grand unification’ are Pythagoreans. They believe that the universe can be completely understood through mathematical equations, and they are engaged in a quest to find these equations.

Pythagoras’s father was Mnesarchus, while his mother was Pythais and she was a native of Samos, off the coast of modern Turkey. During Pythagoras’s formative years, Samos was a thriving cultural hub known for its feats of advanced architectural engineering, including the building of the Tunnel of Eupalinos, and for its riotous festival culture. It was a major centre of trade in the Aegean where traders brought goods from the Near East. According to Christiane L. Joost-Gaugier, these traders almost certainly brought with them Near Eastern ideas and traditions. Pythagoras was taught mathematics by Thales, who brought mathematics to the Greeks from Ancient Egypt, and by Anaximander, who was an earlier student of Thales.Thales was a philosopher, scientist, mathematician, and engineer, also known for a special case of the inscribed angle theorem. Thales advised Pythagoras to visit Egypt, which he did when he was about 22 years old. Pythagoras must have liked Egypt. He lived there for about the next 22 years of his life, mastering mathematical ideas AND spiritual ideas.
He emigrated to southern Italy about 532 BCE, apparently to escape Samos’s tyrannical rule, and established his ethico-political academy at Croton (now Crotone, Italy). Because of anti-Pythagorean feeling in Croton, he fled that city in 510 BCE for Metapontum (now Metaponto, Italy) where he died.
It is difficult to distinguish Pythagoras’s teachings from those of his disciples. Pythagoras himself likely wrote no books, and Pythagoreans invariably supported their doctrines by indiscriminately citing their master’s authority. Pythagoras, however, is generally credited with the theory of the functional significance of numbers in the objective world and in music. Other discoveries often attributed to him (the incommensurability of the side and diagonal of a square, for example, and the Pythagorean theorem for right triangles) were probably developed only later by Pythagoras, Pythagorean school. More probably, the bulk of the intellectual tradition originating with Pythagoras himself belongs to mystical wisdom rather than to scientific scholarship.
The Greeks made mathematics rigorous, meaning nothing could be accepted as true until it had been proved logically; they also carried out pure mathematics – maths that had no practical purpose – and so they were the first ancient mathematicians to have the same priorities as modern mathematicians.
The Proof of Pythagoras’s Theorem
For a right-angled triangle the sum of the squares on the other two shorter sides equals the hypotenuse squared. Pythagoras learned this rule from the Egyptians and Babylonians. It bears his name because Pythagoras was probably the person who proved it was true for ALL right-angled triangles.

Pythagoras continued to be regarded as a great philosopher throughout the Middle Ages and his philosophy had a major impact on scientists such as Nicolaus Copernicus, Johannes Kepler, and Isaac Newton.
A list of theorems attributed to Pythagoras, or rather more generally to the Pythagoreans.
(i) The sum of the angles of a triangle is equal to two right angles. Also the Pythagoreans knew the generalisation which states that a polygon with n, n sides has sum of interior angles 2n – 4 right angles and sum of exterior angles equal to four right angles.
(ii) The theorem of Pythagoras – for a right angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. We should note here that to Pythagoras the square on the hypotenuse would certainly not be thought of as a number multiplied by itself, but rather as a geometrical square constructed on the side. To say that the sum of two squares is equal to a third square meant that the two squares could be cut up and reassembled to form a square identical to the third square.
(iii) Constructing figures of a given area and geometric algebra. For example they solved equations such as a (a – x) = x^{2} by geometrical means.
(iv) The discovery of irrationals. This is certainly attributed to the Pythagoreans but it does seem unlikely to have been due to Pythagoras himself. This went against Pythagoras’s philosophy the all things are numbers, since by a number he meant the ratio of two whole numbers. However, because of his belief that all things are numbers it would be a natural task to try to prove that the hypotenuse of an isosceles right angled triangle had a length corresponding to a number.
(v) The five regular solids. It is thought that Pythagoras himself knew how to construct the first three but it is unlikely that he would have known how to construct the other two.
(vi) In astronomy Pythagoras taught that the Earth was a sphere at the centre of the Universe. He also recognised that the orbit of the Moon was inclined to the equator of the Earth and he was one of the first to realise that Venus as an evening star was the same planet as Venus as a morning star.