**Pythagoras of Samos** was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. The theorem now known as Pythagorean theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it.

- Unlike many later Greek mathematicians, where at least we have some of the books which they wrote, we have nothing of Pythagoras's writings.
- The society which he led, half religious and half scientific, followed a code of secrecy which certainly means that today Pythagoras is a mysterious figure.
- We do have details of Pythagoras's life from early biographies which use important original sources yet are written by authors who attribute divine powers to him, and whose aim was to present him as a god-like figure.
- What we present below is an attempt to collect together the most reliable sources to reconstruct an account of Pythagoras's life.
- There are accounts of Mnesarchus returning to Tyre with Pythagoras and that he was taught there by the Chaldaeans and the learned men of Syria.
- All accounts of his physical appearance are likely to be fictitious except the description of a striking birthmark which Pythagoras had on his thigh.
- There were, among his teachers, three philosophers who were to influence Pythagoras while he was a young man.
- One of the most important was Pherekydes who many describe as the teacher of Pythagoras.
- The other two philosophers who were to influence Pythagoras, and to introduce him to mathematical ideas, were Thales and his pupil Anaximander who both lived on Miletus.
- 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.
- In about 535 BC Pythagoras went to Egypt.
- The accounts of Pythagoras's time in Egypt suggest that he visited many of the temples and took part in many discussions with the priests.
- It is not difficult to relate many of Pythagoras's beliefs, ones he would later impose on the society that he set up in Italy, to the customs that he came across in Egypt.
- For example the secrecy of the Egyptian priests, their refusal to eat beans, their refusal to wear even cloths made from animal skins, and their striving for purity were all customs that Pythagoras would later adopt.
- Pythagoras was taken prisoner and taken to Babylon.
- In about 520 BC Pythagoras left Babylon and returned to Samos.
- The deaths of these rulers may have been a factor in Pythagoras's return to Samos but it is nowhere explained how Pythagoras obtained his freedom.
- Darius of Persia had taken control of Samos after Polycrates' death and he would have controlled the island on Pythagoras's return.
- This conflicts with the accounts of Porphyry and Diogenes Laertius who state that Polycrates was still in control of Samos when Pythagoras returned there.
- Pythagoras made a journey to Crete shortly after his return to Samos to study the system of laws there.
- Pythagoras left Samos and went to southern Italy in about 518 BC (some say much earlier).
- Pythagoras was dragged into all sorts of diplomatic missions by his fellow citizens and forced to participate in public affairs.
- Pythagoras founded a philosophical and religious school in Croton (now Crotone, on the east of the heel of southern Italy) that had many followers.
- Pythagoras was the head of the society with an inner circle of followers known as mathematikoi.
- They were taught by Pythagoras himself and obeyed strict rules.
- Of Pythagoras's actual work nothing is known.
- His school practised secrecy and communalism making it hard to distinguish between the work of Pythagoras and that of his followers.
- Certainly his school made outstanding contributions to mathematics, and it is possible to be fairly certain about some of Pythagoras's mathematical contributions.
- First we should be clear in what sense Pythagoras and the mathematikoi were studying mathematics.
- Rather Pythagoras was interested in the principles of mathematics, the concept of number, the concept of a triangle or other mathematical figure and the abstract idea of a proof.
- Pythagoras believed that all relations could be reduced to number relations.
- This generalisation stemmed from Pythagoras's observations in music, mathematics and astronomy.
- Pythagoras noticed that vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole numbers, and that these ratios could be extended to other instruments.
- Pythagoras made remarkable contributions to the mathematical theory of music.
- Pythagoras studied properties of numbers which would be familiar to mathematicians today, such as even and odd numbers, triangular numbers, perfect numbers etc.
- Of course today we particularly remember Pythagoras for his famous geometry theorem.
- Although the theorem, now known as Pythagoras's theorem, was known to the Babylonians 1000 years earlier he may have been the first to prove it.
- (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.
- 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.
- 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.
- Primarily, however, Pythagoras was a philosopher.
- Pythagoras went to Delos in 513 BC to nurse his old teacher Pherekydes who was dying.
- In 510 BC Croton attacked and defeated its neighbour Sybaris and there is certainly some suggestions that Pythagoras became involved in the dispute.
- Pythagoras escaped to Metapontium and the most authors say he died there, some claiming that he committed suicide because of the attack on his Society.
- He approached Pythagoras, then an old man, but was rejected because of the character defects just described.
- When this happened Cylon and his friends vowed to make a strong attack on Pythagoras and his followers.
- Because of this Pythagoras left for Metapontium and there is said to have ended his days.
- This seems accepted by most but Iamblichus himself does not accept this version and argues that the attack by Cylon was a minor affair and that Pythagoras returned to Croton.

Born about 570 BC, Samos, Ionia. Died about 490 BC.

View full biography at MacTutor

Ancient Babylonian, Ancient Chinese, Ancient Greek, Ancient Indian, Architecture, Astronomy, Chinese, Origin Greece, Number Theory, Physics, Puzzles And Problems, Special Numbers And Numerals

Epochs: 1

Propositions: 2

Sections: 3 4 5 6 7

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive