Pythagoras of Samos is often described as the first pure mathematician. He is an extremely important figure in the development of mathematics yet we know relatively little about his mathematical achievements. 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 is fairly good agreement on the main events of his life but most of the dates are disputed with different scholars giving dates which differ by 20 years. Some historians treat all this information as merely legends but, even if the reader treats it in this way, being such an early record it is of historical importance.
Pythagoras's father was Mnesarchus ([12] and [13]), while his mother was Pythais [8] and she was a native of Samos. Mnesarchus was a merchant who came from Tyre, and there is a story ([12] and [13]) that he brought corn to Samos at a time of famine and was granted citizenship of Samos as a mark of gratitude. As a child Pythagoras spent his early years in Samos but travelled widely with his father. 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. It seems that he also visited Italy with his father.
Little is known of Pythagoras's childhood. All accounts of his physical appearance are likely to be fictitious except the description of a striking birthmark which Pythagoras had on his thigh. It is probable that he had two brothers although some sources say that he had three. Certainly he was well educated, learning to play the lyre, learning poetry and to recite Homer. 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.
Thales of Miletus was the son of Examyes and Cleobuline. His parents are said by some to be from Miletus but others report that they were Phoenicians. J Longrigg writes in [1]:-
But the majority opinion considered him a true Milesian by descent, and of a distinguished family.
Thales seems to be the first known Greek philosopher, scientist and mathematician although his occupation was that of an engineer. He is believed to have been the teacher of Anaximander (611 BC - 545 BC) and he was the first natural philosopher in the Milesian School. However, none of his writing survives so it is difficult to determine his views or to be certain about his mathematical discoveries. Indeed it is unclear whether he wrote any works at all and if he did they were certainly lost by the time of Aristotle who did not have access to any writings of Thales. On the other hand there are claims that he wrote a book on navigation but these are based on little evidence. In the book on navigation it is suggested that he used the constellation Ursa Minor, which he defined, as an important feature in his navigation techniques. Even if the book is fictitious, it is quite probable that Thales did indeed define the constellation Ursa Minor.
Proclus, the last major Greek philosopher, who lived around 450 AD, wrote:-
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