Mathematicians and their Contributions

Thales of Miletus

about 624 BC
about 547 BC

Thales was the first known Greek philosopher, scientist and mathematician. He is credited with five theorems of elementary geometry.

Thales of Miletus

Born: about 624 BC in Miletus, Asia Minor (now Turkey)
Died: about 547 BC in Miletus, Asia Minor (now Turkey)

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:-

[Thales] first went to Egypt and thence introduced this study [geometry] into Greece. He discovered many propositions himself, and instructed his successors in the principles underlying many others, his method of attacking problems had greater generality in some cases and was more in the nature of simple inspection and observation in other cases.

There is a difficulty in writing about Thales and others from a similar period. Although there are numerous references to Thales which would enable us to reconstruct quite a number of details, the sources must be treated with care since it was the habit of the time to credit famous men with discoveries they did not make. Partly this was as a result of the legendary status that men like Thales achieved, and partly it was the result of scientists with relatively little history behind their subjects trying to increase the status of their topic with giving it an historical background.

Certainly Thales was a figure of enormous prestige, being the only philosopher before Socrates to be among the Seven Sages. Plutarch, writing of these Seven Sages, says that (see [8]):-

[Thales] was apparently the only one of these whose wisdom stepped, in speculation, beyond the limits of practical utility, the rest acquired the reputation of wisdom in politics.

This comment by Plutarch should not be seen as saying that Thales did not function as a politician. Indeed he did. He persuaded the separate states of Ionia to form a federation with a capital at Teos. He dissuaded his compatriots from accepting an alliance with Croesus and, as a result, saved the city.

It is reported that Thales predicted an eclipse of the Sun in 585 BC. The cycle of about 19 years for eclipses of the Moon was well known at this time but the cycle for eclipses of the Sun was harder to spot since eclipses were visible at different places on Earth. Thales's prediction of the 585 BC eclipse was probably a guess based on the knowledge that an eclipse around that time was possible. The claims that Thales used the Babylonian saros, a cycle of length 18 years 10 days 8 hours, to predict the eclipse has been shown by Neugebauer to be highly unlikely since Neugebauer shows in [11] that the saros was an invention of Halley. Neugebauer wrote [11]:-