BEGINNINGS IN GREECE 49 



PYTHAGORAS AND HIS SCHOOL. The register of mathemati- 

 cians proceeds : " After these Pythagoras transformed the occu- 

 pation with this branch into a true science, by considering the 

 foundation of it from a higher standpoint, and investigated its 

 theorems in a more abstract and intellectual way. It is he also 

 who invented the theory of the irrational and the construction 

 of the cosmical bodies." These few words like those quoted of 

 Thales are full of meaning. The Egyptian priests knew 

 geometrical facts, the raw material of mathematical science; 

 Thales adapted this material to building purposes, Pythagoras 

 began the systematic foundations of the structure. Both in 

 name and in substance mathematics as a science begins with 

 Pythagoras. 



Pythagoras founded in the Greek cities of southern Italy a 

 school which had much of the character of a fraternity or secret 

 society, this with political tendencies ultimately arousing hos- 

 tility which proved destructive to it. Beyond these undisputed 

 facts his life and work are obscured by a great mass of tradition 

 and myth, even the date of his birth being doubtful. A native 

 of the island of Samos not far from Miletus, he appears to have 

 been much affected by Egyptian influences during a residence in 

 that country. A visit to Babylon even is alleged, but with doubt- 

 ful authority. The etiquette of the Pythagorean school required 

 that all discoveries should be attributed to the " Master " and 

 not revealed to outsiders. To Pythagoras himself must probably 

 be ascribed the so-called Pythagorean theorem, this forming the 

 necessary basis for the theory of the irrational mentioned in the 

 register. A similar inference may be drawn in regard to the reg- 

 ular polyhedra. On the other hand, Pythagoras appears to have 

 interested himself in the theory of numbers, particularly in con- 

 nection with music and geometry. He is said to have first in- 

 troduced weights and measures among the Greeks. 



The attribution of particular results or beliefs to individuals of 

 this period is however very doubtful on account of the fact that 

 Pythagoras left no writings whatever, that his school was es- 

 sentially a secret society, and that in later centuries it became 

 f 



