Max Gromann's List: Pythagoras

• 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.
• Pythagoras's father was Mnesarchus
• while his mother was Pythais

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• • Nature and the whole reality has an underlying mathematical structure
   
  • That philosophy should be used for spiritual purification
   
  • That the soul which is pure can rise to experience the union with the divine
   
  • That certain symbols (including mathematical) have a mystical significance.
• Mathematikoi were both men and women, while the outer circle of followers, known as akousmatics lived in their own families and homes, and attended the society's meetings and lectures during the day. They were not required to follow the strict rules as mathematikoi.

• If the triangle had a right angle (90°) ...

   

  ... and you made a square on each of the three sides, then ...

• Pythagoras and his followers became politically powerful in Croton in  southern Italy, where Pythagoras had established a school for his newly  formed sect, or group of followers. It is probable that the Pythagoreans    took positions in the local government in order to lead men to the pure  life that was directed by their teachings. Eventually, however, a rival  group launched an attack on the Pythagoreans at a gathering of the sect,  and the group was almost completely destroyed. Pythagoras either had  been forced to leave Croton or had left voluntarily shortly before this  attack. He died in Metapontum early in the fifth century     B.C.E. 

• In politics the Pythagorean sect belonged to the aristocratic party. Hence the Pythagorean doctrines gained supporters among the aristocratic classes in many Italian cities, and secured for the aristocratic party a certain intellectual standing. But these aristocratic leanings excited the opposition of the democratic party, and brought about the final extinction of the sect. Pythagoras himself, it is said, after twenty years' residence at Crotona, was expelled by a rival party under Cylon, and forced to retire to Metapontum, where he died soon after.