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bettermarks »Math glossary» Pythagoras of Samos

**Surname:** Pythagoras of Samos

**Born: **around 570 BC On the island of Samos (Greece)

**Died: **around 500 BC In Metaponto (today's Italy)

**Teaching / research areas**: Geometry, astronomy, number theory

Pythagoras was an ancient Greek philosopher, mathematician and founder of an influential religious-philosophical movement, the so-called school of the Pythagoreans. In mathematics, his name is primarily associated with the Pythagorean Theorem, even if Pythagoras probably wasn't the discoverer of the theorem himself. The legacy of Pythagoras is controversial: some see him as a pioneer of natural science and mathematics, others emphasize the mystical character of his religious and philosophical teachings.

**Life**

Everything that is known about Pythagoras comes from later, partly contradicting sources, which make an objective presentation and evaluation of his teachings difficult. Pythagoras grew up on the Greek island of Samos. He studied the teachings of Thales, Anaximander and Pherecydes of Syros, who is considered to be his teacher. He traveled to Egypt for study purposes and is said to have entered a priestly school there. 525 BC The Persians conquered Egypt and took Pythagoras as a prisoner to Babylon. Soon after his return to Samos, Pythagoras settled in Croton, a Greek colony in southern Italy. There he founded an influential philosophical and religious school. Under his leadership, its members formed a close community and committed themselves to a certain disciplined and humble way of life. They mainly dealt with the theory of numbers. The influence of the Pythagorean School on politics in southern Italy led to conflicts between the community and the citizens of Croton. Pythagoras then moved to Metaponto, where he lived around 500 BC. Died.

**The scientific contributions of Pythagoras and the Pythagoreans**

Little is known of Pythagoras' own contributions to mathematics. In many cases it can be assumed that the knowledge ascribed to him can be traced back to his students. The one named after him *Pythagorean theorem* was known to Egyptian, Babylonian or Indian mathematicians before him. It says that the area of a square above the hypotenuse of a right triangle corresponds to the sum of the area of the squares on the other two sides (\ (a ^ 2 + b ^ 2 = c ^ 2 \)).

The Pythagorean theorem is a special case of the cosine theorem.

The Pythagoreans discovered the irrational numbers and expanded their knowledge of proportions. In music they could apply and illustrate mathematical theorems. They discovered that the intervals of a scale can be expressed as ratios of whole numbers. The scale so defined is called *Pythagorean mood* designated. In astronomy, the Pythagoreans were the first to view the earth as a sphere and to try to explain the harmonious order of the celestial bodies with the help of their theory of numbers. Pythagoras believed that a "music of the spheres" was created by the movement of the heavenly bodies along ordered paths.

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