Pythagoras was born in Samos, a small island off the coast of Asia Minor.  He lived circa 582 BC to 502 BC.  He was famed in the ancient world for his speculations on cosmology and reincarnation; however, he is most remembered to this day as one of the founding fathers of Mathematics, and the man responsible for the famous theorem bearing his name.

Pythagoras is believed to have studied the geometry of Thales, whom he met as a young man, and Anaximander under whom he studied.  This is probably true as his famous theorem bears the hallmark of Ionian geometry.  [Pythagoras’ Theorem: A² = B² + C² the square of the hypotenuse of a right-angled triangle is equal to the sum of the square of the two other sides.  This translates to: the longest side of a right-angled triangle multiplied by itself, is equal to, both the other sides multiplied by themselves and then added together]

Pythagoras seems to have traveled extensively in Egypt, where he undoubtedly learned and developed mathematical skills and techniques.  He eventually settled in Croton on the east coast of Bruttium (present day Calabria in southern Italy) sometime around 525 BC where his teachings attracted great following.

History records Pythagoras as a great man of science but also somewhat of a mystic.  He founded a school in Croton, which was at the same time both scientific and religious.  Pythagoras left no written work, so again we are reliant on his disciples and historians for an accurate account.  It is said that his followers held him in almost godlike esteem.  His influence and reputation extended over the centuries to his becoming a revered legend and man of wisdom, whose name was often invoked in matters of science and mysticism.  Certainly, he appears to have had a great influence on Plato, to whom we are indebted for knowledge on his life and works.

Pythagoras taught the doctrine of rebirth.  He believed the soul was constantly reborn due to ignorance of the way of the universe, resulting in behavior that merely continued the cycle.  Pythagoras preached that the only way to break the cycle was the cultivation of wisdom.  Only through wisdom would man be capable of coming into line with the true order and harmony of the universe.

History’s main concern with Pythagoras seems to lie with his interest in mathematics.  Pythagoras discovered the mathematical laws of musical pitch.  He saw these laws as governing the pattern and harmonies of music.  He later extended this idea to the idea of mathematics governing the harmony of all things in the universe.  He thus developed a philosophical belief in mathematics as the fundamental nature of the structure of the universe.  This was a powerful idea and was instrumental in convincing Galileo, some 2,200 years later that, “the book of nature is written in the language of mathematics”.

Pythagoras believed that the basic essence of the universe was not substance but “form”.  He saw geometric form as being composed of number, as represented by an individual discrete unit.  He therefore considered geometry and number as the keys to the explanation and understanding of the natural world.  Pythagoras explained reality as being a structure composed of a discontinuous series of instantaneous moments.

His extensive mathematical investigations are considered partially responsible for giving mathematics a formal technical foundation.

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