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Pythagoras (of Samos)

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[piy tha goruhs] ( c .560–480 BC ) Greek mathematician, astronomer and mystic: founder of a cult united by the belief that ‘the essence of all things is number’.

Although his name is so familiar, rather little is known of Pythagoras’s personal life. Born on the Greek island of Samos in the eastern Mediterranean, he travelled widely before settling about 530 BC at Croton, then a Greek colony, in south-east Italy. There he founded the sect that survived for a century after his death. With Pythagoras as their cult leader, the sect was devoted to a life of political and religious mysticism, in which astronomy, and especially geometry and the theory of numbers, was central. Number was seen as pure, magical and the key to religion and philosophy. This secret society became powerful and aroused hostility, which eventually destroyed it.

Pythagoras himself is said to have discovered the theorem on right-angled triangles named after him; and to have begun the science of acoustics with his work on the tones produced from a stretched string, which are perceived as harmonious to the ear provided that the lengths of string for the two tones have a simple number relation (for example a length ratio of 2:1 corresponds to a musical octave). This was probably the first mathematical expression of a physical law, and the beginning of mathematical physics. A variety of arithmetical and geometrical relations were discovered by members of the sect, which inspired their belief in number as a basis for astronomy and even for morality. In their view the Earth was a sphere, and it and the stars moved in circles in a spherical universe, because these were ‘perfect’ forms in a mystical sense. They were dismayed by the discovery that the square root of two is irrational (ie is not expressible as a perfect fraction) and are reputed to have put to death a member of the sect who revealed this secret to others. The political ambitions of the sect led to its persecution and Pythagoras was exiled to Metapontum about 500 BC . At an unknown date later in the century the Pythagoreans were involved in a democratic rising in which many were killed, and the rest dispersed.

Although Pythagoras’s ideas on the significance of numbers were erroneous, his contributions were important in mathematics: few ideas are more fundamental than that of irrational numbers.


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