Brief biography of Greek great thinker Pythagoras who explained reality in terms of numbers and gave us the Pythagorean Theorem.

Greek thinker Pythagoras (c.580-c.500BC), philosopher, mystic, mathematician and astronomer, is famous for his Pythagorean Theorem, and the belief that number is the ultimate nature of reality. He was born in Samos around the mid-6th century BC, and later, settled in Croton, a Greek colony in southern Italy.

The Pythagorean Theorm states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the remaining two sides.

Pythagoras the Mystic and Philosopher

In a way, Pythagoras was a somewhat shadowy figure who wrote nothing himself, like Socrates who followed after him. Known to be a mystic as well as a thinker, perhaps the school he founded would nowadays be thought of as a religious cult that taught unusual and strange doctrines including the veneration for, and abstinence from, the eating of beans.

He also preached reincarnation and the transmigration of souls and is largely responsible for the modern belief in numerology, later popularized by Nostradamus, a 16th century French physician and astrologer known for his prophesies.

Pythagoras the Mathematician

According to Pythagoras, the ultimate nature of reality is number. The idea developed out of his theory of music, in which he proved that the intervals between musical tones could be expressed as ratios between the first four integers, that is, the numbers one to four. Connecting to his religious teaching and claim that music has a special power over the soul, what followed was the belief that number is the ultimate nature of reality.

The Pythagoreans further explain certain numerical patterns, especially the so-called 'tetractys of the decad.' The tetractys is a diagram that represents the first four numbers in a triangle of 10 dots: usually represented as in the position of the 10-pin in bowling.

Both the triangle and the number 10 – the decad – become objects of worship for the Pythagoreans. In Pythagorean thought, the number 10 is the perfect number because it is made up of the sum of the first four integers.

Pythagoras the Astronomer

The integers themselves were thought to represent fundamental ideas – the number one representing the point, two the line, three the surface and four the solid. Further, that there were 10 heavenly bodies – five planets, the sun, the moon, the earth and a mysterious and invisible 'counter-earth' all revolving around the central fire.

Pythagorean Effect

After Pythagoras' death, his school of thought was divided into two camps. One maintained his religious and mystical teachings, while the other concentrated on his mathematical and scientific insights. The latter continued to believe the nature of the universe must be essentially arithmetical. Units of number, points, were somehow thought to possess spatial dimensions and be the ultimate constituents of objects.

The Pythagorean cosmogony also encountered grave problems due to one of Pythagoras' own discoveries. For instance, Pythagoras showed how the ratio of the diagonal through a square to its sides could not be expressed as a whole number. The problem of the 'incommensurability of the diagonal' led to the discovery of irrational numbers, which may be a major problem for the Pythagorean cosmogony or those involving the study of the universe and the solar system. However, irrational numbers have proved a major and lasting development in mathematical thinking.

Sources:

Biographical Dictionary, edited by Una Mcgovern, Chambers (2002)

Philosophy, the Great Thinkers, by Philip Stokes, Capella (2007)