Archimedes and Pythagoras
A common belief among ancient cultures was that the laws of numbers have not only a practical meaning, but also a mystical or religious one. This belief was prevalent amongst the Pythagoreans. Prior to 500 B.C.E., Pythagoras, the great Greek pioneer in the teaching of mathematics, formed an exclusive club of young men to whom he imparted his superior mathematical knowledge. Each member was required to take an oath never to reveal this knowledge to an outsider. Pythagoras acquired many faithful disciples to whom he preached about the immortality of the soul and insisted on a life of renunciation. At the heart of the Pythagorean world view was a unity of religious principles and mathematical propositions.
In the third century B.C.E. another great Greek mathematician, Archimedes, contributed considerably to the field of mathematics. A quote attributed to Archimedes reads, "There are things which seem incredible to most men who have not studied mathematics." Yet according to Plutarch, Archimedes considered "mechanical work and every art concerned with the necessities of life an ignoble and inferior form of labor, and therefore exerted his best efforts only in seeking knowledge of those things in which the good and the beautiful were not mixed with the necessary." As did Plato, Archimedes scorned practical mathematics, although he became very expert at it.
The
Abacus: A mechanical counting device
The Greeks, however, encountered a major
problem. The Greek alphabet, which had proved so useful in so many ways,
proved to be a great hindrance in the art of calculating. Although Greek
astronomers and astrologers used a sexagesimal place notation and a zero,
the advantages of this usage were not fully appreciated and did not spread
beyond their calculations. The Egyptians had no difficulty in representing
large numbers, but the absence of any place value for their symbols so complicated
their system that, for example, 23 symbols were needed to represent the
number 986. Even the Romans, who succeeded the Greeks as masters of the
Mediterranean world, and who are known as a nation of conquerors, could
not conquer the art of calculating. This was a chore left to an abacus worked
by a slave. No real progress in the art of calculating nor in science was
made until help came from the East. next