He Lived with Numbers

By Williams, Michael R. | The World and I, May 2001 | Go to article overview

He Lived with Numbers


Williams, Michael R., The World and I


Known to students around the world for his famous theorem, Phythagoras led a school of number mystics whose collective efforts helped define much of what we know today as mathematics.

Schoolchildren who venture beyond elementary arithmetic soon encounter the Pythagorean theorem ( a2 + b2 = c2), an expression relating the two sides of a right triangle to its hypotenuse. And adults who have long since forgotten most of their math may still remember the name Pythagoras even if they don't fully appreciate his theorem's place in mathematics.

Despite his achievements, the man is as much myth as reality. Pythagoras was one of the earliest Greek philosopher/mathematicians, and few contemporary records survive from his day. Most references to him come from the writings of Aristotle (384--322 b.c.), who lived a few hundred years after Pythagoras' time. It is rather like trying to reconstruct the life of George Washington from your great-grandfather's vague memories of things he heard as a child. One difference is that the ancient Greeks maintained a largely oral tradition, so their unwritten stories no doubt spanned centuries better than unwritten stories would today. Some facts about Pythagoras are clear, while others seem to have been made up to explain how this remarkable man became one of the founding fathers of mathematics.

The merchant's son

Pythagoras' father, Mnesarchos, was a merchant trader in the eastern Mediterranean. He settled on Samos after he was made a citizen of the island in appreciation for his having delivered a shipload of grain during a famine. Mnesarchos married a local woman, Pythais, and Pythagoras was born on Samos between the 50th and 52d Olympiads (580-- 568 b.c.; one Olympiad equals four years).

Mnesarchos continued his trading business, and Pythagoras probably traveled with his father for at least part of his youth. He was well educated for a young man of his day. By the time he was a teen he had mastered the arts of poetry. He could recite the great Greek epics about the battles for Troy and could play the lute, a talent he would later use in an attempt to heal the sick.

At the time there would have been almost no formal education in anything resembling science or mathematics. Pythagoras' travels brought him into contact with many different people, however. He evidently picked up some appreciation of Babylonian technology and philosophy through contact with scholars at Tyre and might even have been exposed to Egyptian culture, if not directly, then certainly through contact with other merchant traders. While stories abound of his early travels to such faraway places as India, these must be considered legends rather than facts.

Pythagoras was born into a situation that suited him and his inquiring mind. Although great progress had been made in areas such as architecture and government, civilizations were still asking why rather than how. For some reason, the sixth century b.c. saw the simultaneous beginnings of the rise of reason in many parts of the world. The Greeks began their tradition of philosopher mathematicians, Buddha (c. 563-- 483 b.c.) began to ask philosophical questions in India, and, in China, Confucius (c. 551--479 b.c.) was proposing his own system. It was certainly an age when new ideas were being explored and abstract generalizations began to replace the more concrete realities of life.

The only real formative incident we know of occurred when Pythagoras was in his late teens. The philosopher Thales (c. 625--546 b.c.) and his student Anaximander (c. 610--547 b.c.) lived in Miletus, a town located on the mainland of Asia Minor not far from Samos. It is known that Pythagoras visited these two and the school they had established. Although Thales was by then an elderly man, and so might not have had any direct influence on Pythagoras, we do know that he attended lectures given by Anaximander. Thales was one of the first Greeks to become interested in mathematics. …

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