Proof and progress

The early Greeks, living as they did on the coasts and islands of the Mediterranean Sea, had a taste for travel and sea-trade. It brought them wealth, as well as knowledge, from other lands. With slaves to do most of their day-to-day work, the wealthy free citizens of the Greek settlements had time on their hands to debate the affairs of the city. Having mastered the new alphabet writing, they were able to leave a record of some of their arguments for all times. When travellers brought back news of what they had learned in navigation outside the Mediterranean, each announcement was a challenge¹ to debate. Men skilled in the fashionable pastime of argument gathered around them disciples² eager to study their methods.

Such a man was Pythagoras. Before 500 В. С. he founded a brotherhood of young men to whom he imparted his mathematical knowledge only after they had sworn an oath³ never to pass it on to an outsider⁴. Despite this secrecy and despite the fact that he mixed magic and religion with such instruction, Pythagoras was thus a pioneer of the teaching of mathematics. A century later there were, in Athens, schools where philosophers such as Plato taught young men law, politics, public speaking and mathematics. In these new schools there were no oaths of secrecy. Teachers and pupils were free to put whatever they wished in writing for all to read.

Public study and debate led to a new way of thinking about mathematics. While the peoples of ancient world knew many useful rules for finding areas and measuring angles, they had never attempted to link those rules in a train of reasoning to prove that they are reliable. The argumentative Greeks insisted on putting every rule to the text of debate and answering every objection brought against it.

Notes

1. challenge - вызов

2. disciples - ученики

3. had sworn an oath - давали клятву

4. outsider – посторонний

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