In northern China, near the Yellow River, city-states were united under the Chou dynasty, but each was run by independent lords who taxed the people heavily and had little concern for the poor. Partly in response to social chaos, the philosopher Confucius (-551 to -479) worked toward political change. His teachings mixed respect for authority with ethics in government, and humility with concern for the poor.
Toward the end of this period, the philosophy of Daoism also developed in reaction to poor government. Daoists believed that the universe had a natural order, which could be found through simplicity, peace, accommodating opposites and benevolent government.
As far as we know, the major accomplishment of Chinese mathematicians during this period was the introduction of a symbol (actually, a space) for zero as a placeholder in the decimal number system.
Out of the economic prosperity (and helped by a lot of slaves) grew a leisure class of free citizen men. These citizens produced great sculpture (Phideas, Polyclidos, and others), literature (such as Sophocles, Aristophanes, and Sappho), history (Herodotus and Thucydides), and medicine (Hippocrates).
And they produced philosophy. The best-known philosopher of the age was Socrates, followed by his student Plato and Plato's student Aristotle. These philosophers created an intellectual climate that influenced the work in other fields. For example, they stressed that the senses could not be trusted, and that truth and beauty could be found not in what was observed by the senses but only in the ideal. So the subjects of sculpture, such as the spear-bearer, or Dorypheros of Polyclidos, were not actual people, but rather were idealized people. This kind of abstract thinking extended to Greek mathematics as well.
Here are some of the mathematical problems the Greeks explored:
These questions are indeed abstract. They're less obviously useful than the questions raised in the Age of Computation, yet their very abstractness led to mathematics that could be used in a wide variety of areas, besides intriguing mathematicians for centuries to come.
Burton, David M., The History of Mathematics (USA: William C. Brown Publishers, 1991).
Eves, Howard, An Introduction to the History of Mathematics (Chicago: Saunders College Publishing, 1990).
Katz, Victor J., A History of Mathematics (New York: HarperCollins College Publishers, 1993).
Kline, Morris, Mathematical Thought from Ancient to
Modern Times (New York: Oxford University Press, 1972).
© 1996-2008 Institute for Studies in Educational Mathematics
Please do not reproduce without permission.
Last updated: 10 June, 2008
MATtours project team led by Larry Copes
The Teaching S!mulatorTM | MATtours Home | ISEM Home