One of the most well defined and clearest examples of the legacy of the ancient world is that owed to Greek Civilization. Within that legacy, much of the modern world owes a debt in the areas of philosophy, science, education, architecture, social and governmental theory, and the like. An interesting example of a line of thought carried through from the Greek World to the Middle Ages, finally developing at a greater extent in the Renaissance, Reformation, and Age of Discovery, is that of Greek Mathematics. Primarily known for their contributions in the field of geometry, the Greeks nevertheless established the basis for modern mathematical thinking in the fields of logic, real and unreal numbers, and abstract equations. However, since this paper will primarily deal with the cultural aspects of ancient Greece, an emphasis will be placed on the mathematical philosophies rather than the individual contributions by great thinkers and individual personalities.
Two questions must be raised, however, within the examination of Greek mathematics. The first must ask about the role that Greek culture as a whole played in the development and evolution of Greek mathematics. Secondly, one should also inquire as to the place of the Greeks within the educational framework itself since it was through that framework that mathematics was transferred within Greek culture and finally down to the contemporary world.
Before discussing Greek culture, mathematics, and the resulting influences each had upon the other, it is first necessary to give a brief history of the Greek civilization. That civilization included a complex societal code, commerce and economic systems that rivaled the other great powers of the Mediterranean world, and a legal and governmental system that was one of the most liberal for the time.1
The Greeks were descendent from Indo European tribes that spread from the Indian and Middle Eastern Regions into the European subc...