Why did Mathematics begin in Greece? (1650 words)

Write an essay to explain: Why did (proof-oriented) mathematics begin in Greece and not somewhere else?
Here are several points:
• Geographic condition limited Greece’s size. There were no powerful kings and powerful priesthoods there.
• Greeks had a unique political system. There were Greek courts which did not appeal to the God, or a king, but to a judge and jury. The jury was made up of people who had to be convinced.
• In Ancient Greece, for ancient Greek thinkers as free men, there were no priests to limit to their thoughts.
• Greeks like to argue. Just like athletics challenged one another in stadium, Greek thinkers challenged one another in public contest, which were governed by strict rules.
• Like politicians and lawyers, Greek thinkers were skilled in the art of persuasion. They did not only satisfy persuasion, they wanted to completely convince the audience and
to eliminate all doubts. This was the origin of “proof.”
• Ancient Greek philosophy focused on the role of reason and inquiry. In many ways, it had an important influence on modern philosophy, as well as modern science.

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Introduction
The overarching purpose of large scale research study was to gain understanding of the high school mathematics perceptions related to the integration of the History of Mathematics (HOM). One of the goals of the study, which address in this paper, was to identify those factors that encourage or discourage choice to include the HOM as a systematic part of their mathematics courses.
Assumptions
Several key assumptions, well known to the community of mathematicians and mathematics educators, served as a basis of our research. First, HOM provides a background for gaining a rich and deep understanding of the evolution of mathematical concepts. Second, understanding how and why basic mathematics concepts were developed by individuals through years of hard work, sacrifice, trials and tribulations one has an opportunity to trace the intellectual development of humankind. In this manner, mathematics is placed within a clear and practical human context demonstrating the utility of mathematics concepts. Third, learning HOM may increase students' interest and enhance positive attitude toward mathematics.
While there is not enough explicit empirical proof for such assumptions, it is apparent that the teaching of historical development of basic concepts has become central to the teaching of all the basic sciences and virtually all of the social sciences. Indeed, since the work of Thomas Kuhn (1996), the history of science has been a rapidly growing field of research and publication. The popularity of the science histories of Stephen Jay Gould in biology and Stephen Hawking in physics, to name...