Ancient Mathematical Concepts

In this chapter we will focus on ancient mathematical concepts. Before calculus, analysis and geometry, mankind first learned to count. This concept is not so easy and many, many methods have been used.

Several peoples developed number words that could apply to one category or another. Yet, it required millenia for, as Bertrand Russell indicated, mankind to distinguish two birds or two rabbits or two stones from the abstract concept of "twoness." Exactly when this happened cannot be known for some peoples have had no such concept up to modern times. We conclude that the development of mathematics has been "local."

Then where did mathematics arise? We know that China, India, Egypt and Babylon were the original centers. Study the similarities between these locations.

Goals.

• Was counting originally based on the notion of the ordinal or the cardinal?
• What did China, India, Egypt and Babylon have in common?
• What were the earliest causes for the creation of mathematics?
• Why were so many different bases (i.e. 2,3,5,10,20,60) used?
• Was early mathematics recreational, theoretical, applied, or what?
• Was the idea of proof or justification used or needed?

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