Position paper

What is or what should be the history of mathematics?

The history of mathematics can be divided into at least five parts:

1. Origins of mathematics. The is basically the Paleolithic portion of mathematical history. Where and why did mathematics arise? What are mankind's basic instincts toward mathematics?
   
   
2. Mathematical fact gathering. When did this happen? Who did that? Proving the facts? Establishing that certain facts are unprovable. The impact of new discoveries.
   
   
3. Historical interpretation, Why has the subject arrived here? How has a mathematical subject migrated to its present form? What were the epochs? Who pulled the levers? Was the effort more collective or more individual?
   
   
4. Personalities of mathematics: Biographies: ranging from the simple mathematical life to explorations of the personality of the mathematician. Psychological interpretive life.
   
   
5. Understanding humankind's ability to understand mathematics. Applications to the present.

Please write an essay on one or more of the categories above? Take a position on some aspects and support them with facts, with dates, and with authoritative sources.

Length: 3-6 pages typed.