As we start of the semester in the The History of Math, it is only appropriate to begin where math began in ancient Egypt and Mesopotamia in roughly 3100 B.C.E. At this point and time within the culture of the region, it is interesting to see how not only mathematics began taking shape, but the different writing forms as well. Although the hieroglyphic and hieratic writing forms originated from the same region, they were quite different in how the mathematic calculations were formed. Both included multiple sets of questions and answers but not always algorithms, or an ordered list of instructions designed to produce the answer, therefore leaving no evidence as to why these processes work or what their limitations are.

Hieroglyphic algebra topics of adding, subtracting, multiplying and dividing were much simpler than that of the hieratic. One simply used the doubling method by doubling both integers, whether it was multiplication or division, without having the number go over the desired integer in the left column by crossing out numbers exceeding this value when added. What was left uncrossed in the right column was added to become the solution. This was possible for both multiplication and division because it was discovered by experimentation that dividing was the inverse of multiplying. When these numbers did not come out even, the Egyptians were forced to use fractions.  Because at this point in time there were still no symbols, there were a limited number of fraction combinations that could be made. These included unit fractions and the fraction of two-thirds. As algebra became more defined, geometry began to take off with new formulas for geometric shapes specifically circles, triangles and pyramids. The area of a circle was equal to pi*radius squared, the circumference of a circle was equal to two*pi*radius and the volume of a pyramid was discovered by using a pile of sand that resembled the pyramid shape. The Babylonians alongside began determining square roots, Pythagorean triples but of course most importantly developed algebra.

Reflective Tag

Before reading these first two chapters, I really had no knowledge about where math all began. The text has really opened my eyes as to how intelligent the people of this region and time period really were. It amazes me that the ways they discovered and used mathematics are still methods that, although sometimes longer in process, still work today. It makes me wonder what sort of mathematics is out there that has not been discovered yet and what the human intelligence is truly capable of. The best way for me to retain and better understand their usage of these methods mathematics is through practice and repetition which I am hoping to have an abundance of as the semester continues.

HR: In class notes

Citations: The History of Mathematics by Victor J. Katz