Jovan Choongh - Math History

It really puzzles me that on the surface there seems to be a sense of practicality in the Babylonian word problems which is a complementing contrast to the theoretical, abstract Greek mathematics, however, when diving deeper practicality diminishes. Robson addresses a valid idea in that Babylonians may have surpassed the needed amount of word problems for actual applications, and that problems which addresses real life applications which were getting outdated. Hoyrup's perspective on the notion of Babylonians utilizing applied mathematics and word problems to illustrate abstract contracts is enticing, giving intuition into absurd numbers and unknowns which were in some of the Babylonian word problems. Perhaps, exists some form of mathematics where once practical applications have been exhausted, mathematicians and practitioners now seek to exercise mathematics for the sake of exercising mathematics and "solving" some sort of problems. The latter which then results i...

Originally 12 = 1/12 + 1/3   + 1/2 12 = 1/12 + 4/12 + 6/12 With one less horse 11 = 1/2 + 1/3 + 1/12 11 = 6 + 4 + 1 Assuming round 1/2 of 11 is six horses, and 1/3 of is four horses and 1/12 of 11 is one horse. The allocation using unit fractions does not change. The benefits of unit fractions from Ancient Egyptian times still exist today, when dividing or allocations n number of items amongst x people, giving the unit fraction x/n, useful back then in rationing and still today.

I find it very fascinating in which the ways Babylonians denoted mathematics in certain notations when no such thing as current algebraic notation existed.  The fact Babylonians utilized words such as "ush", "sag," "lagab," and "zud" to symbolize different unknown quantities Prior to algebraic notation, stating mathematical principles was done through the usage of statements, tables, and numerical tablets dedicated for specific principles. I believe that mathematics is about reproducible logical statements, I think you must generalize in the sense of being able to substitute specific numbers for a general span of numbers n, and the statements must follow certain steps. I do not think one must be abstract entirely when discussing mathematics, I think that specific examples provide intuition. However, generalization and abstraction lead to logic which is reproducible without using specific numbers. In the case of the Babylonians, their refere...

Column I           Column II 2                       22,30 4                       11,15 5                       9 6                       7,30 12                     3,45 20                     2,15 30                     1,30

The first thing that surprised me was the ignorance of research pointing to the development mathematics in Mesopotamia and Egypt, and the sole focus of the classic Eurocentric view that mathematics is a "product of European civilization." I had never heard of such a view establishing Europeans as the sole developers of mathematics as stated in Figure 1.1. Another astonishing notion was the fact India was a key centric geographic location for the transmission of the mathematic ideas, and that the Indian had established itself significantly before the Ptolemaic Egypt and Rome's Eastern empire had established itself. I had no idea India had such an influence on European sciences and medical studies, where Greeks highly regarded India's studies on medicine. I think it was also fascinating to learn of the medium of transmission which the Arabs played in transporting key mathematical concepts originating from India and China. In all honesty, I had never delved much into...

60 may be convenient and/ or useful as the base for a number notational system because of size, where perhaps the Babylonians lived in tribes or clans of 60 individuals rather than 10 which is quite small. Another speculative guess may be that 60 is the number of Gods or deities Babylonians worshiped, or that the number 60 has cultural significance in terms of religious events or phenomena. 60 may also be approximately the number in which a certain significant crop grew or yielded or sold that was consumed on a regular basis. 60 is different from 10 because of the number of factors it has relative to 10, whereas 10 only has four factors. 60 is of course, still used in our current time-telling system in which it the basis for minutes and seconds where 1 hour and 1 minute are composed of 60 minutes and 60 seconds respectively. 60 is also significant because of the number of days of year is approximately 360 which is divisible by 60. I would also speculate that Babylonians were able to a...

Prior to reading the article regarding the integration of mathematics, my preconceived notion of incorporating history into math was simply that math history should be taught to an extent, such that reasoning for the existence of the subject is logical. Moreover, I believe that history of math is crucial for secondary students and university in understanding the fundamental building blocks of concepts for mastery. The history of mathematics and its applications in history enable students to appreciate a sense of feasibility of the relevant concepts being taught. I still remember going to watch a math play at a performing arts center in Surrey as a part of my ninth grade high school math class, and being in awe of Eratosthenes' calculations of Earth's circumference.  Getting out on a field-trip really made me appreciate math in a way where I began to see how profound applications could be. Reading upon the segment of using historical problems as platform to integrate history i...