David's Mathematical Blog

I interpret practicality as being able to solve real life problems using a set of methods. Abstraction is taking practicality a step further: it adds a “what if” situation that may not have any resemblance to the real world. Thinking abstractly can widen the scope of applications and generalize new connections among concepts. My interpretation of practicality and abstraction does rely on familiarity with contemporary algebra. It would seem difficult for me to solve a word problem without being able to utilize the tools of algebra, namely numbers, symbols, and operations. Word problems in Babylonian mathematics appear practical at first, but they are often taken to the extremes by the measurements they give and the actual practicality of the problem. They take on a simple problem, such as calculating the amount of grain in a pile, but give measurements far from reality, such as the height of an eight-story building. Babylonian mathematics was born out of applied mathematics problems, an...

 The first thing in the article that surprised me was the existence of intellectual debt. I have always thought of debt as something physical that one party owed to another. It is difficult for me to grasp that intelligence was used like currency, because information today is widely public and free. The next thing that surprised me was how countries interacted with each other in terms of scientific exchange. India and China connected through Chinese Buddhist pilgrimages into India, bringing with them their own findings. Egypt and Greece connected through knowledge sharing from the Egyptians, which led to the intellectual debt stated before. I found interest in knowing that information was shared in many different ways.  The last thing that surprised me was how the Maya developed their mathematics compared to the rest of the world, despite being cut off from the rest of the world. Their calculations involved basic mathematical tools, but their results rivalled Europe's precisio...

I think 60 was a convenient number in Babylonian time because the concept of time was important to them. They did not have electricity for light, so time dictates what activities they do. This concept translated to everything else they did. I predict that 60 was a useful number because there are many factorizations of 60 compared to 10. Merchants in the early times needed to show their wares to do efficient trading. If they were to display their wares in groups of 60, it may be easier for the customer to count than in groups of 10. Today, we use 60 in time-telling, and maybe even in geometry. There are 60 seconds in a minute, and 60 minutes in an hour. There are 360 (6 times 60) degrees in a full rotation around a point. I don't know exactly why 60 is so significant in time and space, but I know that it works extremely well in today's society. After some research, I found that some of my predictions were correct. The number 60 is a highly composite number, meaning it has many f...

Math has been a rich part of history for the longest time, spanning even before the ancient Babylonians. In math, there are often many different ways to solve a problem. The tools we have today would make the problems of the past appear trivial. How did society transition from ancient mathematics to modern mathematics? I believe that studying math history provides a different perspective on how the ancient people solved problems that will be useful in teaching students. If students are able to understand and replicate the early math techniques, then they often show a high level of mastery. After reading the article, I resonated with the idea that math is often messy initially. Equations and formulas today are eye-catching, but the journey to that beauty is often hidden in sight. As a future math educator, I am curious on how to show the students the methods used by the ancient people to solve problems in a fun and engaging way. The article also mentions that mistakes, uncertainties and...