Sijie Yang

The big picture of pure mathematics has emerged in my mind since I started pursuing my master's degree in mathematics. It was the first time that I encountered the world of “symbol” in abstract algebra, mathematical analysis, and especially classic geometry which is totally different from the geometry I knew in my secondary school. After that period of time, the boundary between pure mathematics that I learned in graduate program and applied mathematics that I learned in undergraduate program became clear. However, the history of Babylonian word problems brings me a brand-new perspective on the idea of pure and applied mathematics, illuminating the era before the bloom of modern symbolic algebra and re-establishing an ambiguous connection between “pure” and “applied” instead of drawing a dichotomy between two realms. According to Jens Hoyrup’s distinction between Babylonian scribal school mathematics and Greek mathematics, we can visualize the trajectory of transformation of mathem...

The first thing astonishing me is the fact that the term Greek refers to “a number of independent city-states that exhibit close ethnic or cultural affinities, and share a common language” in the context of mathematical history (Joseph 7). The term Greek is more like an allusion to “cosmopolitanism.” After reading Joseph’s explanation on the history of Greek mathematics, I believe that the early development of mathematics in 332 BC can be rendered by a metaphor of a crucible in which various mathematical traditions coming with Egyptian, Greek, Jews, Persians, Phoenicians, Babylonians and even scholars and traders from India fused into the so-called “Greek mathematics.” It might be misleading to speak of Archimedes and Diophantus (who were Alexandrian mathematicians) as Greek. Secondly, I found it interesting that the contribution of other civilizations such as the Arabs, China and India is underestimated or even ignored in the ‘classical’ Eurocentric view of how mathematics developed o...

The sexagesimal system invented by the Babylonian brings us a very different perspective on our current place value system. At first glance, it is a bit inconvenient and challenging for us to use 60 and its powers for representing numbers or doing calculations. Some people like me might prefer solving sexagesimal problems by firstly converting them into base 10 numbers before doing calculations. However, we cannot deny the fact that the number 60 is to some extent more attractive and useful as the base for a number notational system. For instance, 60 is divisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60, whereas 10 is only divisible by 1, 2, 5 and 10. Most importantly, the prime number 3 is one of the divisors of 60 whilst all the multiples of 10 can not be divided by 3. Having a variety of divisors made calculation more convenient in the past, especially for merchants who attempted to divide up a huge amount of goods [1]. It is interesting that the sexagesimal system still exis...

Integrating the history of mathematics into our math classes is not dispensable because the fusion of math and its history can demonstrate how the mathematical idea was invented and what we can learn from those mathematicians’ problem-solving techniques. Although history might be boring to some students, I believe that incorporating math history into our daily teaching in an appropriate manner can stimulate students’ motivation. For instance, before introducing the Pythagorean theorem to our students, we can present the vast chronicle of the theorem and arouse students’ curiosity by asking them who is credited with the invention of the theorem.  “No mathematical idea has ever been published in the way it was discovered. Techniques have been developed and are used, if a problem has been solved, to turn the solution procedure upside down . . . [and turn] the hot invention into icy beauty,” the quote taken from Freudenthal makes me reflect on our current didactic method. I begin to un...