Undergraduate student Shane Wang has secured second place in the 2024 HOM SIGMAA Student Paper Contest. This contest, organized by the History of Mathematics Special Interest Group of the Mathematical Association of America (MAA), recognizes exceptional student research in the history of mathematics. Wang wrote the paper titled "Theories on the Origins of the Sexagesimal System," in the Conceptual Foundations of Mathematics course, taught by Professor Sylvia Nickerson. In another class also taught by Professor Nickerson, Shane developed an interest in the number concept within ancient societies. “We tend to take for granted the conceptual technology we use today for counting: a decimal (base-10) number system, with the use of zero and a decimal point. These conventions are the result of thousands of years of development of the number concept across cultures. While we no longer rely on base-60 for most calculations, the Mesopotamian number system still exists in the present day in our measurement of time. Arcseconds and arcminutes, used in astronomy, cartography and navigation, can also be traced back to the Mesopotamians use of base-60,” says Professor Nickerson.
The final paper for HPS411 examined the historical and mathematical reasoning behind the ancient Mesopotamian use of the sexagesimal (base-60) numeration system, concluding that its divisibility properties were the primary factor, aligning with Theon of Alexandria's argument. In his analysis, Shane refutes other hypotheses by scrutinizing historical evidence, ultimately supporting the divisibility theory. According to Professor Nickerson “Shane explored what influences language, culture, and the natural environment may have had on Mesopotamians’ preference for the number sixty as the basis of everything numeric, from school multiplication tables to tracking the movements of stars to daily commerce.”
The winners of the 2024 HOM SIGMAA Student Paper Contest will have their papers published on Convergence, the MAA's online journal. “Such recognition can motivate a student to gain greater research experience and develop a profile among readers of MAA’s online magazine where the paper will be published.” This is a great achievement, says Professor Nickerson, because this is the publication of “the largest professional association of mathematical researchers, teachers, and students in the United States.” Besides, “publishing experience as an undergrad could lead students to be motivated towards further study in a graduate school program, as they can see an audience exists to appreciate their work. Such awards also raise the profile of IHPST’s HPS undergraduate programs as prospective graduate students who read Convergence may become aware of our programs through Shane’s piece.”
Shane, who is pursuing an economics major at the University of Toronto, and minors in history and statistics, originally took the history and philosophy of science (HPS) courses out of sheer interest. Despite his primary focus on economics, his diverse academic background provided a unique perspective that enriched his exploration of the ancient numeral system. His achievement demonstrates that intellectual curiosity and cross-disciplinary study can lead to professional recognition and contribute valuable insights to the academic community.
Shane shared with us the curious inspiration behind his paper and the research challenges he faced:
Can you tell us a little about what inspired you to research the theories on the origins of the sexagesimal system?
The primary inspiration for my research is, quite embarrassingly, The Earth Chronicles, a series of books on a metaphysical theory on the origins of human civilizations. In the series, the author used the complex and unintuitive natures of the Sumerian sexagesimal number system to support his hypothesis that ancient deities gave birth (quite literally!) to the first human civilizations, arguing that only highly intelligent extraterrestrials to whom the number 60 has significant astronomical meanings would develop and adopt a sexagesimal number system, which they then taught the first civilized humans. During my research, I found evidence that the Sumerians had first developed a primitive decimal system before replacing it with the sexagesimal one, which disproved the theory from The Earth Chronicles. Though I did not mention any of that in my paper due to its pseudoscientific nature.
What challenges did you face while researching and writing your paper, and how did you overcome them?
A unique challenge I faced during my research was the lack of concrete evidence. Unlike most other historical inquiries, the origins of the sexagesimal system could not be convincingly proven by physical objects (i.e. books, artifacts, etc.). All I have to work with was a bunch of competing theories, all but one of which I had to convince my readers to not be the case. In the end, I decided to tackle only a few of the most prominent theories, using errors and inadequacies in their logic and evidence to disprove them. My arguments for the divisibility theory were not particularly strong and was mostly supported by circumstantial evidence; but since the other theories were less sound, I hope the readers would be convinced that the divisibility of the number 60 was the primary reason it was used as a base.