Editor’s note: This article was initially published in The Daily Gazette, Swarthmore’s online, daily newspaper founded in Fall 1996. As of Fall 2018, the DG has merged with The Phoenix. See the about page to read more about the DG.
Last Monday, Professor David Mumford of Brown University gave a lecture titled “Discovering the same things in two such different ways – Indian and Western Calculus.” This was the first of the two math department lectures by Mumford this week.
Mumford opened the lecture by giving general background about studying the history of math. He noted pitfalls he hoped to avoid, such as assuming linearity in the development of history toward the future that is rarely the case. He also discussed briefly the nature of his approach to the topic as a mathematician.
Over the course of the lecture, Mumford discussed different developments in mathematics as they came about it different parts of the world. His focus was on the parallels between discoveries in India and Greece and later, Europe, but he also discussed developments in China.
His first large example was the development of the “Pythagorean” Theorem. He showed slides with pictures of proof of the development of the theorem in cultures as early the Babylonians.
Mumford also pointed out that there were major differences between Greek mathematical thinking and Indian and Chinese mathematical thinking. He argued that Greek thinking was more abstract, but also pointed out that the Greeks ruled out the use of negative numbers for hundreds of years while China and India allowed their use.
The principle example of parallel development in the lecture was the development of calculus. The final third of the lecture consisted of multiple slides giving examples of proofs demonstrating that calculus was developed in some form at multiple times in Greece, India and Europe.
Mumford closed the lecture by stating that different styles of doing math have historically lead to similar and equally impressive mathematical discoveries. He also argued that levels of rigor ebb and flow across history. He finally concluded that this historical perspective could show that the emerging fields of applied mathematics, despite having a different style as other contemporary mathematics, are just as legitimate.