Mumford Lectures on Math Around the World

October 24, 2007

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.

Sample advertisement

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.

Leave a Reply

Your email address will not be published.

Previous Story

Fall Anemone

Next Story

Coming Out Week Chalkings

Latest from Sports

Swinging Through the Glass Ceiling 

The Swarthmore men’s golf team has welcomed numerous women as walk-on players over the years. Currently there are two female players competing on the men’s team: Ava Chon ’26 and Bori Chung ’28. Chon is a senior from Princeton, NJ, who went

Athlete of the Week: Melissa Eyer ’28

Melissa Eyer '28 runs the volleyball court with her elite ball control and defensive capabilities. Read on to hear more about her fourth Centennial Athlete of the Week selection!

Garnet Soccer Takes on Johns Hopkins in Baltimore

On Sept. 20, Swarthmore men’s and women’s soccer packed their bags and boarded buses for Baltimore to play their long-time conference rival Johns Hopkins University. The day began Centennial Conference play for both Garnet teams. The men came into their game carrying

The Best Quotes of Jalen Hurts

We live in a current age of heat checks, lyric drops, motivational apps and posters, and speeches about “locking in” or “walking through fire.” And then there is Jalen Hurts — the starting quarterback for the Philadelphia Eagles, an outright contemporary Nietzsche,
Previous Story

Fall Anemone

Next Story

Coming Out Week Chalkings

The Phoenix

Don't Miss