Schedule: Tuesdays and Thursdays, 1:00-2:15 pm, Room B223 Van Vleck (note room change!).
In the seventeenth century, French mathematician Pierre de Fermat claimed to have proved a result of unprecedented scope, but he did not divulge his proof. Professional and amateur mathematicians alike wrestled with this problem for hundreds of years. A proof was finally found by Princeton mathematician Andrew Wiles in 1994. Why do so many of us mathematicians think Fermat's proof must have been invalid, and why did it take so long for us to find a valid proof? How does the problem fit in among the accomplishments and ambitions of modern mathematics, and what can the story of Fermat's Last Theorem tell us about the nature of intellectual progress in general?
In this discussion-based seminar, students will read selections from published books and articles on number theory and the history of mathematics, along with material from a book-in-progress by Prof. Propp directed toward the non-mathematical reading public. We will also watch videos (some popular and some technical).
Students will be expected to participate in seminar discussions and to submit weekly one-page written responses to the reading, as well as a final paper or project. Prior knowledge of elementary number theory might be helpful but is not required. Willingness to argue about ideas is essential.
James Propp is Associate Professor in the MIT Department of Mathematics. He is writing a book for the general public on Fermat's Last Theorem that will be published in 2001, entitled "Who Proved Fermat's Theorem?: The Curious Incident of the Boasting Frenchman". A web-site will also be created as a companion to the published book; the comments of the students who take this seminar will help shape both the book and the web-site, and will be acknowledged in print.
If you are interested in this seminar, please send e-mail to Prof. Propp at propp@math.wisc.edu. Meanwhile, you can look at a list of some of the questions that we'll be addressing during the term, along with pointers to some of the books and articles we'll be discussing during the term, and some of the videos we'll be watching.
Here's a write-up of the class's first exploration of Pythagorean triples.