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MathFest 2008
Aug. 14th, 2008 08:10 pmI'm just going to hit some of the highlights of MathFest 2008; a lot of it would be of little interest to most people.
1. The History of Mathematics SIG originally planned to hold two sessions - one of 10-15 minute contributed papers, and one of half-hour invited papers. So many people submitted papers for the CP session, though, that they added two more CP sessions. The papers were a mixed bag, but there were a number of them that I found interesting:
2. The Hedrick Lectures - three of them - were given by Erik Demaine of MIT, who is on track to top Paul Erdös' record for most collaborators; he's already got well over a hundred, less than ten years after earning his PhD. Mostly he talked about recreational mathematics (although he did show some applications), such as origami (applications to airbags and satellite modules), linkages (robotics), and polygon dissection. One remarkable example: he displayed a red-and-white paper checkerboard, then shook it out to reveal that it had been folded, without any cutting, from a single sheet of paper, red on one side, white on the other. (The third lecture conflicted with the History of Mathematics IP session, so I only saw the first two.)
3. Donald Saari, whom I knew as an expert in the theory of voting (and who gave a minicourse on that subject, which I attended), also gave a lecture on the three-body problem in celestial mechanics and the origins of chaos theory. He traced the history of theories of the heavens from Ptolemy to Poincaré; among other things, he talked about epicycles, and showed how to represent them in modern notation. He went on with the familiar story of the elaboration of epicycle theory in the Middle Ages, until it collapsed in the face of the simpler models of Copernicus and Kepler. Of course, Kepler's picture, with its neat conic-section orbits, only works perfectly if there are only two bodies in the universe; any more than that, and things get extremely complicated. (It was in an attempt to solve the three-body case that Poincaré discovered chaos theory.) Today, said Saari, we know that the way to represent planetary orbits is by means of quasi-periodic functions, and he wrote the formula for such functions on the board. I started laughing: the obvious way to interpret what he had just written was as representing a metric ton of epicycles.... I'm going to have to buy his book on the subject.
4. Of course, there was a dealer's room. I was a bit concerned about buying anything, since there was only so much free space in my luggage, but there was a Send-It-Now station in the room, so I went ahead and bought the five books I wanted. One was the autobiography of Saunders MacLane. MacLane was still teaching at the University of Chicago when I was there, and introduced me to "topos theory", one of my secondary interests, which will eventually rate a mention in the Ramble if I get that far. Another was The Symmetries of Things, by the polymath John Conway. (That's "Game of Life" Conway, if that means anything to you.) One of his hobbyhorses is the development of good notation, and he's come up with a nice approach to the classification of the tiling groups - a question which was answered in the nineteenth century, but which makes more sense as organized by Conway. I also bought a book on the Langlands Program, a decades-long and large-scale investigation of certain abstruse relations between number theory, Lie groups, and God knows what else. (In my grad-student days I bounced off the Program, and I'd like to get a clearer picture of what they're trying to do.) Steven Brams' The Presidential Election Game - another book on the mathematics of voting - and a collection of essays by Gian-Carlo Rota rounded out the selection, which I immediately shipped home. (Book count for trip: 8.)
5. My talk on "Special Conics and Special Quadrilaterals" was reasonably well-received. No one asked any questions, but none of the other speakers in the Euclidean Geometry session were drawing questions either. Later, though, one of the other speakers caught up with me and asked whether I'd written up my results and, if so, would I send him a copy? I admitted that the current version needed some revisions, but said I'd get it to him one way or another. It's always nice to know that someone else is interested. (I'd work on it even if no one else were, but still....)
Overall, the conference was very interesting, and I picked up some pedagogical ideas that deserve consideration. Plus the books, of course.
1. The History of Mathematics SIG originally planned to hold two sessions - one of 10-15 minute contributed papers, and one of half-hour invited papers. So many people submitted papers for the CP session, though, that they added two more CP sessions. The papers were a mixed bag, but there were a number of them that I found interesting:
- A discussion of George Berkeley's critique of calculus, with some details I hadn't been aware of;
- The mathematical achievements of Omar Khayyam;
- The history of the mathematics of projectiles, before and after Galileo;
- Fermat's approach to (something resembling) integration.
2. The Hedrick Lectures - three of them - were given by Erik Demaine of MIT, who is on track to top Paul Erdös' record for most collaborators; he's already got well over a hundred, less than ten years after earning his PhD. Mostly he talked about recreational mathematics (although he did show some applications), such as origami (applications to airbags and satellite modules), linkages (robotics), and polygon dissection. One remarkable example: he displayed a red-and-white paper checkerboard, then shook it out to reveal that it had been folded, without any cutting, from a single sheet of paper, red on one side, white on the other. (The third lecture conflicted with the History of Mathematics IP session, so I only saw the first two.)
3. Donald Saari, whom I knew as an expert in the theory of voting (and who gave a minicourse on that subject, which I attended), also gave a lecture on the three-body problem in celestial mechanics and the origins of chaos theory. He traced the history of theories of the heavens from Ptolemy to Poincaré; among other things, he talked about epicycles, and showed how to represent them in modern notation. He went on with the familiar story of the elaboration of epicycle theory in the Middle Ages, until it collapsed in the face of the simpler models of Copernicus and Kepler. Of course, Kepler's picture, with its neat conic-section orbits, only works perfectly if there are only two bodies in the universe; any more than that, and things get extremely complicated. (It was in an attempt to solve the three-body case that Poincaré discovered chaos theory.) Today, said Saari, we know that the way to represent planetary orbits is by means of quasi-periodic functions, and he wrote the formula for such functions on the board. I started laughing: the obvious way to interpret what he had just written was as representing a metric ton of epicycles.... I'm going to have to buy his book on the subject.
4. Of course, there was a dealer's room. I was a bit concerned about buying anything, since there was only so much free space in my luggage, but there was a Send-It-Now station in the room, so I went ahead and bought the five books I wanted. One was the autobiography of Saunders MacLane. MacLane was still teaching at the University of Chicago when I was there, and introduced me to "topos theory", one of my secondary interests, which will eventually rate a mention in the Ramble if I get that far. Another was The Symmetries of Things, by the polymath John Conway. (That's "Game of Life" Conway, if that means anything to you.) One of his hobbyhorses is the development of good notation, and he's come up with a nice approach to the classification of the tiling groups - a question which was answered in the nineteenth century, but which makes more sense as organized by Conway. I also bought a book on the Langlands Program, a decades-long and large-scale investigation of certain abstruse relations between number theory, Lie groups, and God knows what else. (In my grad-student days I bounced off the Program, and I'd like to get a clearer picture of what they're trying to do.) Steven Brams' The Presidential Election Game - another book on the mathematics of voting - and a collection of essays by Gian-Carlo Rota rounded out the selection, which I immediately shipped home. (Book count for trip: 8.)
5. My talk on "Special Conics and Special Quadrilaterals" was reasonably well-received. No one asked any questions, but none of the other speakers in the Euclidean Geometry session were drawing questions either. Later, though, one of the other speakers caught up with me and asked whether I'd written up my results and, if so, would I send him a copy? I admitted that the current version needed some revisions, but said I'd get it to him one way or another. It's always nice to know that someone else is interested. (I'd work on it even if no one else were, but still....)
Overall, the conference was very interesting, and I picked up some pedagogical ideas that deserve consideration. Plus the books, of course.
