Sunday Puzzle Easy for Us

If everyone submits, maybe one of us will win the NPR Sunday Puzzle: This Week’s Challenge from the Grabarchuk family: Take 15 coins. Arrange them in an equilateral triangle with one coin at the top, two coins touching below, three coins below that, then four, then five. Remove the three… Continue reading »

Math in Asia

As Vice-President, I represented the American Mathematical Society at the first joint meeting with the Korean Mathematical Society in Seoul in December, 2009. At a luncheon of society presidents, in excitement over the future of math in Asia, began plans for a six-country Asian speaking tour. My log… Continue reading »

Extraordinary Students

A little event last week reminded me of what I admire most in students. I was giving a guest presentation in Robert McCann’s freshman seminar at the University of Toronto. As I was setting up, I realized I needed a power strip. I said to the gathering class,… Continue reading »

Decisions and Priorities

Our decisions process should reflect our mission as a liberal arts college. (Published in The Williams Record, May 5, 2010) At a time of important decisions, Williams must remember its mission and purpose. I see Williams College as a joint student-faculty/staff enterprise dedicated to the proposition that understanding… Continue reading »

Math in Asia

At the December 2009 joint meeting of the American and Korean Mathematical Societies, it was inspiring to hear at the panel of presidents and throughout the meeting of the great potential, though up against scarce resources. Korea will support 1000 mathematians from developing countries at its 2014… Continue reading »

Soap Bubbles Everywhere

Since soap bubbles minimizing surface area or energy provide the typical model for my research in the calculus of variations, I receive lots of related and unrelated reports from friends. My former student Kevin Hahm ’07 sent me a link to an amazing video of water droplets… Continue reading »


Write-up of a departmental faculty seminar, October 2, 2009 Solutions to problems in geometry and physics and even in the social sciences tend to be symmetric. As prime example, the solution to the isoperimetric problem, which seeks the least-perimeter way to enclose given volume in R3, is a sphere, the most symmetric of all shapes. One way to prove this is to show that anything else improves as you make it more symmetric. For thousands of years, mathematicians have been looking for good ways to make shapes more symmetric and to prove that as they get more symmetric they “get better,” for example, enclose the same volume with less perimeter. My favorite references are Burago and Zalgaller [BZ, §9.2] and Ros [R1, §3.2]. This talk is based on [MHH]. Gromov [G, §9.4] provides some sweeping remarks and generalizations, including most of our results. 1. Steiner symmetrization [St, 1838] replaces every vertical slice of a region in R3 with a centered interval of the same length, as in Figure 1. By calculus, the volume does not change, but one can show that the perimeter decreases (or remains the same).             Figure 1. Steiner symmetrization replaces every vertical slice with a centered interval of the same length. Continue reading »