Alumni Newsletter: Spring '00

Sesquicentennial soap bubbles

Soap bubbles, soap films and computer graphics will mark the mathematics department's contribution to the sesquicentennial celebration at the University of Rochester. Alumnus Prof. David Hoffman ('66) from the Mathematical Sciences Research Institute (MSRI) in Berkekely, California will speak on "Getting to the surface: Visualizing the mathematics of soap-film and soap-bubble surfaces."

Hoffman's lecture, complete with computer generated images of mathematically discovered "minimal surfaces," will take place at 3:30PM Friday, October 13, 2000 in the Computer Science Building Room 209. Following the lecture at 4:30PM the mathematics department will host an open house and reception for Prof. Hoffman and all alumni in the new Undergraduate Mathematics Lounge on the 9th floor of the Hylan building.

We're look forward to reuniting graduates from the math and math/compsci programs with each other and taking the opportunity to showcase the recent accomplishments of the mathematics program.

The math department open house is just one of the many the activities planned to celebrate the University of Rochester's 150th birthday. For a complete list of speakers and programs planned for the weekend of October 13, 2000 visit http://www.rochester.edu/sesqui.

Soap films and soap bubbles are a particularly appropriate topic for Rochester, since they lie at the intersection of art, mathematics and material science and illustrate the centrality of mathematics in a liberal arts education. Their beauty and grace attracted the attention of physicists and mathematicians over a century ago, and the problem of describing mathematically the possible shapes of a soap film stretched across a wire frame became known as Plateau's problem. Lagrange showed that soap films effectively minimize surface area while spanning their wire boundaries. As a result, soap films became known as 'minimal surfaces' or 'zero mean curvature surfaces', whereas soap bubbles, which exert a constant elastic force on the air inside the bubble, are described as 'constant mean curvature surfaces'.

The plane, the catenoid and the helicoid were the first examples of infinite, embedded, minimal surfaces -- soap films which do not self-intersect and which extend off to infinity -- and for 200 years it was thought that there were no others, although many self-intersecting minimal surfaces were discovered.

In 1984 at the University of Massachusetts David Hoffman used the new experimental computer graphics software designed by James Hoffman to create an image of the surface suggested by Costa. His observations soon lead to a proof that the surface, now called the Costa-Hoffman-Meeks surface, was in fact the first of a new family of infinite, embedded minimal surfaces. These new surfaces divide space in new and unexpected ways and possess delightful symmetries, and have become favorite graphic icons for mathematics and science magazine covers.

For this surface and other accomplishments, Hoffman received the 1997 LVMH Vinci of Excellence award. This Moët Hennessey-Louis Vuitton (LVMH) 'Science for Art' Prize annually rewards artists and scientific researchers from all over the world for the potential impact of their discoveries on artistic or aesthetic creation. The 1997 prize was awarded for work falling under the theme "Genesis of Forms: Part II -- Mathematics, Physical and Earth Sciences."

Meanwhile, Hoffman has explored the connection between soap film and soap bubble surfaces and the boundaries that occur between immiscible fluids and other materials. A version of his 1996 article in Nature can be found on-line at http://www.msri.org/publications/sgp/david/papers/nature96/. He has also lectured frequently on this subject and produced a video entitled "Natural Minimal Surfaces via Theory and Computation." The ability to produce good computer images of the mathematical surfaces has helped considerably in facilitating communication between the mathematicians and material scientists interested in this boundry layer phenomena.

Much of Hoffman's work as a math professor at the University of Massachusetts and in his present position at the Mathematical Science Research Institute consists of crossing boundaries and fostering communication between different intellectual cultures, allowing them to realize how much they can learn from each other. His view of the cohesiveness of intellectual understanding was already in evidence when he attended Rochester, where he majored in both history and mathematics. In 1996 when it seemed possible that the graduate program in mathematics would be terminated, Hoffman was one of many who wrote strong letters, suggesting that a better alternative must be found. Hoffman wrote from the point of view of one who had direct experience with undergraduate education at the Unversity of Rochester:

At Rochester, I was exposed to a great deal of science, first-hand, in an atmosphere that highly valued the humanities and the arts. It is evident to me and I hope it is clear to you that this has been a strong influence on my career. For me, all these things came together around mathematics. Without a strong graduate program in mathematics, I could not possibly have had this formative undergraduate experience.

and a few paragraphs later:

The vastly increased speed at which mathematical ideas find use in scientific disciplines, and then bounce back to mathematics in new forms--wavelet theory is one example, modern cryptography schemes another--has accelerated the tempo and expanded the scope of mathematics. It is no wonder that there is some confusion about what should be at the core of the mathematics curriculum and much controversy about how it should be taught. These are signs of change in a period of transition; they are not indications of irrelevance or decay. Mathematics is becoming more, not less, important in the sciences and in engineering.

Hoffman's words, and the words of hundreds of others who wrote on this subject in 1996, have not gone unheeded,and a better alternative has indeed been found. As math department chair Doug Ravenel wrote in the last newsletter,

The mathematical community has been watching Rochester closely ever since 1995/96 when the threat to our graduate program made us a cause celebre. On numerous occasions I have been asked to speak to professional groups about what has happened here since then. The story keeps getting better and better.

The interest and ability in mathematics among our students has increased dramatically with the advent of the Renaissance Plan; the enrollment in all of our calculus classes has increased, even as the size of the freshman class has decreased, and our honors calculus classes have the highest enrollment of any 'Quest' courses in the university.

We hope that many of you will come see this for yourselves and join David Hoffman and the students and faculty of the Math Department as we celibrate the sequescentennial birthday of the University of Rochester on October 13-15, 2000.