It happened on a typically foggy morning soon after I had arrived at the Mathematical Sciences Research Institute (MSRI) in Berkeley, Calif. Glancing out of my office window at the waves of mist swirling around the building, I caught a glimpse of a herd of goats. Confined within a temporary fence, the goats were busily chomping away on thick clumps of yellow grass and the green leaves of scraggly bushes scattered across the steep hillside down below.
Part of an effort to reduce the risk of fire sweeping through the Berkeley hills, the goats served as natural grass eliminators, able to go where no lawn mower dare venture.
There’s even more to see in the brilliant sunshine of a Berkeley summer afternoon. About 230 steps down the hill from MSRI via several narrow parking lots and sets of stairs is the Lawrence Hall of Science, which itself overlooks the domed accelerator facility and other buildings of the Lawrence Berkeley National Laboratory. From there, many more steps take you down to the main campus of the University of California. San Francisco Bay and the Golden Gate Bridge glint in the distance.
Housed in a three-story structure clad in weathered, dark-brown wood, MSRI occupies a spectacular location—longitude 122 degrees, 14 minutes, 23 seconds West, latitude 37 degrees, 52 minutes, 49 seconds North, and elevation 1,260 feet above sea level. In such a setting, it isn’t difficult to imagine MSRI as an important center of the mathematical world.
Indeed, the institute’s programs, conferences, and workshops attract mathematicians from all over the world. Some stay just for a few days; others spend a semester or more at the center, often focusing on some hot topic in mathematical research. This August, attention shifted to the specialized mathematical fields of noncommutative algebra and Galois groups.
"For the semester that we’re running a program, we like to think ... that we are usually the strongest center in the world in that field," David Eisenbud, MSRI director, noted in a recent issue of SIAM News.
The idea is to gather a diverse group of mathematicians representing, when possible, different approaches to and interests in a given topic. In some cases, physicists and other scientists join in the discussions and presentations. The resulting interactions turn such programs into exciting learning experiences for everyone involved, as they did in the recently completed session on random matrices, which had links to both number theory and quantum mechanics (see The Mark of Zeta, June 19, 1999).
In many ways, MSRI programs represent an effort to overcome the fragmentation of mathematical research into private conversations and highly specialized endeavors accessible only to a handful of experts.
It’s not unusual to hear a variety of accents and languages when MSRI members and visitors compare notes and trade tips. Each office has a blackboard (and plenty of chalk). Additional blackboards are strategically located in the atrium, along corridors, and even outdoors at the patio, ever ready to bear the scribblings that inevitably accompany an impromptu seminar.
Even in an age of instant communication via e-mail, telephone, fax, and the Internet, nothing beats face-to-face encounters—at a blackboard or over a table—to work things out. Afternoon teatime, in particular, draws people out their offices and away from their solitary pursuits.
Remarkably often during my three-month sojourn at MSRI (see MSRI Journal, June 12, 1999), I witnessed a mathematician standing at the ubiquitous blackboard, coffee cup or cookie in one hand and stick of chalk in the other, answering a question or patiently explaining some new mathematical wrinkle to interested bystanders. A book could be written about mathematical advances that came about because of chance encounters at afternoon tea (see The Return of Zeta, June 26, 1999)!
The skylights, floor-to-ceiling windows, white walls, gray carpeting, and potted bamboo plants create a subdued environment pleasantly conducive to mathematical thought and interchange. "It’s a nice place to work," Eisenbud insists, gently understating the pleasure he takes in being at the institute.
A noncirculating library with an extensive array of journals, a quirky collection of old and new books, and an assortment of mathematical games and puzzles provides handy reference material and entices the mind. Members can also glance at the morning New York Times or the latest issues of Nature, Science, Science News, The Chronicle of Higher Education, Scientific American, American Scientist, Communications of the ACM, and The Nation.
Some MSRI efforts reflect the enormous need for programs that bridge the gap between mathematics and the other sciences and foster interdisciplinary approaches. The coming year will feature workshops devoted to mathematics and imaging, the future of mathematical communication, quantum computation, and computational biology.
This summer saw the addition of a two-week program for graduate students interested specifically in the application of mathematics. The subject of the course was low-dimensional continuum mechanics, and students had a chance to try out their understanding of both mathematical model and physical theory in simulation projects ranging from microfluidic mixing to turbulent convection and pattern formation in liquids (see Row Your Boat, July 17, 1999). Next year’s course will focus on mathematical issues in molecular biology.
Even during a lengthy hike (led by intrepid outdoorsman David Eisenbud) into nearby Tilden Park for a lunchtime picnic and barbecue, the students taking this summer’s course continued to puzzle over their projects, in between comparing experiences at different universities, exchanging gossip, telling travel tales, and pondering job prospects. Those conversations, too, represent an affirmation of the collaborative nature of contemporary mathematical research.
Mathematical outreach can extend to all sorts of audiences. In July, a class of high school math students visited MSRI to learn a little about what mathematicians do and what makes them tick. From Hugo Rossi, outgoing deputy director, they obtained a glimpse of both the immense appeal and the inevitable frustrations of mathematical research at the frontiers of thought. They even got a brief lesson in the curious arithmetic of the ancient Egyptians.
The students also saw an impressively dramatic demonstration of juggling with balls and clubs, performed by Joe Buhler, incoming deputy director. They got a feel for the combinatorics of juggling—how numbers can be used to represent different juggling patterns (see Juggling by Design, July 31, 1999). To their delight, the students discovered that they could tap into some of the mathematical talent on display to glean hints on how to handle homework problems involving slope (rise over run) and linear equations.
MSRI offers more for the mind than mathematics. Special art exhibitions add provocative color and form to the white walls and the space within the high-ceilinged atrium. The current display features the collage-style work of Berkeley artist Mari Marks Fleming—visually rhythmic speculations on "time, nature, and the space between."
A more permanent fixture is an artwork by sculptor and mathematician Helaman Ferguson (see Minimal Snow, March 6, 1999). Called The Eight-Fold Way, the sculpture sits in the middle of the patio, framed by a backdrop of hills, pines, and eucalyptus trees. Carved out of a block of Vermont white marble, the roughly tetrahedral form rests on a black serpentine column. Covered with mysteriously indented curves and sinuous ridges, the sculpture invites comment and touch.
My final image is of a late afternoon concert in the atrium—of sunlight streaming in through the skylights to illuminate the members of the Peregrine Trio and of the sublime music of Mozart, Beethoven, and Haydn sailing throughout the building. It seemed a fitting finale to a stimulating summer spent immersed in a world devoted to the pursuit of mathematics.
Comments are welcome. Please send messages to Ivars Peterson at email@example.com.
Ivars Peterson is the mathematics/computer writer and online editor at Science News (http://www.sciencenews.org). He is the author of The Mathematical Tourist, Islands of Truth, Newton's Clock, Fatal Defect, and The Jungles of Randomness. He and his wife, Nancy Henderson, have just completed Math Trek: Adventures in the MathZone, a book for children of middle-school age to be published in the fall by Wiley.MATHEMUSEMENTS: Look for math-related articles by Ivars Peterson every month in the children's general-interest magazine Muse (http://www.musemag.com) from the publishers of Cricket and Smithsonian magazine.