Ivars Peterson's MathTrek

August 26, 1996

Math Camp

From the Space Needle and monorail to the surrounding mountain landscape, Seattle offers a variety of attractions to any visitor of the city. For a group of high school students, however, the real attraction this summer was a chance to listen to, meet, and work with a number of prominent mathematicians.

For four weeks, 98 students housed at the University of Washington mixed mathematics with field trips, tennis, swimming, volleyball, and a host of other activities. It was a unique summer camp that kept them busy listening to lectures, pondering daily problem sheets, viewing math videos, trying things out on computers, and searching for proofs -- in effect, cultivating the art of doing mathematics.

The enthusiasm, spirit, and sense of fun were readily apparent when I visited the camp midway through its program. Equally evident was the camaraderie that had developed among the students, representing schools and communities throughout the United States and Canada, with a smattering from countries such as Singapore, Germany, and Turkey.

"Our backgrounds and ages don't matter," remarked Stephen Liang II, who attends the Thomas Jefferson High School for Science and Technology in Arlington, Va. "We're mathematicians. We're all here for the same purpose."

Many of the students were veterans of math competitions. Several had attended earlier incarnations of Mathcamp. A number had participated in local math programs and in summer institutes emphasizing math. What brought them to Seattle was the impressive roster of faculty and lecturers that had been assembled for this particular program.

Kenneth Ribet of the University of California, Berkeley, who had contributed key ideas that led to the recent proof of Fermat's Last Theorem, presented the inaugural lectures. These talks were videotaped, which initially had a somewhat intimidating effect on the students. They were hesitant to ask questions during the lectures for fear of disturbing the taping. But their strong curiosity quickly overcame this barrier, and Ribet had dozens of queries and comments to handle by the time his series of four lectures ended.

The students also heard from other distinguished mathematicians, including Atle Selberg, Joel Spencer, Herbert Wilf, and Richard Askey. John Selfridge, director of the more advanced of the two Mathcamp divisions, Richard Guy, and Loren Larsen were present for the entire program.

One benefit of this approach was that the students were exposed to a great deal of mathematics that they had not previously encountered. "You get an idea of the broadness of mathematics, how much there is out there," says Andrew Chi, who goes to Woodrow Wilson Middle School in Terre Haute, Ind.

The subjects were often covered in sufficient depth that the participants could begin formulating their own questions and problems. They learned about the many conjectures still not proved or disproved and of the many opportunities for doing mathematical research on their own.

As the camp continued, more and more of the math problems assigned daily came from the students themselves. They were quick to invent new questions, to suggest conjectures, and to point out errors.

"It's a great experience," Chi notes. "You learn how to express your ideas and thoughts clearly. You learn how to work with other people."

The combination of a talent for invention and the ability to work cooperatively came into play when the group designed its own camp T-shirt. The front features the statement "A mathematician is cautious in the presence of the obvious" encircling an "impossible" triangle. The back of the T-shirt shows the names of all the camp participants written in symbols from the Greek alphabet, along with a geometric diagram related to one of the quiz questions that the students had to answer to qualify for the Seattle Mathcamp.

The Mathcamp program now operates under the auspices of the Mathematics Foundation of America, a nonprofit organization created last year. It was the vision and hard work of George Rubin Thomas, however, that brought the camp into being, starting modestly with a small program in Vancouver in 1993.

Trained as a physicist in India, Thomas is now a research mathematician specializing in graph theory. He is also executive director of Mathcamp and divides his time (when not conducting Mathcamp) between homes in London, Ontario, and South Carolina.

"One of my goals is to give students a sense of the unity of mathematics," Thomas says. "But the camp should also be fun for the students. That's another one of my guiding principles."

This year's Mathcamp is now over, and the students have returned to their homes and schools carrying with them a portfolio of new math to ponder and use in the years ahead. The location for next year's Mathcamp has not yet been set, but preparations for that program are under way.

Know anyone interested in participating? Here are some of the questions from this year's qualifying quiz:

1. Two straight guy wires run from a point 24 feet above the base of a telephone pole to points on the ground. One wire is 1 foot longer than the other and hits the ground at a point 3 feet farther from the base of the pole. How long is the shorter wire?

2. A line passes through the point (2,2) and cuts a triangle of area 9 square units from the first quadrant. What are the possible values of the slope of the line?

3. Prove that every integer greater than or equal to 12 is the sum of two composite numbers (meaning integers that are not primes).

4. Place the numbers 1, 2, 3, ... 10 at the vertices and midpoints of a regular pentagon so that the sums of the three numbers along the sides are all the same.

Copyright © 1996 by Ivars Peterson.

References:

Additional information about the Mathcamp program is available at: http://www.mathcamp.org/.

George Rubin Thomas, Mathcamp executive director, can be reached at info@mathcamp.org.

Comments are welcome. Please send messages to Ivars Peterson at ipeterson@maa.org.