Around Tappan Square

Math Made Merry
They take the test because they want to, and it’s OK to score a zero.

story and photos by Yvonne Gay

Someone passing by the classroom of Professor of Mathematics Michael Henle last November might have mistaken the loud bursts of laughter and excited chatter as a teacher’s lesson plan gone terribly awry. That is, until the passerby realizes that the hubbub was centered on whether or not a “countable infinite set can have an uncountable collection of non-empty subsets, such that the intersection of any two of them is finite.” This was just one in a series of complex math problems that students pondered in preparation for the national William Lowell Putnam Mathematical Competition in December.

During weekly practice sessions last fall, Henle provided 12 students with “vintage” problems from previous competitions. Students took advantage of the informal atmosphere, choosing to gather in small groups or work independently while nibbling on snacks and eagerly exchanging ideas about problem solving.

“My background is simply a life of enjoying math,” said Christopher Kelly ’04, a math and physics major. “I have always enjoyed the feeling of working hard to solve a problem and then having it all click. The test is so hard that scoring a zero is quite expected for most people. My only goal is to enjoy myself.”

It’s difficult for the non-mathematically inclined to understand how anyone could get this excited about equations and theorems, but 2,900 undergraduate students from 450 colleges would suggest otherwise.

“This is the most prestigious collegiate mathematics competition in the U.S. and Canada,” Henle explains. “We compete with schools like Harvard, MIT, Duke, and CalTech, which have many more math majors to draw upon and sometimes offer whole courses in problem solving to train their students for the competition. It’s a good experience for our students.”

Launched in 1938 by the Mathematical Association of America, the Putnam competition “stimulates a healthy rivalry in mathematical studies in higher education.” The two-part, six-hour exam, which takes place at each participating school, is composed of 12 problems worth 10 points each. In theory, the top score is 120, but in actuality, it is typically 100 or less. Scores are usually less than 80, and nearly half of the participants often score zero.

The exam is not limited to mathematics majors (to a lesser extent, physics, computer science, and chemistry majors also take part), although most students have a strong background in the subject. Math major Alexander Zorach ’03 handled a course load of advanced calculus, rings and fields, and geometry while training for the test last fall; he also dedicated 40 hours a week to math outside the classroom.

“I enjoy solving math problems, and I like being challenged,” he said after one of the group’s weekly practice sessions. “Last night, I worked on one problem for an hour-and-a-half straight before solving it. It’s not so much the final product, but the process that I enjoy. Often the most fascinating and rewarding parts of a problem-solving competition are the partial results and interesting tricks that you find halfway through. I also feel that it improves my thinking skills.”

On December 1, Oberlin’s competitors painstakingly pored over each test question, hoping to land a score of 10 or better. Three months later, Henle received the good news. His students had finished in an impressive 47th place out of 450 schools. Two of the teammates—Jed Davis ’03 and Raymi Dyskant ’02 —ranked in the top 17 percent out of 2,900 students.

“My goal is to see interesting problems. I hope that one day I’ll be able to solve more of them,” says Nan Wong ’04, already setting her sights on next year’s competition. “[I also want to] get the highest score in the College someday.”