Integrating Math and Students

It is said that some of Harvard's most renowned professors are so concerned with their own academic research that they have little time to devote to undergraduates. However, one Harvard math professor, who many call one of the most brilliant members of the department here, can often be found in Lowell House dining hall or in his office talking with undergraduates on all sorts of topics.

Hollis Professor of Mathematiks and Natural Science Andrew M. Gleason, who 30 years ago solved one of the most difficult math problems proposed this century, devotes much of his time today to thinking about ways to improve the teaching of math at Harvard and around the world.

"He started his career by solving the famous Hilbert's fifth problem as part of a team, which is quite an outstanding achievement," says colleague Raoul Bott, Graustein Professor of Mathematics. "But he's always been very interested in the undergraduates as well. His office is always full of them."

Gleason, who was granted tenure without a Ph.D. after he had solved the notoriously difficult Hilbert problem, focuses his academic work on topology and space mathematics. David Hilbert, a German mathmetician, proposed a series of about 10 problems he considered the most pressing math questions unsolved at the turn of the century. Math scholars are still working on solving some of the problems, which define much of 20th-century math.

"Considering the fact that he's such a superb researcher in math," says Deborah Hughes Hallett, senior preceptor in mathematics, "Andy's done a considerable amount with teaching, which he certainly hasn't had to do. He's done lots as far as undergraduate education and has been extremely important in a number of ways as far as getting things started."

The professor has taught and studied almost every math course in the catalog from Math B, an old algebra course, to Math 212, "Functions of a Real Variable," a course on abstract set theory.

Gleason, who has written two math textbooks, says he most enjoys teaching a freshman honors course, Math 25, "Honors Intermediate Calculus." "It's actually a more sophisticated course than the title suggests," says Gleason. "And it's enjoyable to present the material to students who are excited about the work and able to grasp the concepts easily."

Chairman of the Math Department Arthur M. Jaffe says that Gleason also gets undergraduates interested in math by promoting their participation in the Putnam Math Competition, a national math exam taken by the brightest young math scholars in the U.S. Gleason won the contest three consecutive times as an undergraduate.

QRR or Calculus

At Harvard, Gleason was also the founder of the Core Curriculum's Quantitative Reasoning Requirement (QRR), a test on basic statistical and math abilities that all undergraduates must pass by the end of their freshman year. He currently serves as the QRR's chairman and as a representative to the Core's Board of Advisers.

When the Core and QRR were being formed, several math professors believed that all Harvard freshmen should be required to take basic calculus courses. Gleason instead decided about 10 years ago to focus the QRR on the numerical skills an average student would need to survive college-level courses.

"He did the whole QRR singlehandedly," says Bott. "And while there are some of us who belong to the old school and feel all [students] should have to take calculus, we're very grateful for his new ideas, that he is concerned with those sides of math."

"He was responsible for determining what kinds of math and reasoning would need to be included on the QRR test," says Hughes Hallett. "He has been very important to people in math courses, but he's also been concerned with teaching math to people who are not concentrators as well."

Gleason says that it was not until he began to work with the Core and the QRR, in fact, that he realized the extent to which many students loathe and even fear working with numbers.

"Deborah Hughes Hallet felt that I didn't have a good idea of what students outside the math concentration were like and suggested that I teach some students who were taking math only as a requirement," says Gleason, who will be head tutor of the Math Department this spring.