Mazur Named University Professor

By Alvin Powell

Contributing Writer
Harvard University Gazette

Reprinted with permission from the Harvard University Gazette of October 29, 1998

Barry Mazur, the William Petschek Professor of Mathematics, has been appointed a University Professor, Harvard's most distinguished faculty post, President Neil L. Rudenstine announced this week.

Mazur, a member of the Faculty of Arts and Sciences (FAS), is an internationally known mathematician, recognized for his work in the advanced mathematical areas of topology and number theory.

Mazur, 60, has been named the Gerhard Gade University Professor after a Harvard career that has spanned more than three decades. University Professorships, first created in 1935, are awarded to distinguished individuals whose work is at the forefront of their fields. University professors may teach in any department or faculty.

``I feel enormously delighted by it,'' Mazur said. ``I think it is a nudge, a challenge, to show how your subject -- and pure mathematics is my subject -- has connections to the other great intellectual pursuits.''

Mazur is an appropriate choice for the honor not just for his impact on mathematics, but also for his effect on the university and his students, Rudenstine said.

``Barry Mazur is a perfect match for the Gade University professorship,'' Rudenstine said. ``He thinks deeply. He teaches with great clarity and commitment. He helps trace the ways in which mathematics is integral to the structure of knowledge in the disciplines that may not otherwise seem to be significantly connected. We are indeed very fortunate to have him.''

Mazur's appointment brings the current number of University Professors to 19.

Jeremy R. Knowles, Dean of the Faculty of Arts and Sciences, praised Mazur's appointment, saying, ``Barry is not only a brilliant mathematician, but a wonderful teacher who engages biologists, physicists, economists, and others and seduces them into an understanding of the beauty and use of mathematics. I am delighted by his elevation to the Gade University Professorship.''

The Gade University Professorship was established in 1960 to honor Gerhard Gade, who graduated with the Harvard Class of 1921. Gade was a United States Foreign Service officer who bequeathed Harvard more than $1 million, half of which was used to establish the Gade professorship. Gade died in 1957.

Yum-Tong Siu, the William Elwood Byerly Professor of Mathematics and chair of the Mathematics Department, was thrilled by Mazur's appointment.

``It is definitely well-deserved,'' Siu said. ``He's a very distinguished mathematician. He's contributed a lot to the department and to the University.''

Siu said Mazur is well-known internationally. While most mathematicians contribute to one branch of the field, Mazur has the distinction of having made valuable contributions to both topology, a field of mathematics used to describe complex shapes such as knots in a string, and to number theory, which examines whole numbers and explores their sometimes complex relationships to one another.

``His influence is tremendous,'' Siu said.

Long Affiliation with Harvard

Mazur was born in New York in December 1937. His love of mathematics was sparked by an initial fascination with electronics when he was in his first year of high school. Mazur said he had an older friend who was very interested in the practical applications of electronics. Mazur himself, however, became enamored with the theories behind the applications, theories that ultimately led him to mathematics.

``The real mystery to me then was how energy could propagate through space,'' Mazur said. ``I couldn't understand it and became fascinated by the mathematics that explained it.''

Mazur attended the Massachusetts Institute of Technology, completing most requirements for a bachelor of science degree within two years. He was tripped up, however, by M.I.T.'s requirement that he participate in the Reserve Officer Training Program. He participated, but did badly, he admits. With the ROTC service a requirement to graduate, he said, M.I.T. withheld his degree.

Luckily for Mazur, Princeton University was understanding of his circumstances and accepted him into their graduate school. He received a Ph.D. from Princeton and then spent a year at the Institute for Advanced Study in Princeton.

Mazur left Princeton and came to Harvard in 1959, at age 22, as a Junior Fellow in the Harvard Society of Fellows. He became an assistant professor in 1962, an associate professor in 1965 and a professor of mathematics in 1969. He was named the William Petschek Professor of Mathematics in 1982.

Mazur's current research is in the field of number theory and builds on his background in algebraic geometry. Number theory is an advanced area of mathematics that encompasses things such as the study of very large prime numbers, which are involved in making unbreakable codes.

``The deep questions posed by number have inspired the creation of some of the most powerful mathematical techniques and theories,'' Mazur said. ``The more one studies these questions, the more one comes to realize how central a role they play in so many aspects of math and physics.''

Mazur is a wonderful teacher whose energy and sensitivity have endeared him to his students, Siu said. The large turnout of his former students, many from faraway places, at a celebration of Mazur's 60th birthday last spring is an indication of their high regard for him, Siu said.

Mazur said his teaching and research are interconnected, forming a kind of equilibrium. Even the most basic mathematics classes help provide a framework and perspective within which one can better view advanced topics.

``In order to get the full resonance of what one is thinking about, even if it is the latest idea in a technical realm, it's better if one is in touch with people who are just beginning to grasp the ideas,'' Mazur said.

In addition to his role teaching Harvard students, Mazur was recently sought out by the public television program NOVA to help viewers understand the complexities and drama involved in the solution of an advanced mathematical problem known as Fermat's Last Theorem.

Mazur has won numerous prizes and honors over the course of his career, including the Mathematical Association of America's 1994 Chauvenet Prize, the American Mathematical Society's 1982 Cole Prize for work in number theory, and the American Mathematical Society's 1965 Veblen Prize in Geometry for his work in topology.

He was awarded the Veblen Prize for work on ``the generalized Schoenflies Theorem,'' a famous topology problem that has to do with the placement of curved surfaces in three-dimensional space and their analogs in higher dimensions.

The theorem says that while a one-dimensional string can occur in three-dimensional space in a knotted configuration which cannot be undone without cutting, a seemingly knotted two-dimensional balloon can always be untwisted into the shape of a perfectly round balloon, again without cutting or piercing. It also says that the analog of this is true in higher dimensions.

Mazur solved this problem and proved the theorem is true, using a technique now called the ``Mazur Swindle.''

Mazur was awarded the Cole Prize in number theory for developing methods in the arithmetic theory of elliptic curves. These methods proved essential to the later solution of Fermat's Last Theorem -- which had defied proof for 350 years -- by Princeton University Professor Andrew Wiles. Wiles' work included a collaboration with Harvard Professor of Mathematics Richard Taylor.

Fermat's Last Theorem says that the sum of two N-th powers of whole numbers is never equal to an N-th power, when N is greater than 2. This is in sharp contrast to what happens when N is equal to 2, for example, 9 + 16 = 25.

Mazur was elected a member of the National Academy of Sciences in 1982.

He has written about a hundred articles, the most recent of which are, ``Hypersurfaces of Low Degree,'' co-authored with J. Harris and R. Pandharipande, which appeared this year and ``Introduction to the Deformation Theory of Galois Representations'' last year.

Mazur has frequently been a visiting professor at the Institut des Hautes Etudes Scientifiques in Bures-sur-Yvette. Most recently, he has been a Miller Visiting Fellow at the University of California in Berkeley and was the John Harvard Visiting Professor at Emmanuel College in Cambridge, England.