Preface
The best-known recent biographer of mathematicians is Constance Reid, the San Francisco writer, whose life of David Hilbert was highly praised when it was published in 1970. Her sister Julia Robinson was a distinguished University of California, Berkeley mathematician married to Raphael Robinson, also a Berkeley mathematician. Julia’s marriage to Raphael and Berkeley’s close proximity to San Francisco brought Constance in frequent contact with many mathematicians, and she found that she enjoyed their company and the culture in which they were embedded. Her interest in them eventually reached the point that she decided to write the Hilbert book, followed by volumes on Richard Courant, Jerzy Neyman, and E. T. Bell. After observing mathematicians for some time, she summarized her impression of them: “Mathematics is a world created by the mind of man, and mathematicians are people who devote their lives to what seems to me a wonderful kind of play!” It’s true—if you’re around a group of mathematicians excitedly talking about mathematics, you come away with a sense that whatever they’re doing, it’s fun.
Martin Gardner, the most widely read expositor of mathematics of the twentieth century, during the twenty-five years that he wrote a monthly column on mathematics in the Scientific American, came to know hundreds of mathematicians, many of whom had been inspired by his work. He corresponded with some of the best mathematicians in the world, who regularly sent him news of mathematical developments that he often fashioned into wonderful columns that were enjoyed by thousands of readers every month. One of us interviewed him a few years ago, and he had this to say about mathematicians: “There are some traits all mathematicians share. An obvious one is a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics.”
Both of us have interacted with large numbers of mathematicians in our professional lives as professors, journal editors, and officers of the Mathematical Association of America. We have interviewed dozens of mathematicians over the last thirty years, and our conversations with and personal observations of scores of mathematicians lead us to strongly agree with the descriptions of mathematicians provided by Reid and Gardner.
Historically mathematics has often been motivated by questions in astronomy, mechanics, the physical and biological sciences, and, more recently, in economics. It is therefore widely appreciated because it works. It tells us about phenomena that are otherwise hard to explain and yet are important to society. Modern, so-called abstract, mathematics is not so easy to justify on the grounds of utility because much of it is developed from within the discipline of mathematics itself, just because it is interesting. But then the miracle occurs—suddenly recondite properties of seemingly useless prime numbers, for example, become essential as your ATM machine communicates safely with its central bank. Modern-day mathematics is certainly an example of the remark of the eminent physicist Eugene Wigner on “the unreasonable effectiveness of mathematics.” Some abstract forms of mathematics seem far removed from practical scientific questions, and then sometimes we find these ideas popping up in applications when we least expect them.
Who then are these people who devote their lives to mathematics? Like other people, they come in a variety of shapes, sizes, and temperaments. Some are gregarious and outgoing, others reserved. In these interviews we see a wide range of people drawn to this beautiful subject. They come from diverse family backgrounds: blue collar, white collar, the socially prominent, or from long-standing academic families. Some are seriously religious, others are not, at least outwardly. Some were thinking about mathematical ideas in the early grades, and others did not come to the subject until high school, college, or graduate school. As you read these interviews, profiles, and memoirs you will come to the conclusion that there is no such thing as a typical mathematician. But all of them share a passion for mathematics (and, in many cases, other fields as well).
One common myth about mathematicians is that they are especially interested in music. It is true for some but not for others, although mathematics and music both deal with patterns. Scanning the mathematicians in our three volumes of Mathematical People interviews, we find no evidence of a strong music-mathematics connection. Mathematics is one of a very short list of disciplines where we find some child prodigies. We don’t see historians who are child prodigies. To write good history one needs a lifetime of experience, something unnecessary in observing some deep pattern in the whole numbers, for example. Of course, not all successful mathematicians were prodigies, either.
In reading these interviews and profiles, the reader can perhaps recognize some patterns. But the diversity is probably the more interesting observation about their lives. Diversity is also evident in the range of talents of mathematicians within their subject. Some are great problem solvers. Others are less talented at solving concrete problems but see vast structures within mathematics. Both talents are valuable. These structural questions are rewarding in themselves. For example, sometimes we see an enormously rich structure come from a minimal investment. Four seemingly straightforward and simple properties define the idea of a mathematical group, but they lead to an amazingly subtle and deep branch of mathematics that solved not only classical problems but a couple of centuries after their formulation still provide a way of approaching difficult problems in the sciences. One sees the same phenomenon in the seemingly small investment in the definition of an analytic function and then beholds the most amazing developments of the field of complex analysis. Small wonder that the subject is described as beautiful!
Does exceptional mathematical talent run in families? There’s some evidence to suggest that it does. In these pages we read reminiscences of Alice Beckenbach whose father and brother were professional mathematicians of note. She married A. W. Tucker, the topologist and long-time head of the Mathematics Department at Princeton. She has two sons who are professional mathematicians, one at Colgate, the other at the State University of New York, Stony Brook. One of those, in turn, had a son, now a mathematician at the University of Rochester, and a daughter, who is a biologist now at the National University of Singapore. In that family there clearly were some “mathematical genes.” The most renowned mathematical family in history was the Bernoulli clan, a Flemish family living in Basel: in addition to the obvious progenitors, Jacques, Jean, and Daniel, there were Bernoullis active in mathematics through three generations. They are the mathematical counterparts of the phenomenal musicians, the Bach family, in Eisenach and Leipzig. The Bernoullis do not make it into the current collection, nor do some more recent father-and-son combinations: Elie and Henri Cartan, George David and Garrett Birkhoff, as well as the earlier Benjamin and Charles Sanders Peirce.
Some here—Ahlfors, Cartwright, McDuff, and Selberg—are in the very top ranks of research mathematicians of the twentieth century, invited to be major speakers at International Congresses and, in two cases, winners of Fields Medals, the equivalent in mathematics, in some ways, of Nobel Prizes. Others are major figures in mathematics who have extensive publication records—Apostol, Banchoff, and Taylor—but have also acted as mentors and dissertation advisors, thus having had an influence on research mathematics far beyond their own campuses.
Then there are the extraordinary teachers, a list including some of those above but also others who have fine research records but who have had broad influence on twentieth-century science and mathematics: Bacon, Benjamin, and Gallian. Who is to say whose overall influence on the future directions of mathematics and science will be greatest?
There are also present here people working around the edges of traditionally central areas of mathematics: Saari (physics and astronomy, as well as, in later years, economics and social sciences) and Tondeur (public policy and mathematical administration).
It is not easy, however, to categorize these people because in large part they often excel in various activities, not just research or not just in teaching or administration. There is Bankoff, who probably could have had a good career in mathematics but chose instead to be a dentist, who just happened to edit a problem section of a mathematical journal and wrote mathematical articles on the side. He was the dentist of choice for many Hollywood stars and rock musicians. He was also a jazz pianist.
Gallian, a great teacher, is also an international expert on the Beatles. Benjamin enjoys a second career as a professional magician who has performed on a number of network television shows and on a host of national stages. Guy and Taylor are highly accomplished mountain climbers.
We are certain as you read this volume that you will encounter several mathematical people whom you would like to know better and with whom you would enjoy having dinner.
Donald J. Albers
Gerald L. Alexanderson
January 2011