Know Your Wisconsin Mathematician
Interview with Professor Ranjan Roy, Beloit College by J.
Sriskandarajah, Madison College.
Tell us something about your education and how you got
interested in mathematics.
I received my secondary education at an Irish Christian Brothersschool in the hills of India. I had an excellent mathematics teacher,and a well-rounded education, including lots of sports. Aftersecondary school, I stayed at home with my parents for about
eighteen months studying mathematics very intensively, working atleast fourteen hours per day. My parents gave me greatencouragement and practical and emotional support in my studies. I got my B.S. in mathematics,physics, and chemistry at Indian Institute of Technology, Kharagpur, West Bengal, where I had
good teachers of mathematics. In spite of the fact that this was an engineering college, I got aliberal education at Kharagpur. I received my M.S. in mathematics at I.I.T Kanpur, U.P. where
the math department was quite strong. At Stony Brook University on Long Island, NY, I studied
under Irwin Kra and Bernard Maskit, students of Bers, and received my Ph.D. in 1973.
Where have you worked and how did you end up at Beloit College?
After receiving my Ph.D., I taught at the University of Kentucky for a short time. There, Icollaborated with S.M. Shah and published many papers with him. Then I returned to India
where I was first at I.I.T. Delhi and then at Himachal Pradesh University in Simla, in the hills.
Soon I received a fellowship at the Institute for Advanced Study in Simla where I was able to do
my own research. In Simla I collaborated with Mihir Bannerjee in applied mathematics topics.
After this two-year fellowship, I was appointed Reader at the Mathematics Institute at Punjab
University in Chandigarh. After some time there, I returned to the U.S. and taught for two years
at SUNY Plattsburgh. In 1982, I came to Beloit where I thought my opportunities for researchwould be better and where the students might be of a higher quality. I have been able to pursue
my own work while at Beloit and I have also been able to collaborate with Richard Askey inMadison, as well as with mathematicians from farther away. I have enjoyed and still enjoy mycolleagues, my students, and my teaching at Beloit.
What are your mathematical interests?
I am an analyst with an interest in the history of mathematics. I have done work in differentialequations in the complex domain, Kleinian groups, fluid mechanics, and special functions. I
published a book on special functions with Askey and George Andrews and I am almost finishedwith another, longer book on the development of mathematics. I also contributed to the NIST
Handbook of Mathematical Functions, to appear very shortly.
What makes for a successful mathematics teacher?
First, a good teacher must know and love his subject and also care about his students. In addition,
he should be aware of the background of the students and on that basis devote thought to how thematerial should be presented. One must try to show how a subject arises out of a small number ofideas and attempt to clearly reveal the interconnections among the ideas. A sense of humor andan organized approach are also helpful. Repetition is critical. One must repeat and review thematerial many times. Finally, one must somehow convince one’s students that they will findenjoyment by devoting attention and hard work to the subject.
How has mathematics changed over the years?
This is a very broad question. I will discuss some aspects of mathematical notation andsymbolism and how they have influenced the development of the subject. In the 1500s and early
1600s, very little abstract notation was used. To see this, one may read the original works ofCardano or Bombelli. Theorems and procedures were described largely in words, often
accompanied by diagrams. Even as late as Pascal, we find that he stated important theorems
completely in words. Starting with Viete, mathematical notation began to be more symbolic of
the algebraic operations. Harriot and Descartes took giant steps in this area, so that their notationis almost modern in form. This advance greatly facilitated the manipulation of algebraic
variables and made mathematical calculation much more transparent. Thus, we may read withsome ease the mathematical works written after 1650. To see this, one may study the original
works of Wallis, van Schooten, or Newton.
Starting approximately in the nineteenth century, an abstract, noncomputational, and generalized
approach began to grow, culminating in Hilbert’s first proof of the existence of a finite basis forinvariants. The abstract and existential nature of this result prompted Gordan to exclaim, “This is
not mathematics; it is theology!” Ironically, Gordan’s only student, the great Emmy Noether,became the mother of twentieth century abstract algebra. This trend, epitomized by Bourbaki andGrothendieck, overshadowed for some time the computational and algorithmic approach tomathematics. With the advent of the computer, we have a resurgence of interest in algorithms
and formulas, so that even algebraic geometry was found to contain many interesting andimportant problems of a computational nature.
It appears to me that there have always been mathematicians who love to calculate and those who
prefer to think in broad general terms. Naturally, to be a mathematician, one must do both, but
one may lean one way or the other. For example, Fermat was a big idea man, with penetrating
insights, and he was a sloppy calculator. By contrast, Stirling loved computation; he executed theprodigious task of computationally interpolating the factorial sequence 1, 1, 2, 6, 24, 120… toten decimal places, finding that the midpoint value between the first two terms was .8862269251.
He at once recognized this value as √π/2. Today, armed with powerful abstract theories
accompanied by the computational facility of computers, both types of mathematicians canflourish.
What are your hobbies?
I spend most of my time doing or reading or teaching mathematics. I also read on a wide range oftopics, including history and philosophy, and I like to play handball. In addition, I am an oldmovie buff and I enjoy walking and spending time with my friends and with my family.
Tell us something about your family.
My parents died long back, though my mother in law is still with us, and I have two brothers andtheir families. I have been married to Gretchen Carey for nearly forty years. She has a Ph.D. in
philosophy from Stony Brook and she is very supportive of my work. We have a daughter and ason, both married to wonderful people, and they each have one child. My wife and I are happy
grandparents.