Prof. Bruce C. Berndt of the University of Illinois talks to Hema Vijay about his research on Ramanujan's theorems and the enigma in his lost notebooks
His favourite photograph of himself is one in which he grins happily, holding an ancient scribbling slate in front of his chest. The slate is no ordinary one; it happens to be the one on which India's prodigious mathematician Srinivasa Ramanujan worked out numerous ground-breaking math theorems, as paper was a commodity the math genius could ill afford.
Bruce C. Berndt, Michio Suzuki, Distinguished Research Professor of Mathematics at the University of Illinois, editor of The Ramanujan Journal, and a recipient of the Steele Prize from the American Mathematical Society (for his work explicating the theorems in Ramanujan's Notebooks), was in Chennai recently to meet Indian collaborators such as R. Sivaraman of the Pie Mathematics Association. In his earlier visits, Prof. Berndt had even visited the Town High School at Kumbakonam that Ramanujan studied in, the Port Trust office in Chennai that once employed Ramanujan, and his house in Triplicane, where he met Ramanujan's wife Janakiammal — once in 1984, and again in 1987. “All this gives me more insight into Ramanujan,” he says, adding, “Some of the papers that Ramanujan had left behind got stolen, Janaki told me. How much math was lost, we will never know.”
For over 25 years now, Prof. Berndt has been unravelling the mind of Ramanujan, proving the brilliant but often undecipherable theorems the genius had scribbled down in his famous ‘notebooks'. Not surprisingly, K. Srinivas, Institute of Mathematical Sciences, Taramani, say: “Prof. Berndt is not only an authority on Ramanujan's math, he is an inspiration to all of us.”
“In some ways, it is fortunate that Ramanujan didn't have formal training in math. If he had had to undergo the European kind of math training, he would have had to spend time proving his results vigorously, and would consequently have discovered far less,” says Prof. Berndt. “Some of Ramanujan's math is simply startling. If he had not discovered them, nobody would ever have. These equations make connections between entities you would never have supposed to have connections.”
Prof. Berndt, however, does not feel that Ramanujan had a mystic insight into math. “Sometimes we do wonder how he came across such beautiful ideas, but I think that every one of his theorems was worked out, and not devised in a flash.”
Ramanujan's works will continue to create intellectual ripples, besides practical applications, apparently. “Theories of partition functions that Ramanujan worked on has enormous scope, like applications in an area called combinatorics — the science of counting, and of course in computing, for choosing the best algorithms for computing,” comments Prof. Berndt.
In the last few years, many mathematicians have been working on mock theta functions that Ramanujan worked on extensively, as also his probabilistic number theories and work in highly composite numbers.
Also, as Prof. Berndt points out, Ramanujan's math ignites minds. For instance, mathematician Atle Selberg and physicist Freeman Dyson have stated that coming across Ramanujan's number theory problems motivated them to pursue math as teenagers.
Would India ever produce more mathematicians like Ramanujan? “If creative math is to be encouraged, teachers should not insist that students solve problems in the only way they prescribe,” Prof. Berndt says.
Recently, the concept of memorising has come under a lot of criticism. “I think that students need to both memorise information and be exposed to projects that apply their knowledge,” feels Prof. Berndt. “For instance, one of my brightest Ph.D. students is an Indian, Atul Dixit; he has a wonderful memory, and it helps his work enormously. Obviously, his schooling had inculcated this memory power in him.” Incidentally, another of this professor's Ph.D. students was James Atler, whose work has revolutionised the area of functional equations.
Prof. Berndt is now working on the set of Ramanujan's papers that were rediscovered at the Trinity College Library in 1976, and enigmatically named the ‘lost notebook'.
In parting, Prof. Berndt reveals an interesting facet of Ramanujan as a boy — of Ramanujan's math score in his F.A. exams to get a collegiate education. “He was marked only 85 points out of a maximum of 150 in math! My guess is, Ramanujan probably worked only on the problems that interested him.”