Why Fields medalists are unlikely to emerge from the Indian education system

Of the four Fields medals—awarded every four years for outstanding mathematical work done by the age of forty—announced recently, three attracted attention for reasons that went beyond exceptional achievement. These three medals were awarded to Artur Avila, a Brazilian, Manjul Bhargava, a Canadian, and Maryam Mirzakhani, an Iranian. Mirzakhani became the first woman and Iranian to win the medal, Avila the first Brazilian and Bhargava the first person of Indian origin to do so. But while Avila and Mirzakhani were products of the educational systems of their respective countries of origin, Bhargava was emphatically not.

In a recent interview in the Times of India, among the several carried in the Indian media, which has rushed to claim him as India’s own, Bhargava seemed well aware of the failings of our system. “My sense is that mathematics is sometimes not taught in India as a subject in itself and/or a career in itself,” he said. “It is taught to be a tool for engineering and an eventual engineering career.” The familiar combination of bad teachers and learning by rote is compounded by a society that has an overly utilitarian attitude towards life and learning. Perhaps, the problems of this attitude are best summed up by looking at a recent editorial in the Business Standard, a paper that has covered the awards in some detail, titled “Why Maths Matters.”

The editorial argues that

... no matter how ‘abstract’ pure mathematics seems, it tends to find practical applications, sooner or later. ... A string of recent prizes and awards designed to reward pure maths research indicates that the world is coming to understand how important this is. ... These new incentives will hopefully inspire more children to consider pure research as a career. The world depends on technology—and technology depends on maths. What is more, maths that seems utterly obscure and abstract can suddenly become essential. Nurturing the gifted and giving them an atmosphere conducive to pure research could turn out to be mission-critical for civilisation.”

While this utilitarian argument may sound like a good pitch for a country to invest more money in teaching mathematics, it also seems to suggest that producing great mathematicians is a little like attracting people to investment banking. Well-meaning though the piece may be, it reduces the question of nurturing the gifted in mathematics to providing the right monetary incentives.

It is in this context that it is important to return to Bhargava’s interviews and read his description of mathematics as experienced by a mathematician:

“I always found the three subjects—music, poetry, and mathematics—very similar. In fact, I find that I think about them all in very similar ways. In school, mathematics is generally grouped in the ‘science’ category. But for mathematicians, mathematics—like music, poetry, or painting—is a creative art. All these arts involve—and indeed require—a certain creative fire. They all strive to express truths that cannot be expressed in ordinary everyday language. And they all strive towards beauty.”

To believe that instituting more awards for mathematics can produce outstanding mathematicians is akin to believing that instituting more literary awards such as the Booker will throw up a new Joyce or Proust. The problem with mathematics in India has little to do with the number of awards in the subject; it has everything to do with the problem glossed over in the editorial: that of nurturing the gifted.

On the average, Indians are no more (despite what we may believe about ourselves) or no less gifted at mathematical pursuits than the citizens of any other country, but given the size of our population, it is not difficult to see that we potentially have a far larger pool of children gifted in mathematics to draw from. If more Indians are not represented among the very best of mathematicians, it is largely to do with how even the most privileged section of our educational system is structured, both in terms of the curriculum and the stress on conformity.

We believe students learn only at one pace, and even more damagingly in the case of mathematics, in only one way. Far too many parents in this country have told me about their children being penalised in tests for solving a mathematics problem by a method other than the one taught in the class. It should be quite the contrary, a student who correctly solves a problem by innovatively thinking her way to a solution deserves more marks rather than less.

The problem stems from the fact that the vast majority of teachers themselves have been taught in the same way; their own idea of mathematics is of a subject with a rigid set of procedures leading to predetermined results. They carry the burden of finishing a pre-determined syllabus in a fixed period of time according to a prescribed text. They would not recognise creativity if it slapped them in the face. But if a student is to enjoy mathematics, she has to be able to play with the material, use it to uncover something till then unknown to her, arrive at a truth she has never accessed before. It is only through this sense of play that an appreciation for the creative process that lies at the heart of mathematics begins to develop in a student.

But given the way mathematics is taught in most schools and by most teachers, a fear of the subject is the most likely result—a natural reaction from children to a rigidly enforced code of procedures. Well-to-do parents, who have often experienced this same fear in their times, react in ways that are more damaging, by laying an even greater stress on rote learning through tuitions or by enrolling their children in one of the many systems such as “Vedic” mathematics or the latest fad from Japan—which are simply grab bags of simple mathematical tricks designed to do what a calculator can do much better, at much less emotional and financial cost.

Children who are successful in this system are designed to be anything other than great mathematicians. In a perceptive blog post, the late Rahul Basu, a theoretical physicist at the Institute of Mathematical Sciences in Chennai, compared the IIT-JEE examinations to the Tripos system that once prevailed at Cambridge. At the time of GH Hardy, Ramanujan’s benefactor and collaborator, it was an examination that mathematics students were required to take. “Since the Tripos was impossible to ‘max’ without adequate practice, a whole alternate system of education cropped up around it,” Basu wrote.

These were the coaching classes. Private coaches, for handsome fees, would coach you, not in the subtleties of mathematics but in how to take the Tripos. They would pour over old exams, make useful notes for solving problems, give you hours of practice all for the single minded purpose of taking the Tripos—what someone called codifying mathematical knowledge into neat bundles.

... The Indian analogy is obvious. The JEE is perhaps as stultifying, as mechanical as the Tripos. ... It stresses little knowledge of or ability in the subject, mainly a quickness of intellect and an ability to be able to use tricks to solve problems in the given time period. ... The Tripos system did produce some great scientists though few from amongst the toppers. Can the JEE boast of that? The numbers here are negligible and the names that spring to mind ... are hardly in the world class category of the Tripos toppers. More often than not, they end up in management, becoming CEOs or VPs of companies and only rarely a distinguished academic.

The way out of this quandary is not to institute more prizes and greater purses for mathematical results. Eventually, mathematics will thrive only in those places where the creative play of the intellect counts for far more than the drudgery of a corporate VPs job, however well-paid.