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Students must be taught to appreciate the beauty of mathematics

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Ten years ago as India celebrated the year 2012 as the year of mathematics in honor of 125th birth anniversary of Ramanujan,  Alladi Krishnaswami, a leading Ramanujan scholar and professor of mathematics at the University of Florida (USA) who was also the Associate Editor of Notices of the American Mathematical Society and the founder editor of The Ramanujan Journal (published by Springer) besides editor of the book series Developments in Mathematics in a conversation with Autar Nehru in New Delhi had talked on his interest in Ramanujan’s work and reviving his legacy as also on some of the issues mathematics is faced with.

You are a leading Ramanujan scholar and in fact one of the big reasons behind the revival of his legacy in India and abroad in the last 15 years or so. Your book titled, ‘Ramanujan’s place in the world of mathematics’ has also been recently released. How were you attracted to Ramanujan and his mathematics?

I learnt number theory as was fascinated by it. It was not because of Ramanujan that I read it but I had a brief expose to it as a student. But then this theory led me to Ramanujan and his work. Inspired by what I saw and heard during the Ramanujan Centennial in 1987, I wanted to create something that would be a permanent and continuing memorial to Ramanujan, namely, The Ramanujan Journal, devoted to all areas of mathematics influenced by Ramanujan. This idea received enthusiastic support from mathematicians worldwide, many of whom have served, or are serving, on the editorial board. The journal was launched in 1997 by Kluwer Academic Publishers, which published four issues of one hundred pages per year in one volume. Now the journal is published by Springer, which publishes nine issues per year of one hundred fifty pages each in three volumes. The rapid growth of this journal is a further testimony to the fact that Ramanujan’s work is continuing to have major influence on various branches of mathematics.

Since the Ramanujan Centennial, I have written articles annually comparing Ramanujan’s life and mathematics with those of several great mathematicians in history, such as Euler, Jacobi, Galois, Abel, and others. These articles, which were written to appeal to the general public, appeared in The Hindu. The collection of all these articles, along with my book reviews and other Ramanujan-related articles, has just appeared as a book Ramanujan’s place in the world of mathematics’ for Ramanujan’s 125th anniversary.

Do you think declaring 2012 as the year of mathematics as a befitting tribute to genius of Ramanujan and inspiring young children towards mathematics was a great idea and initiative by the Government of India?

The wide recognition to Ramanujan’s achievements and his mathematics helps both the cause of mathematics and the country. By remembering him and creating his legacy, India’s flag flies high. Declaring year of mathematics is a good thing to do and encourage the kind of conferences we just attended and it also draws attention to the issues. But these things also need a follow up. Emphasis on mathematics education and to check its fading popularity and relate it to contemporary research and issues is a continuous effort. These kind of things are not a moment, you can’t stop at that but then as we know there is generally no follow up to these kind of initiatives in India. The Government must take this call seriously and set up follow up programmes and action plans with a funding commitment. After another 125 years, we’ll really see that.

There is a lot of concern over the dwindling interest and research in mathematics education among students. Your thoughts.

Actually mathematics teaching is less and less competent these days in schools not just India but throughout the world and is a matter of great concern. It used to be taught quite well until some years but now what has happened is that in order to rush to teach and learn calculus, most subjects are taught in slip short fashion and this is harmful for mathematics. Mathematics is an art as well. One should enjoy the symmetries, beauty of equation and structure, so the students must be taught to appreciate the beauty of mathematics. Of course usefulness is always there but the emphasis should also be on beauty especially in schools as people are always drawn to things which are beautiful.

Do you think the aggressive marketing of ICT tools like computers and other technology is hampering the natural way of mathematics learning?

For mathematics, it is important to learn concepts first. Just because you use calculators or computers doesn’t mean you understand mathematics. In fact, too much dependence on computers and calculators hampers your learning of mathematics. What one should do is, first learn mathematics concepts, start proving it yourself, then use computer and other aids or guides to discover more. I would hesitate using of computers and other aids in the beginning and once concepts are understood, then whatever technology and tools are to be used serve a purpose. I see it in classes in USA at university where I teach students that they rush to use calculus and computers to find answers. Unfortunately, with this trend, I can see the mathematics ability has gone down. I don’t mean IQ has come down rather it improves with every generation and students are in fact intelligent, but mathematics training of this generation has been hurt and this has been a recognized problem. It is like laying too much emphasis on T 20 cricket where the players forget the art of classic strokes like leg glace, square cuts and ability to build innings and stay at wicket. Mathematics is about thinking deeply and to give proof, which is amiss these days.

How can this trend be arrested or turned around?

The thing is that you don’t only need good mathematics teaching but also need good teachers. Therefore universities have dual purpose one is of course to have professors, faculties, PhD students for research, which are necessary for advancement of the discipline but at the same time they also share a responsibility to train good mathematics teachers. The teachers must be have well grounding of subject because they must have advanced understanding of the subject, then only can they answer difficult questions asked by students.

Do you agree that the game of chess improves mathematical ability?

Chess is a logical game. The player has to think about possibilities and counter move of his opponent. It is sheer logic. Mathematics is also logic applied to numbers and systems but it is not a game. A great chess player has the ability to think about patterns, it is an intellectual game, so definitely it must improve mathematics ability as well.

Vedic mathematics is often seen as a matter of pride for Indians and some people have taken to commercialize its formulas as a quick fix solution to teach children mathematics.

I am not an expert on Vedic mathematics. Having said that we shouldn’t make loose statements and put everything in poetic form. Our ancient people have made great contributions to mathematics including the decimal system which is basis for all numerical calculations. But to say that they knew everything including about atom bomb is not right. We should be able to analyze the formulas of Vedic mathematics and say this is something they achieved. An impartial, penetrating systematic analysis of the formula contained in Vedic mathematics must be undertaken in a study. Government of India can set up some funds for it and in addition to historic significance, the whole world can have a proper mathematical perspective.

You have kept your involvement with India despite having a busy professional and personal life in USA?

I come to India twice every during vacations. I often lecture high schools students in Chennai, which I enjoy that is the age to attract them to mathematics. Even if one or two students are inspired to pick up every research, it is satisfying. The other thing I do on regular basis is holding of the annual conference for Sastra University around December each year. With the institution of Srinivas Ramanujan’s Award, I chair the prize committee. The award is doing good to as much to profession as it is beneficial to the standing of India. Through this the flag of India flies high and we can take pride in the achievements of Ramanujan.

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