MATHEMATICS – The music of reason Mathematics is quintessentially about the world of ideas SUBJECT MATTERS PROF M A SOFI Where does India and, in particular, the state of Jammu & Kashmir stand in the development of mathematics as an important human endeavour? Before one begins to understand the subtext of this question, it is important to point out the ways in which mathematics is grossly misunderstood by the general public, not excluding the educated fraternity whose view of mathematics is pathetic, at best. This is so because of the general perception that mathematics serves as a useful tool in science and technology where its role has no doubt been immense, and that one who is good at mathematics is naturally good at manipulating numbers – a skill which comes in handy in our day-today activities. The fact is that whereas these mundane useful aspects of mathematics in science and technology are merely a trivial by-product of the practice of mathematics as an art of sorts, it is rarely the case that mathematics has anything to do with numbers, at least in the sense in which it is generally perceived by the public. There is, though, a part of mathematics which deals with numbers, not in the conventional sense but as part of the mathematical enterprise that seeks to discover patterns where there apparently aren’t any. This aspect of mathematical activity reveals mathematics both as a science – the science of patterns and more importantly, as an abstract art – the art of explanation through mathematical proof which seeks to explain in a logical and rigorous manner the truth underlying a mathematical pattern. To quote Paul Lockert, “A beautiful proof should explain, and it should explain clearly, deeply and elegantly. A well- written, well-crafted argument should feel like a splash of cool water, and be a beacon of light – it should refresh the spirit and it should illuminate the mind. And it should be charming”. Here we witness the beauty of music in mathematics as it doubles up as an art and as science: the music of reason in concert with the music of spheres. What a symphony! To what extent is mathematics the creation of the human mind or in what way is mathematics rooted in the physical universe around us are some of the vital issues which should inform the understanding of a culturally evolved, educated individual. When Bill Thurston, a famous topologist from Berkeley who died recently, says that a mathematician is one who helps in the human understanding of mathematics, he is only endorsing the view that mathematics is divine and that it resides entirely in the human mind. All the same, we know that mathematicians conceived of black holes long before physicists actually found them, even when certain important problems in mathematics – and, more importantly, their solutions – belonging to the so- called low-dimensional topology were motivated by certain considerations arising in theoretical physics! This dual nature of mathematics combining in itself elements of art and science is singularly unique to the practice of mathematics and is not encountered in any other domain of human endeavour. However, just because something happens to have practical consequences does not mean that is what it is all about! It is sad that the current system of assessment and evaluation of mathematical research has led to a culture where one has to learn to bend backwards to give mathematics the relevance that is quantified in terms of its ‘practical applications’. Just because a subject happens to have practical use does not mean that we have to make that use the single focus of teaching and learning. The main purpose of teaching beyond imparting the mundane skill to read and write is allowing our students access to the world of beautiful and meaningful ideas, something that will help them grow into right thinking, cultured and cultivated human beings. There is also this morbid trend aimed at making mathematics ‘interesting’, even when one must note that it is already more interesting than one can possibly handle, provided it is allowed to be taught in the way it is supposed to be. That entails approaching mathematics with a view to engage in an act of discovery, conjecture, intuition and inspiration in an atmosphere unencumbered by the demands of the contemporary system whereby a huge premium is placed on scoring high at the school level on the one hand, and on increasing the points tally at the university level on the other. By assigning numerical values to certain parameters that include, among other things, the number of publications and the so called impact factor which, at least in mathematics, has ceased to be a reliable measure of the ‘achievement co-efficient’ of a mathematician. These self-appointed votaries of ‘quantification’ would do well to know that the beauty of mathematics consists in pursuing it as an art for art’s sake and that the utilitarian aspect of it involving its practical applications is only a welcome bonus of this purely artistic and cerebral activity. An unpleasant consequence of this lopsided emphasis on ‘quantifying research’ has been the abysmal level to which the teaching standards have fallen at all the levels involving schools, colleges and the universities. In such a scenario, coupled with the fact that teaching and research enjoy a symbiotic relationship, it is all but natural that the quality of research in our universities will be adversely affected with a fall in the standards of teaching. What is important to note is that teaching is not about passing of information to the students – it’s about an honest, intellectual relationship with them, with the ability to be real. You will never be a real teacher if you are not willing to be a real person. Teaching is synonymous with openness and honesty and the ability to share excitement and a love of learning. Such an approach towards teaching can only come from total commitment and dedication which can no doubt be inculcated, but which cannot be taught as it involves individual passion and personal integrity. A piece of mathematics is like a poem where one can ask if it satisfies one’s aesthetic criteria. The trouble, however, is that like poetry or painting, mathematics is creative hard work and it is a slow, contemplative process. This brings to mind Pushkin’s famous words: “Inspiration is needed in poetry as much as it is need in geometry”. However, the similarities between these art forms and mathematics end right there. As G H Hardy had aptly put it: “a mathematician, like a poet or a painter is a maker of patterns and that if his patterns are more permanent than theirs, it is because they are made with ideas.” Mathematics is and always has been quintessentially about the world of ideas. However, it is true that not every educated individual shall have the necessary background for appreciating these ideas. Indeed, what may arouse the curiosity of a mathematician may excite no interest or passion in a person who is not initiated in the practice of mathematics and thus, completely oblivious to the breathtaking order and inner harmony that characterise the world of mathematics. It is an undeniable fact that our colleges and universities do not provide the right combination of factors that would help foster an atmosphere where scientific activity could be pursued and sustained so as to conform to the broad guidelines involving teaching and research in mathematics as outlined above. Though the situation is far from rosy in the rest of the country – apart from certain centres of excellence which have come up in different parts of the country – it is considerably worse in the state of Jammu & Kashmir which is lagging far behind in this respect. With the aim of reversing this trend and to create conditions for imparting quality training and education to students and teachers of mathematics working in different educational institutions in the state of Jammu & Kashmir, serious efforts have been initiated by a group of people, including this author, over the past couple of years which has finally led to the state government agreeing to the idea of establishing an institute of mathematics in Srinagar which will be exclusively devoted to the cause of improving mathematical pedagogy and research in the state. The author would like to place on record his deep appreciation for the alacrity with which the idea of establishing the institute was accepted by the minister of education Mr M A Lone. As an important part of the academic activities proposed to be pursued at the institute, it is planned to arrange visits by distinguished mathematicians, both from within the country and abroad, who would spend extended periods of stay at the institute to interact with and impart training to all segments of the mathematical community drawn from schools, colleges and universities of the J&K state. The good news is that the institute was recently inaugurated by the Hon’ble chief minister at Amar Singh College, Srinagar and pending the establishment of an independent campus of the institute – to which the government has promised full support – it is expected to start functioning soon from the Kashmir university campus which is the natural launching pad to kick-start these activities and where necessary infrastructure in terms of library facilities including online access to research journals is available, besides of course sufficient space, which has been earmarked for the purpose.
Posted on: Thu, 22 Aug 2013 02:28:29 +0000
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