A LIFE OF MATHEMATICS

A Life of Mathematics

January 10-31, 2001
Sponsored by The Hindu, India's leading national daily

Introduction to A Life of Mathematics

The ICICI Centre for Mathematical Sciences invited three eminent mathematicians, Professor Henry Helson (Berkeley), Professor Peter Fillmore (Dalhousie, Canada) and Professor Garret Etgen (Houston) to spend three weeks at the Centre in January, 2001.

All the three mathematicians have had rich careers of great distinction and are well known as teachers and as researchers.

During the three weeks they gave a series of lectures. These included lectures at the research level, talks for undergraduates on mathematics from an advanced standpoint and lectures as well as workshops on the history; the future, and the teaching of mathematics.

A brief introduction to our visitors:

Professor Garret J. Etgen is Professor of Mathematics at the University of Houston. His area of specialisation is in Differential Equations. Professor Garret Etgen has done considerable work in Differential Equations and in Applied Mathematics. He has also rewritten the classic book by Hille and Salas on Calculus and has been involved in mathematics education.

Professor Peter Fillmore is Professor Emeritus with the Department of Mathematics at Dalhousie University, Canada. His research area is Operator Algebras & Operator Theory. Professor Fillmore was President of the Canadian Mathematical Society from 1994 to 1996. Of his work, the Brown-Douglas-Fillmore Theorem is one of the most important results in the area of Operator Algebras.

Professor Henry Helson, is Professor Emeritus with the Department of Mathematics at University of California, Berkeley. Professor Helson has been an inspiration to several generations of mathematicians. As a specialist in Harmonic Analysis, he is far too well known to require any introduction. A number of deep theorems that he has discovered have been named after him. He is also the author of several well-known books and monographs (apart from numerous research papers).

This event, the first of its kind in the India, generated enormous enthusiasm not just amongst the students and faculty of the college but also amongst mathematicians in the country. An indication of this is the fact that participants for this event consisted of professional mathematicians, research scholars and students. They came from institutions in Chennai, Kolkatta, Bangalore, Allahabad, Varanasi, Mumbai, Gujarat, Pune, Meerut and Aligarh besides institutions in Delhi.

None of this would have been possible but for the generosity of `The Hindu which sponsored `A Life of Mathematics.

The event began with an inaugural function on January 12, 2001. Professor K R Parthasarathy, ISI Delhi formally inaugurated the three week Mathematical Extravaganza. During the inaugural function, Professors Helson, Fillmore and Etgen spoke about their lives as mathematicians and about how they chose Mathematics as a career.

In the days following the inauguration, Professor Etgen gave a research level talk on "Self-Adjoint Differential Systems". This session was presided over by Professor K. B. Sinha of ISI, Kolkata. On two subsequent days, Professor Fillmore and Professor Helson gave research level talks entitled "The Classification Problem for Operator Algebras" and "Analyticity of Flows" respectively. Professor Ajit Iqbal Singh, University of Delhi was the chair for Professor Fillmores lecture while Professor U B Tewari, IIT Kanpur presided over Professor Helsons talk. Although, these were research level talks the speakers made an attempt to make the material comprehensible to undergraduates.

Professor Helson gave a series of eight lectures. These lectures on "Evaluation of Sums and Integrals" were aimed at undergraduates but were from an advanced standpoint. In this series undergraduates were shown how to use advanced techniques to evaluate certain sums and integrals some of which they were familiar with. It was heartening to find the lecture room overflowing during these lectures, consistently from the first lecture to the last lecture of the series. It is hoped that Professor Helsons lecture notes will be available in a published form later this year.

Professor Fillmore also delivered two lectures titled `Diagonalising Infinite Matrices: the Pleasures and Perils of the Infinite to a largely undergraduate audience. By concentrating initially on diagonalisation of finite matrices, Professor Fillmore was able to give his audience a gentle and comprehensible introduction to the infinite case. Despite the fact that the subject matter being discussed was of a research level, he communicated the essential ideas in the area successfully to his undergraduate audience. He was able to introduce the index theorem to the undergraduates.

There were two workshops organised during `A life of mathematics. The first was a workshop on the teaching of mathematics. The workshop was well attended with participation by teachers and students from Delhi and elsewhere. There were three sessions in the workshop. These were presided by Professors Helson, Fillmore and Etgen. The sessions were interactive with the last part spent on discussion of the various issues raised by the speakers and other points brought forth by the audience. Various facets of teaching philosophies generated a good deal of discussion and some humor. (in particular, the discussion on the Moore method of teaching was on a humorous note.)

Towards the end of January, there was a workshop on the history and future of Mathematics. This event was aimed at a general audience. Professors Fillmore, Helson and Yadav presented a fascinating history of and glimpses into the future of Mathematics by speaking about the mathematical world that they had personally been a part of. Professor Yadav's lecture gave a perspective on the growth of Indian mathematics and put forth ideas which were discussed in detail.

There was a day of interaction with Mathematicians where the undergraduates interacted with Professors Helson, Fillmore and Dinesh Singh who discussed their personal growth and the various Mathematicians who were their role models and who had influenced their work. The students then put forth all kinds of questions on different aspects of mathematics and being a mathematician. Some of these were: How is research done? How is the topic of research chosen? How is the area of research chosen? How does a student choose a thesis advisor. During this session amazing insights emerged. For instance, Professor Helson said he had learned Functional Analysis before he studied Linear Algebra. They also discussed the fact that in major departments senior professors teach entry level courses and the benefit the students derive from this.

The visit of these eminent mathematicians was conceived in a much wider spirit than simply as a set of seminars or lectures. Thus the programme was aptly titled: A Life of Mathematics. It enabled the students to interact with the mathematicians in settings that ranged from formal and semi-formal lectures and workshops to impromptu walks on the campus and informal chats during and after lunch and tea sessions. It is gratifying to note that several students have been motivated enough to pursue mathematics and/or related disciplines as a career.

I would like to conclude with the following description of these events given by a first year Mathematics student. "From the many conversations with our visitors I learnt about how many questions in Mathematics had been left unresolved. How much new mathematics was being created. What life as a professional mathematician entails. What the state of education was like. Much more was absorbed in these three weeks than the many symbols linked with implication signs and the numerous integrals strewn across my notes."