# Speeches

### Speech by Professor Louis Chen, IMS Director

RAdm Teo Chee Hean, Minister for Education and Second Minister for Defence;

Prof Shih Choon Fong, Vice-Chancellor, National University of Singapore;

Prof Roger Howe, Chairman, IMS Scientific Advisory Board;

Prof Chong Chi Tat, Chairman, IMS Management Board;

Distinguished Guests;

Ladies and gentlemen:

Welcome to the Official Opening of the Institute for Mathematical Sciences.

The Institute for Mathematical Sciences was conceived more than 10 years ago. It materialized last year after three submissions of proposal.

The first proposal was submitted to the University by the Department of Mathematics in 1991. And in 1996, at the request of the Dean of Science, the Department submitted a much-revised proposal. In 1998, the succeeding Dean of Science asked the Department to resubmit its proposal. A new proposal was redrafted and submitted to the Ministry of Education through the University. In January 2000, the Ministry gave its approval for the setting up of the Institute.

I believe that the success of the third attempt is linked to three important factors: the developments of the Department of Mathematics and two closely related departments, the new mission of the University, and the national emphasis on a knowledge-based economy.

Since 1991, the Department of Mathematics has grown from strength to strength both in terms of the number of faculty and the quality of research. With the setting up of the Department of Computational Science in 1996 and the Department of Statistics and Applied Probability in 1998, the total number of faculty in these three departments today is about 130. A sizable number of their faculty members are internationally known for their research work. Some of this outstanding research work is home grown.

In the same period of time, the University has embarked on a mission to transform itself from a teaching university to a research university and then to a world-class university. Dramatic changes and restructuring of the University have taken place, particularly in the last 3 years.

Singapore is now moving towards a first world status. It needs to create niches in Science and Technology in order to compete with the developed countries. In its transition to a knowledge-based economy, it has shifted its focus from the training of a competent and professional workforce to the nurturing of knowledge workers and knowledge creators.

Against the backdrop of all these developments, the setting up of the Institute is timely. The Institute will build on the strengths of the three departments. Through synergy with these departments it aims to promote multidisciplinary research, help build strengths in niche areas in Science and Technology, and create knowledge in a knowledge-based economy.

Allow me now to give a short presentation on the Institute.

As you can see, the Institute is situated in a picturesque part of the campus and next to a forest. It has a peaceful environment free from distractions. It is an ideal place for research.

For this, I would like to thank the Vice-Chancellor for kindly permitting me to pick the two bungalows, the Office of Estate and Development for their professional support and assistance throughout the renovation process, and the PWD Consultants for skilfully translating our ideas into beautiful design and finally into this resort-like haven for research.

I would also like to thank the Institute of Molecular Agrobiology for allowing us to use this auditorium for the official opening.

It now remains for me to invite all of you to visit our website at http://www.ims.nus.edu.sg.

Thank you.

Copyright @ 2001 Institute for Mathematical Sciences. All Rights Reserved.

### Speech by Professor Roger Howe, Chairman of Scientific Advisory Board

Rear Admiral Teo Chee Hean, Minister for Education;

Professor Shih Choon Fong, Vice Chancellor; National University of Singapore;

Professor Chong Chi Tat, Chairman of the IMS Management Board;

Professor Louis Chen, Director of IMS;

Distinguished guests;

Ladies and gentlemen:

I take pleasure in addressing you today. Although the number of witnesses to this opening is not large, I believe that the beginning of the Singapore Institute for Mathematical Sciences (IMS) has the potential of being a watershed in Singapore's impressive and still unrolling development. It is an undertaking both inevitable and audacious.

It is inevitable because Singapore sees itself (I believe correctly) as being a full participant in the information revolution. Few if any subjects are so deeply and broadly engaged with information technology as is mathematics, and mathematics research can be expected to be fruitful and even essential to the full realization of the capabilities of information technology. This will happen in both expected and unexpected ways.

That mathematics is relevant to the information revolution is acknowledged, at least among the technically able. It is of course the stuff of which computation is made. But that mathematical research, across a fairly broad spectrum, should be important for furthering information technology is perhaps less widely appreciated. I would like to take a few minutes to reflect on the nature and history of mathematical research.

Most people are surprised even to hear that there is such a thing as mathematical research. They are under the impression that mathematics is school mathematics - arithmetic, algebra, geometry, and maybe trigonometry and calculus - and that it was handed down to us, from long, long ago, and a universe far, far away. To some extent, this is true about school mathematics, but even here there are issues - for example, the formulation of the "laws of algebra", the definition of the integral, the concept of function, and even such a basic question as: "What is a number?" - that are relevant to school mathematics, and also were very much live research questions during the 20th century. But however true it may be that school mathematics has long been codified, more knowledgeable people, including most scientists, know that there is a huge realm of mathematics beyond school mathematics, and that mathematical research is actively pursued today, by several 10000s of people all over the world.

However, even many of this more mathematically aware group seriously underrate mathematical research, and doubt its eventual usefulness. They may see current pure mathematical research as being overly refined, concerned with the modern analog of placing angels on the head of a pin. This attitude afflicts even mathematicians. Such a figure as John von Neumann, whose mathematical credentials include the definition of Hilbert space, criticized modern mathematics as being more and more 'l'art pour l'art' - art for art's sake. Yet such pronouncements have routinely been famously wrong. It is salutary to remind ourselves that much mathematics which seems fundamental today seemed strange and even fantastical when it first came into the world. Linear algebra was reviled as a useless abstraction for the first several decades of its existence, but now just one of its many applications, linear programming, saves large corporations billions of dollars annually. Linear algebra also forms the backdrop for quantum mechanics, whose most elemental formulation is in terms of a Hermitian linear operator on a Hilbert space.

Having mentioned quantum mechanics, I can easily turn to my own main research love, representation theory, or what physicists usually call "group theory". It is the mathematics of symmetry. Every physicist today knows that the story of 20th century theoretical physics is the story of group theory, with symmetry ideas being the main guide as investigations advanced into the realm of the very small and the very large. The most fundamental quantum mechanical systems - the hydrogen atom and the harmonic oscillator - are simply exquisite in the degree of symmetry they exhibit, and this symmetry can only be seen fully using representation theory. However, at the beginning of the century, group theory was regarded as a hopelessly abstract topic. Its study and uses had been confined to pure mathematics (although a codification and systematization of the principles of geometry had been one of its applications). In 1905, the eminent physicist Sir James Jeans, as part of a discussion of the necessary mathematical training for physicists at Cambridge University (which was at that time clearly a (if not the) leading center in the world for physics), said "Well, we can leave group theory out of it." Yet 1905 was the year that Einstein introduced special relativity, which was immediately interpreted by Hermann Minkowski as the simple statement that the Lorentz group is the symmetry group of space-time. A quarter-century later, Lorentz invariance was one of the desiderata that P.A.M. Dirac used to guide him to his equations for quantum electrodynamics.

The point is, the future is a complicated place. We don't know, we cannot know, what the future holds. We cannot select which of today's many lines of investigations will prove invaluable, and which will deserve forgetting.

This point, of the unpredictability of important ideas, is key, but is hard to absorb. To give a sharp example of it, let me refer again to von Neumann. One of his last mathematical creations was what are now known as von Neumann algebras. These are a generalization, based on very abstract and theoretical principles, and in a purely infinite dimensional context, of the (now mundane) idea of a matrix algebra. After an initial wave of interest because of connections with group representation theory, research on von Neumann algebras had devolved into a domain for specialists which may well have been seen even by typical mathematicians (and I will confess here to being among them!) as being a self-preoccupied theory, out of the proverbial 'main stream'. Then, in what must count as one of the most dramatic confluences of 20th century mathematics, Vaughan Jones discovered a connection between a technical topic in von Neumann algebras which he had been investigating, and the theory of knots, the study of how strings wind around themselves in space. This led to a frenzy of research, with the outcome being not only new classes of invariants for low-dimensional topology, but new mathematical tools for molecular biologists studying the three-dimensional configurations of DNA.

To reiterate: we cannot predict the future. We can see it only very hazily, as through a glass, darkly. The best we can hope for is to be ready to receive it when it arrives. Time and time again, a diverse and well-articulated arsenal of mathematical theory has proved invaluable in being prepared. The rapid advances in knot theory mentioned above, and their incorporation into the toolkit of molecular biology, could not have happened without the presence of a large group of experts prepared to appreciate Jones's extraordinary insight, to exploit it, and to explicate it to other scientists. The more tools we have at our disposal, the more avenues of thought that we have explored, the more connections that we have made, the better prepared we are to order and make sense of, and sometimes even to create, the unexpected constellations of ideas and events we will encounter. I think that this is a key part of the importance of mathematical research - it is about imagining and exploring possible futures.

This is a very hard lesson for us to learn, even for mathematicians. The impulse to second guess is overwhelming. We all want to push the subjects we know, to bet on the sure things. Yet in doing so, we close off the unexpected, the flashes of illumination that change the world and pay many times over for the whole enterprise, for the time we spend traveling up blind alleys or simply wandering in the dark. While we would be silly not to follow paths of investigation that show clear promise, and while applications are an integral part of the mathematics enterprise, the portfolio of a mathematics research institute must always include subjects chosen for their lively internal agendas, irrespective of known prospects for application.

This is perhaps enough about the exploratory nature of mathematical research, and the need to tolerate and even champion it. Let me talk a little now about why, besides being imperative, IMS is an audacious undertaking.

A few numbers may put things in perspective. Let me make a few elementary comparisons of Singapore with the U.S. First, population:

Next, mathematics Ph.D. population:

Thus, there are about three times the number of Ph.D. mathematicians per capita in the U.S. as there are in Singapore.

Third, mathematics institutes. The U.S. has about a half dozen, and Singapore will have one:

Thus, in the U. S., there are over 30 times the number of mathematicians per mathematics institute than there are in Singapore. While a mathematics institute in the U. S. will serve and can draw on a population of 4000 - 5000 mathematical scientists, the Singapore IMS has 100 give or take a few. Furthermore, while the mathematics institutes in the U.S. can specialize, the Singapore IMS will have as portfolio the whole spectrum of mathematical activity. It is in contemplating these facts that the audacity of this enterprise sinks in.

I think that these figures hold some implications for how the Singapore IMS should operate. It cannot focus solely on responding to ideas from the mathematical research community. It must also work to enlarge, deepen, and enhance the capabilities of that community. It must serve as an advocate for mathematical research and for the mathematics research community, to government and to business. It must seek to strengthen the ties between mathematical research and other sectors in Singapore. It must educate as to the possible roles of Ph.D. mathematicians in business. Software development, both of a more standard sort and of the type represented by the recently founded Akamai internet services company, presents relatively obvious job opportunities for mathematics Ph.D.s. Modeling of various technical and business process can also make good use of a high level of mathematical expertise. In America over the past decade, large banks and other financial institutions have found that the skills developed by mathematics Ph.D. programs, notably the skills and tolerance for thinking in non-routine situations, bring substantial value-added to their activities.

The Singapore IMS will also have to give careful thought to promoting mathematical research in Singapore, to strengthening existing research groups, and to extending the range of topics in which Singapore has a research presence. In doing this, the Singapore IMS will have to reach out, to the region and to the world. It will have to identify areas which can strengthen Singapore's mathematical presence. It may have to lay the groundwork for programs by organizing 'pre-programs', in which local personnel travel to centers of expertise and return with the knowledge base needed to run a successful program in a given area. It may have to work with local groups to formulate programs that will most benefit them. It may have to develop collaborations with other mathematical institutions in the region. For example, recently in Hong Kong, several university-based mathematics institutes have started operation. It may be possible to work with them to develop mutually beneficial programs. Other countries in the region may have groups in areas in which Singapore is not strong. Possibilities for fruitful interaction should be explored.

This all will not be easy. The Singapore IMS will need creative leadership, and enlightened and sympathetic support from funders. But given Singapore's goals and its extraordinary energy, which are so well embodied by the first director, Professor Louis Chen, I have high hopes for it. I am honored for a chance to help, and I look forward to the adventure.

Copyright @ 2001 Institute for Mathematical Sciences. All Rights Reserved.

### Address by Radm Teo Chee Hean, Minister for Education and Second Minister for Defence

Professor Shih Choon Fong Vice-Chancellor, National University of Singapore;

Professor Roger Howe Chairman, IMS Scientific Advisory Board;

Professor Chong Chi Tat Chairman, IMS Management Board;

Professor Louis Chen Director, Institute for Mathematical Sciences;

Distinguished guests;

Ladies and Gentlemen:

1. It is a great pleasure to be here today.

__Nature of mathematics__

Throughout the centuries, the development of mathematics has been fuelled by the need to solve real-world problems and the intellectual desire to search for truth.

Mathematics provides the logical foundations for scientific inquiry and the construction of theories of physical science. It also serves a very practical and important function in aiding engineering design and managing financial resources.

__Applications of mathematics__

In the twentieth century, the applications of mathematics have permeated almost every discipline of human knowledge, including the physical and biological sciences, statistics, computer science, engineering, medicine, economics, finance, law and linguistics.

The advances of computer technology in the past two decades have transformed the way mathematics is applied to science and technology. More and more computer intensive methods and algorithms are replacing the traditional analytic solutions to problems. Ever faster and more memory-capacious computers have made it possible to conduct more in-depth and refined studies in a shorter period of time. For example, images and special effects in movies can be simulated by solving mathematical equations using computer algorithms.

New emerging scientific problems, which require a multi-disciplinary approach to their solutions, have also influenced the development of mathematics. Recently, the human genome project has produced a draft human genome sequence. The next step is to understand the way biological cells and their genes and proteins behave. Mathematics will be useful in the modelling of biomolecular systems and the analysis of biological data in the multi-disciplinary research of this new discipline. It will not only contribute to the quality of life but also shed some light on the perennial question of life itself. This will undoubtedly require new ideas in mathematics.

__Science and technology in Singapore__

Singapore has always recognised the vital role of a firm foundation in science and technology for the economic development of a nation. This is especially so for Singapore as it lacks natural resources.

Our schools have played an important part in laying the foundation for Mathematics education. I am very pleased to note that Singapore has emerged first in Mathematics in the 38-country Third International Mathematics and Science Study conducted in 1999. Singapore ranked second in Science. 93% of our students were placed in the international top half for Mathematics.

With this broad and firm foundation, we are better able to build a large pool of highly skilled and well-educated scientific and technological manpower for the new economy. And to compete head-on with the developed countries, we will need to create niches of world-class excellence in science and technology.

The establishment of an institute devoted to the mathematical sciences is testimony to this commitment to build capabilities at the highest levels to support our push to a knowledge economy.

__Role of the Institute__

The Institute for Mathematical Sciences seeks to be modelled after successful mathematical institutes in Europe and North America. Its function is to provide a stimulating environment for scientists of diverse backgrounds, local and foreign, to interact and collaborate in research. It focuses not only on mathematics itself but also on multi-disciplinary research involving the applications of mathematics. Its objective is to solve important scientific problems, produce new results and techniques for theoretical developments as well as applications, and in the process, stimulate interest in the study of the mathematical sciences in educational institutions and train young mathematical scientists. In this, the Institute can look forward to building on the good foundation that our schools have laid in setting high standards especially in Mathematics and Science.

I would urge researchers and professors at the Institute to pay particular attention to igniting in our young an interest in the fundamental disciplines, and encouraging them to consider research as a viable career option. The future quality of the Institute and its long-term sustainability depend critically on your ability to nurture a long succession of curious and intense minds to join you in your area of interest.

You will undoubtedly be helped in your venture by the existence of an attractive lounge. I am told that this is where the researchers and scientists will interact, exchange ideas and debate over coffee. Paul ErdÃ¶s, a prolific mathematician who combined extraordinary talent with great devotion to mathematical research, once said, "A mathematician is a machine for turning coffee into theorems." I hope that this will be an on-going phenomenon at the Institute for Mathematical Sciences.

I understand that the Institute will focus on a different theme or themes on a regular basis and collaborative research will cover a wide spectrum of fields in the course of time in accordance with local needs and international trends. One of the themes of the institute's inaugural programme concerns computer security and data validity, which are crucial for fast, reliable, and secure communication, and are of importance to Singapore.

Through its programmes, the Institute hopes to bring to Singapore talents who, after a period of familiarizing themselves with the country, may wish to relocate and work in Singapore. Ultimately, it also aims to help Singapore establish its leadership in the mathematical sciences in the region and beyond.

The Institute will play a unique role in training young scientists, building research capabilities and creating knowledge in our knowledge-based economy. I wish you every success in this endeavour.

I have the pleasure now of declaring the Institute for Mathematical Sciences open. Thank you.

Reprinted with permission of Ministry of Education.