Towards a global strategic plan for

Canada’s Mathematical Sciences Community

A compendium by Nassif Ghoussoub and Richard Kane

May 10, 2005

This document is a summary of a three day retreat hosted by the Scientific Director of the Banff International Research Station, during October 28-30, 2004 to discuss present and future priorities and directions for the Canadian mathematical sciences community. The Banff retreat was attended by the current leadership of all major Canadian institutions and associations that support and promote the mathematical sciences.

Hermann Brunner, Director, Atlantic Association for Research in the Math Sciences.

Eddy Campbell, President, Canadian Mathematical Society

Ken Davidson, Former Director, Fields Institute for the Mathematical Sciences

Ivar Ekeland, Director, Pacific Institute for the Mathematical Sciences

Barbara Keyfitz, Director, Fields Institute for the Mathematical Sciences

Nassif Ghoussoub, Scientific Director, Banff International Research Station

Arvind Gupta, Scientific Director, MITACS Network of Centres of Excellence

Ken Jackson, President, Canadian Industrial and Applied Mathematics Society

Richard Kane, Former Chair, NSERC Reallocations Exercise

Francois Lalonde, Directeur, Centre de Recherches Mathematiques,

Bill Langford, President-Elect, Canadian Industrial and Applied Mathematics Society

Nancy Reid, President, Statistical Society of Canada

Christiane Rousseau, Past-President, Canadian Mathematical Society

Mary Thompson, Past-President, Statistical Society of Canada

Ali S. Twareque, Directeur, Institut des Sciences Mathematiques, Quebec.

Part I: A New Reality

The past decade has witnessed a dramatic transformation of the Canadian mathematical sciences community. It has recruited a new generation of talented researchers, both junior and senior, resulting in a sharp increase in the scientific quality and a much higher profile in the international community. In the process it has established an impressive international presence in a number of important cutting edge areas of mathematical research. This transformation in the mathematical sciences is reflected by the rise within the same period of a number of university departments within Canada to a status of internationally recognized excellence. The emergence of a wide range of new research areas has led to the creation within these department of a number of innovative training programs, both in core mathematical subjects and in interdisciplinary subjects, designed to prepare a broad spectrum of mathematically literate scientists. The innovative Canada Research Chairs program which has enabled the community to recruit talented international researchers has only reinforced the drive towards excellence in the Canadian mathematical sciences. This newly achieved quality in research and training for the mathematical sciences within the Canadian university system is the bedrock upon which depend all the further initiatives in the mathematical sciences which will be discussed in this document. Such excellence represents the bottom line for the Canadian mathematical sciences.

The mathematical sciences community also has a long history of being extraordinarily well organized and cohesive, and possessing a remarkable sense of national purpose. A major international review of Canadian Mathematics in 1997 commented on its “striking sense of common destiny”. The trend towards interaction, and also towards outreach, has been strongly reinforced by three large and effective professional societies (Canadian Applied and Industrial Mathematics Society, Canadian Mathematical Society, Statistical Society of Canada). In the past decade these three societies have evolved into major forums for research and training, particularly through their large scale national meetings, often jointly organized, involving a wide range of participants from the academic world, the educational community, and the private sector. These societies with their established networking capability are perfect partners for the new generation of more focused institutions which have arisen in the past decade.

The above transformation in scientific research and training has taken place in the context of another fundamental dynamic. It is this dynamic which will be the primary focus of the document.

The New Reality: There is a new reality for the Canadian mathematical sciences. They have become an essential part of the Canadian agenda. The conceptual and computational tools of mathematics and statistics have become essential for progress in many areas of the life sciences, information and communications technologies, nanosciences, and financial and industrial sectors. Mathematical Science has become the key driving force underlying the new knowledge based economy.

The mathematical, statistical and computational sciences, at the core of the natural sciences and engineering research, are playing an increasingly central role in emerging areas of technology in areas as diverse as genomics, finance, climate, and security. It is the remarkable ability of mathematics to model physical, biological and economic systems in ways that permit effective prediction, design and control that makes it so essential for the innovation capacity of Canadian industry. The emerging role of mathematics in new technologies has been accompanied by new ways of practicing mathematical research:

· The collaborative aspect: The "mathematization of all science'' is now necessitating even deeper collaborations between mathematicians and statisticians and almost all other scientists. There is a compelling need to create a manpower resource of mathematical scientists devoted to collaboration with physicists, chemists, engineers, life scientists and to inquire, create and provide solutions and to help train the next generation of Canadian scientists.

· The computational and experimental aspect: Advanced scientific computation, algorithmic mathematics, computer simulation and visualization are more fundamental than ever in dealing with complex mathematical models. One has seen the coining of the term “in silico” alongside “in vivo” and “in vitro” to describe what is now a standard mode of experimentation, by simulation. There is a compelling need to create and develop facilities that will provide adequate infrastructure to support every needed component of the required research from modelling and numerical simulation to scientific computing and mathematical analysis.

· The emergence of a new branch of scientific inquiry: Brute force computational power combined with sophisticated mathematical analysis to implement it, to optimize its capacity, and to extrapolate from it, has been a tremendous stimulus for research in computational mathematics. This conceptual and methodological revolution spanning both pure and applied themes, is indeed becoming more and more viewed as another branch of the mathematical sciences, alongside the traditional ones.  This expertise is now in great demand while Canada has a severe shortage of researchers in this area. There is a compelling need to remedy this problem by assembling in Canada the world-class human resources, as well as the appropriate environment, for the most advanced level of mathematical and computational research.

· The acceleration of the pace of collection of data: Technological advances have led to an overwhelming amount of data in many fields of science, and at the same time the problems being addressed require more statistical input that has formerly been the case. The most prominent examples are particle physics and astronomy, and molecular biology, where new collaborations are forming to address a host of important scientific and statistical problems, but the situation is similar in many other areas of science, including atmospheric and ocean science, resource management, and so on.

The Canadian mathematical sciences community has responded decisively to the challenges and opportunities offered by this new reality.

The New Infrastructure: The mathematics sciences community has wholeheartedly embraced the new reality for their disciplines through the creation of a series of innovative interdisciplinary institutes designed to facilitate the new role for the mathematical sciences in Canadian society. This outstanding achievement is a co-operative partnership reflecting not just extraordinary efforts on the part of our community but also years of investment by both federal and provincial governments and their granting agencies

During the past decade, the Canadian mathematical sciences community has undergone a fundamental re-evaluation and has developed a new mindset with a much greater appreciation of, and commitment to, interdisciplinary research and training, as well as industrial applications of mathematics. This transformation has been distinguished by a strong emphasis on innovation: emerging areas, areas at the interface of different branches of mathematics, areas that cross traditional discipline boundaries. The transformation has also been paralleled by the establishment of a significant new layer of infrastructure for the mathematical sciences dedicated to the advancement of:

· major research programs of international importance;

· partnerships between the mathematical sciences, other disciplines and the financial/industrial sector;

· comprehensive training both at the graduate and postdoctoral level.

Over the past decade a group of diverse interdisciplinary institutions have been specifically created to embody the above goals. These institutions are a truly remarkable achievement and a very substantial contribution to the advancement of all the mathematical sciences. They comprise:

· an ensemble of three large scale interdisciplinary institutes for the mathematical sciences (CRM, Fields Institute, PIMS), regionally based but acting at the national and international level;

· the MITACS network dedicated to the support of national research teams in the financial and industrial sector organized around the pairing of multi-disciplinary academic researchers with societal receptors;

· BIRS, an international research centre dedicated to workshops in fundamental, interdisciplinary, and industrial mathematic and statistics.

Through these institutions Canada has achieved an enviable position on the world stage. No other country has established such a tightly linked and yet diverse network of mathematical sciences institutions. The three major institutes, together with AARMS, comprise a splendid network potentially reaching every mathematical scientist of the country. MITACS is simply unique in the world and others now come to us to learn how we have succeeded. The recent renewal of MITACS federal funding for an additional next seven years at the highest level of any NCE in Canada is a clear recognition of the extraordinary stature and impact of MITACS. BIRS, in only its third year of existence, has already achieved international prominence. The Canadian–USA partnership which launched BIRS constitutes the first major international link at the institutional level for Canadian researchers in the mathematical sciences.

The above institutions collectively provide a national resource for community. They are particularly distinguished by the leadership that they have provided with respect to the expansion of interdisciplinary activity, the innovative training of HQP, and the development of interactions with the private sector. Their expertise and effectiveness in these areas is the main reason that new initiatives are being contemplated at this time

The spectacular success of these institutions is due to a sustained and extraordinary effort on the part of the Canadian mathematical sciences community. It also reflects the clear vision put forward by that community, its cohesion, and the creative and rigorous use of funding to achieve its goals. The efforts of the mathematical sciences community have been complemented and reinforced by the creative funding policies of NSERC. In the case of each institute, NSERC (notably via Reallocation) provided the key strategic investment which lent credibility to these enterprises and allowed the leveraging of considerable other funding from the private and public sector. The impressive diversity of funding sources (NSERC, provincial agencies, ministries, centres of excellence, public and private companies, foundations) ensure the durability of these institutions.

Part II: A Prospectus for Action

Turning to the future, one is struck with the enormous potential offered by the above strategic investment in the mathematical sciences. This is the moment to maintain momentum. The marvelous institutions created in the past ten years can and should be used to advance important aspects of the Canadian agenda at both the national and international level.

· New Goals: The mathematical sciences community is now poised to build on its current achievements by making significant new contributions to the growing needs of Canadian society with respect to the mathematical sciences. A full coordination of all of the community’s regional and national efforts, involving a number of new initiatives, will be needed to increase Canada’s capacity in the mathematical sciences and their applications

· New Priorities: An enhanced role, both nationally and internationally, for the Canadian mathematical sciences should be a major priority for governments, granting agencies and universities in Canada. There is a need to launch a major concerted campaign to establish the mathematical sciences as a priority area for both levels of government, granting agencies and universities in Canada..

The new initiatives being proposed are centered around three major themes: enhanced graduate training, a more comprehensive industrial strategy, and sustained international outreach.

(a) Training the Next Generation

(i) A New Level of Training: There is a need to establish a nationally coordinated and highly effective graduate training program for the mathematical sciences, one that will meet the needs of both the academic and industrial communities and one that will position Canada as a global education center for the mathematical sciences..

Initiatives will include an expanded venue of summer schools, a certificate program in industrial mathematics, industrial internship programs at both the regional and national level and systemic support of the many evolving research groups within the Canadian community of mathematical scientists. .

(ii) Canada as a Global Educational Center: There is an unique opportunity to

position Canada as a global educational center for the mathematical sciences,

Initiatives would include exploiting the country’s unique position within the Francophonie, and its natural links with Pacific Rim countries and Latin America. A rapid increase in training capacity will be achieved via a closer coordination of graduate programs in neighboring institutions, just like the successful model adopted by the Montreal-based. In addition Canada’s strong position in industrial mathematics through MITACS would be extended to an international presence for Canada

(b) An Expanded Industrial Strategy

A comprehensive strategy in industrial mathematics needs to better reflect the "mathematization of all science''. In particular, there is a need for a truly interdisciplinary collaborative research structure within the mathematical sciences.

A Industrial Strategy: There is a need to initiate a coherent and sustainable national industrial strategy which will build on the commendable record of the institutes, especially in their envisioning and creation of the hugely successful MITACS network.

Initiatives will include the establishment of programs for more systematic participation of researchers in the private sector, and the creation of a network of self-sustaining national laboratories in emerging areas of the mathematical sciences

(c) An Enhanced International Presence

After a decade of energetic development at the national level, the Canadian mathematical sciences are optimally positioned to pursue a series of international initiatives leading to substantial new links between Canada and the global scientific community. The community is poised to move beyond its current level of international engagement via the development of a fruitful and large-scale international policy with respect to research, training and industrial needs

(i) An Increased Canadian Role in International Scientific Organizations: The moment has arrived for a significantly increased leadership role for Canadian mathematical scientists in international scientific organizations, one commensurate with the outstanding achievements and the status of its researchers

Such a role is especially desired within the committees of the International Math Union. Initiatives already underway include the campaign to build a substantial new endowment for the Fields Medal, plus bids to hold the 2010 International Congress of Mathematicians in Montreal as well as the 2011 International Congress for Industrial and Applied Mathematics in Vancouver

(ii) Strengthening of Bilateral and Multilateral Ties: It is the time for a major push towards stronger bilateral and multilateral relations, at the institutional level, with researchers in the mathematical sciences in other developed countries, notably the United States, Europe and Russia.

It is both an economic and scientific priority for the Canadian mathematical sciences to move beyond the current level of international collaboration consisting of a multitude of small scale interactions to one consisting of firmly established relations at the institutional level. The Canada-USA-Mexico partnership in BIRS, the efforts of the CMS to build ongoing relations with French and Russian mathematicians, and the recent exchange program established by the SSC between Australian and Canadian statisticians are examples that will be consolidated and emulated

(iii) Reaching out to Developing Countries: There is an opportunity for the Canadian mathematical sciences to assist developing countries in achieving a significant research profile in the mathematical sciences.

Initiatives include export of expertise of the CRM, Fields, PIMS and MITACS in the development of large scale academic and industrial programs, as well as specific outreach to nations of the Francophonie via the Quebec community, and to Pacific Rim countries via the universities of western Canada.