Fields | James Colliander

Budget 2017, Naylor’s review, and the Mathematical Sciences in Canada

Fri, 21 Apr 2017 19:29:59 +0000

James Colliander, Director of the Pacific Institute for the Mathematical Sciences (PIMS)
Nassif Ghoussoub, Director of the Banff International Research Station (BIRS)
Ian Hambleton, Director of the Fields Institute for Research in Mathematical Sciences (Fields)
Luc Vinet, Directeur du Centre de Recherches Mathématiques (CRM)

The direct funding of research initiatives on artificial intelligence (AI) and quantum computing via Budget 2017, and the release of the report of Canada’s Fundamental Science Review present an opportunity to reflect on the role of mathematical sciences within Canada’s scientific heritage and future, but also on our country’s ways of funding research.

The importance of the mathematical sciences (mathematics, statistics and computer science) is deepening in almost all areas of knowledge. Mathematical sciences provide a conceptual infrastructure underpinning advances in biology, engineering, humanities, medicine, social sciences and beyond. Progress in our understanding in all these fields depends upon advanced research and high-level training in the mathematical sciences.

Canadian Mathematician John Charles Fields, the creator of the Fields medal (often dubbed the Nobel prize for mathematics), also played a key role in the founding of the National Research Council in 1916. Today, Canada is served by a collaborative network of mathematical sciences research institutes: the Centre de Recherches Mathématiques (CRM) in Quebec, the Fields Institute for Research in Mathematical Sciences in Ontario, and the Pacific Institute for the Mathematical Sciences (PIMS) in Western Canada.

The institutes amplify Canada’s capacity for discovery and invention through partnerships that intertwine our nation’s universities with academic and industrial researchers from across the globe. Together, the institutes created Mitacs in 1999, which, under the leadership of Arvind Gupta, became a cornerstone of the government’s effort to link our graduate students (in all disciplines) with industry. This accomplishment was amply recognized in Budget 2017. In 2003, they collaborated with Berkeley’s Mathematical Sciences Research Institute (MSRI) to found the Banff International Research Station (BIRS), a unique North-American research infrastructure on Canadian soil, that provides an environment for creative, synergetic, intense and prolonged interactions between mathematical scientists and investigators in other areas of research.

In 2002, the three institutes committed to provide long-term funding to the Atlantic Association for Research in the Mathematical Sciences (AARMS), a network that plays an important role in the mathematical sciences research activities of the Atlantic region.

In 2003, PIMS collaborated with Berkeley’s Mathematical Sciences Research Institute (MSRI) to found the Banff International Research Station (BIRS), a unique North-American research infrastructure on Canadian soil, that provides an environment for creative, synergetic, intense and prolonged interactions between mathematical scientists and investigators in other areas of research.

The need for leadership to advance the mathematical, computational and statistical understanding of information, the development of data science, and the advent of machine learning, prompted the institutes in 2012 to use their own resources to invest in the creation of CANSSI, the Canadian Statistical Sciences Institute. That NSERC did not have the resources to do so at that time sheds some light on the community’s reaction to how Budget 2017 continues to shut out the Tri-Council.

AI rests on mathematical sciences. Indeed, some of this field’s prominent leaders pursued their foundational research within BIRS, CRM, Fields and PIMS. AI needs further advances in the mathematical sciences to thrive. We celebrate strong support of AI research but the disjointed approach used by government for its substantial investment in the area of deep learning totally missed the opportunity to include and exploit the national resource that BIRS, CRM, Fields, PIMS and CANSSI represent.

This example is but one of many examples that illustrate the importance of some of the excellent recommendations of the report of the Science Review Panel. Indeed, Canada developed world leading expertise and operations in science policy during the era of Pierre Elliot Trudeau. The work of the Senate Special Committee on Science Policy, chaired by Senator Maurice Lamontagne, identified principles to guide Canada’s future governments. The consultation of the scientific community overseen by the panel chaired by David Naylor aligns with these best practices. Direct investments disbursed through political channels, instead of through the Tri-Council’s scientific peer review process, undermine the transparency of research funding programs, and can miss opportunities such as the one we described. Funding allocations to support research should follow consistent and rigorous evaluation processes incorporating independent scientific peer review.

Ubiquity of Mathematics: Charles Fefferman

Thu, 02 May 2013 19:03:43 +0000

This is Episode 1 of a 5 part video series entitled Ubiquity of Mathematics. I am grateful to the Department of Mathematics, the Fields Institute, Richard Cerezo, and Andrea MacLeod for making this project happen. I also thankful the mathematicians interviewed for this series:

The other episodes will appear shortly. Here is the transcript and here is the video of the interview with Charles Fefferman:

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Fields Institute Establishes Fields Medal Symposium

Sat, 16 Jul 2011 05:15:36 +0000

I was very happy to receive an email yesterday announcing that the Fields Institute has established a symposium to honor the Fields Medalists. Please find the text of the announcement I received posted below:

FIELDS MEDAL SYMPOSIUM

The Fields Institute is delighted to announce the establishment of the Fields Medal Symposium. The Symposium will take place annually in Toronto at the Institute, celebrating the achievements of one of the recently announced Fields Medalists. The Fields Medal Symposium will be a three-day event featuring an address or a series of lectures for a general scientific audience by the Medalist, as well as lectures and panel discussion by other invited participants on themes related to the Medalist’s work. The Symposium is intended also as an inspiration to young people, and will include public activity with the participation of high-school or undergraduate students. The Symposium will be promoted in the Canadian and international press, and will be broadcast live throughout the world via the Fields Institute’s interactive videoconferencing facilities.

The Fields Medal Symposium is endorsed by the International Mathematical Union. It will be inaugurated in October 2012, on the occasion of the twentieth anniversary of the Fields Institute. The first Medalist honoured in this way will be Ngo Bao Chau (University of Chicago, Fields Medal 2010). The program for the first Symposium will be organized by a Committee consisting of Jim Arthur (University of Toronto, Chair), Bill Casselman (University of British Columbia), Edward Frenkel (Berkeley) and Gerard Laumon (Orsay).

The Fields Medal is the world’s most prestigious prize in mathematics. It is awarded by the International Mathematical Union every four years, to two to four mathematicians (recently four). The Fields Medal, first awarded in 1936, and the Fields Institute are both named after John Charles Fields (1863–1932), who was born in Hamilton, Ontario, and was a faculty member at the University of Toronto. Fields took a strong interest in the global world of Mathematics, and endowed the Medal in order to create an award comparable to a Nobel Prize. (There is no Nobel Prize for Mathematics.) The awards, however, have an interesting difference. The Nobel Prize is usually awarded to mature scientists to crown their careers. The Fields Medal, on the other hand, is awarded to researchers at most forty years old. It is intended not only to crown pioneering achievements but also to encourage further visionary work.

The Fields Medalist honoured on the occasion of the Symposium will receive an honorarium of $25,000. The Fields Institute has been successful in raising private sponsorship support of the Fields Medal Symposium for aneinitial eight-year period. This funding will cover the honorarium, as well as promotion of the event and the Medalist’s expenses. The Institute will provide the venue for the Symposium and cover the expenses of other invited Symposium participants from its scientific budget. The initial eight-year sponsorship will enable the Symposium to become established and attract continued funding to build an endowment.

The annual Fields Medal Symposium will be one of the highest profile events in the global mathematics community. The Fields Institute is extremely grateful to the sponsors whose generous support has made the initiative possible. Following are the current private sponsors of the Symposium. The Institute is actively pursuing corporate sponsorships. The Institute welcomes further support of the Fields Medal Symposium, at any level, as well as any other inquiries about the program. More information about the Fields Institute can be found at http://www.fields.utoronto.ca .

Sponsors of the Fields Medal Symposium

Silver Level $100,000–199,000

James Stewart, Prof. Emeritus, McMaster University, text book author, donor of the Fields Institute Library

Bronze Level $25,000--99,000

Edward Bierstone, Fields Institute and the University of Toronto
George Elliott, University of Toronto and the Fields Institute
John R. Gardner
Philip Siller, BroadRiver Asset Management, L.P.

Canada Should Leverage its Connection to the Fields Medal

Thu, 09 Jun 2011 05:12:17 +0000

John Charles Fields was born in Hamilton Ontario in 1863, graduated from the University of Toronto in 1884, and got his PhD from Johns Hopkins University in 1887. Fields helped establish the National Research Council, the precursor to NSERC. Canadians should be proud that John Charles Fields diplomatically unified the International Mathematical Union during the time between WW1 and WW2 to create the International Medal for Outstanding Discoveries in Mathematics, known colloquially as the the Fields Medal. This award is regarded as the highest honor a mathematician can receive. It is often described as the Nobel Prize of Mathematics although I don’t like that moniker.

The Nobel Prize is 10M Swedish Kronor, about \$1.5M.
The Shaw Prize is worth \$1M. (Yesterday, the 2011 Shaw Prizes were announced. Congratulations to Mathematical Sciences winners Demetrios Christodoulou and Richard Hamilton.)
The Abel Prize is worth six million Norwegian Kroner, about \$1M.
The Chern Medal is worth \$0.25M and includes the opportunity to direct up to \$0.25M to certain charities.
The Fields Medal is worth \$0.015M. Yup, \$15,000. But, it is regarded as the most prestigious mathematical award.

The Fields Medal is awarded to mathematicians under age 40 for outstanding discoveries. As a result, the Fields Medal often highlights emerging mathematical fields with recent breakthroughs made by a vibrant young researcher. The awarding of the Medal often energizes the research activity in these fields.

The Abel Prize was founded in 2003 by Norway with an initial investment of $23M. How should one assess the value of the Nobel Prize system for the country of Sweden? How should Norway value the Abel Prize? Based on the prize amounts, Canada appears to value research differently than her northern neighbors.

A Public Proposal

A one-time-only Canadian investment of ~\$5M (assuming a ~5% return on investment) would generate enough interest to raise the value for 4 Fields Medals each valued at $250K given every 4 years. In the past, the IMU’s prize committee has sometimes awarded fewer than 4 medals so \$5M might generate a fund that sustains value against inflation. Through philanthropy or government investment (and subject to peer review), Canada should raise level of the Fields Medal.

(Why $250K and not $1M? The Fields Medal is awarded when a researcher is in full creative bloom, and before the age of 40 years old. The 40 year rule fundamentally distinguishes the Fields Medal from the Nobel Prize. My view is that the award should be substantial but not life-altering, assuming a typical academic salary and lifestyle. )

Canada should leverage its connection to the Fields Medal starting at the next International Congress of Mathematicians in Seoul in August 2014:

The Prime Minister of Canada should award the medals at the next ICM to be held in Seoul, Korea in August 2014.
The raised award amounts and the participation by Canada’s government will generate interest in mathematics, the Fields Medal and in Canada, as a country that values the advancement of knowledge.
Canada’s mathematical research institutes (PIMS, BIRS, Fields, Perimeter, CRM) should jointly organize a year of concentration targeting the rapidly developing areas highlighted by the Medals during calendar year 2015. The four month interlude between the announcement of the Medals at the ICM and the beginning of 2015 can be used to plan the programs. Summer schools should be designed to bring advanced undergraduate and graduate students into the stream of ideas and discoveries highlighted by the medals. In principle, funds for these activities are already committed by NSERC through its long term commitment to the institutes.
Canada should aim higher and build new mathematics education practices intertwining research universities and the public schools using interactive technologies towards long-term goals like:
- Canada should set a national strategy to win the International Mathematical Olympiad. Milestones: consistent top ten finishes within five years; top five finishes thereafter.
- Canada should rejuvenate K-12 enriched mathematics education toward growing (not importing) a Fields Medalist in the next 12 years.
- Canada should produce a female Fields Medalist.

The International Medal for Outstanding Discoveries in Mathematics, colloquially named after its Canadian founder John Charles Fields as the Fields Medal, is the world’s top honor for mathematical advancement. Canada should make the value of this award commensurate with its prestige and make long term plans to leverage that investment.

Unfortunately, the window for public submissions to the six member expert panel reviewing Canada’s federal research and development policy has closed. Nevertheless, I hope that this proposal is considered by that review panel and by the Science, Technology and Innovation Council. The recent budget announcements by the Harper and McGuinty governments include stunning investments in research on the brain ($100M), the genome ($65M), optics ($45M), the Perimeter Institute (Federal $50M, Ontario $50M) and the SR&ED program (~$4B, yes, Billion) giving tax breaks to business claiming R&D expenses. Research and development investments by governments, like the one proposed here, and those recently announced should be made strategically and through a transparent and robust peer review system.