From the Director
Opportunity Unlimited

Doug Arnold, 
IMA Director 
We believe that mathematics is a field of almost unlimited
opportunity—provided that it looks outward towards its interfaces with
other fields.
This quote, from the influential 1998 Odom report, elegantly
encapsulates the primary motivation for the IMA and its mission of
increasing the impact of mathematics by fostering interdisciplinary
mathematical research. The strengthening of interdisciplinary
research is now widely recognized
as crucial—crucial to the vitality of mathematics, crucial to the
progress of an increasing number of areas of science and engineering,
and crucial to the health, prosperity, and security of our society.
However, it is important to remember that connecting mathematics with
external disciplines and problems has not always been so highly valued
by the mainstream of mathematical researchers. In this column, I hope
to highlight the major cultural change that has taken place in
mathematics research over the last quarter century, and, especially,
the role that the IMA played—and continues to play—in
bringing this about.
In 1982, when the IMA was founded, the academic mathematics community
had largely withdrawn from its historically close relationship with the
sciences, a relationship which had served as a primary source of
motivation and inspiration for mathematics for centuries. Instead, the
community was highly directed towards internally generated problems,
making little effort to communicate mathematical results outside the
discipline, or even outside a particular subdiscipline within
mathematics, and was generally isolated within the scientific
landscape. I believe that the mathematical science community owes an
immense debt of gratitude to the founders of the IMA for taking the
lead in recognizing and helping to reverse this isolation, guiding the
mathematics community from detachment and introspection to centrality
and connectivity.
It is interesting to compare the 1978 National Science Board
memorandum which laid out the motivation for the establishment of a
mathematical sciences research institute, with the visionary proposal submitted
by former IMA directors Hans Weinberger and Willard Miller in response
to it the following
year.
The NSB memorandum states the motivation for a national math institute
thus:
American research in mathematics
is today in a golden age. But there is within the mathematical
community a general consensus that, in order to maintain and even
further to stimulate the unequaled pace of research of the past dozen
years, another mathematical sciences research institute, similar but
not identical to the famous Institute for Advanced Study, should be
established…By the term "research institute" we mean an
organization where mathematical scientists on leave from their
institutions of permanent employment, can congregate in appropriate
numbers for extended periods for the sole purpose of performing
research…The aim of the Institute is, of course, the promotion
of research in the mathematical sciences.
Nowhere in the 8,500 word document is there any suggestion that a
nonmathematician would ever set foot in the institute. Words like
"interdisciplinary" do not appear.
Now read the opening of the original IMA proposal:
The most notable feature [of contemporary mathematics]…is the
isolation of the areas of growth not only from each other but also from
other scholarly disciplines and areas of concern. This aspect of the
problem needs to be addressed if mathematics is to remain both viable
and worthy of support by society as a whole. It is in response to such
problems that we are proposing the establishment of a National
Institute of Mathematics and its Applications.
No talk of a golden age here! Instead the proposal emphasizes the
importance of "exposing the participants to a variety of problems
which arise in the biological, physical, engineering, and social
sciences in order to spawn new and challenging areas of mathematical
research." They emphasize that "no serious program for
communicating new problems from other areas of science to
mathematicians can be successful without the active participation of
research leaders in the field of application under study," and
propose to bring in nonmathematician scientists for both long and
short visits. They repudiate the artificial dichotomy between pure and
applied mathematics which had resulted in a very circumscribed applied
mathematics subdiscipline, disconnected from the exciting recent
advances in mathematics. Instead, they state that "the emphasis
is to be on new applications rather than old ones," and speak of
"the importance of including a major proportion of
'pure' mathematicians," with "the particular
field of expertise not nearly important as the willingness to explore
new problems and think in new ways." They argue that "the
very best mathematical minds, most of whom have not been trained in
what is called 'applied mathematics'" will be
needed to successfully attack the variety of challenging problems which
arise, and declare "interdisciplinary research,"
"substantive collaborative efforts," and the involvement of
"mathematicians with diverse fields of interest present at the
same time" as the foundation of the institute.
The appreciation of the importance of interdisciplinary research is now
widespread, an integral part of the plans of many universities,
colleges, departments, and funding agencies. This is great news for
mathematicians, because mathematics can assume a central role in
bringing together ideas from many disciplines in the assault on
challenging and important problems. As Rockefeller University
biologist Joel E. Cohen wrote recently, speaking of biology,
"mathematics can help biologists grasp problems that are otherwise
too big (the biosphere) or too small (molecular structure); too slow
(macroevolution) or too fast (photosynthesis); too remote in time (early
extinctions) or too remote in space (life
at extremes on the earth and in space); too complex (the human brain)
or too dangerous or unethical (epidemiology of infectious
agents)." (PLoS Biol 2(12), 2004). And biology, although a
major source of opportunities, is just one of many fields where math can
play a key role. There seems to be no end to the new problems
waiting to challenge mathematicians willing to enter into
interdisciplinary collaborations. Fortunately many math research institutes in this country and
abroad have adopted the goal of fostering interdisciplinary
mathematical research, and many research mathematicians have embraced
such research. Ours is a field of unlimited opportunity—as long
as we continue to look outward to other fields.