"Innumerable Connections"
Dr. Rita R. Colwell
Director
National Science Foundation
Board on Mathematical Sciences 2000 Colloquium
National Research Council
November 10, 2000
See also slide presentation.
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2928070.
I'm very pleased to have been invited
to address you during such a momentous weekthe week
of our presidential vote, and an outcome that even
our best mathematical skills could not help us to
foretell. I'm reminded of the way Winston Churchill
described the skill of a politician. It was, he said,
"the ability to foretell what is going to happen
tomorrow, next week, next month, and next year.
And to have the ability afterwards to explain
why it didn't happen."
Whether it did or didn't happen I will leave to you
to decide. However, as I thought about what I wanted
to say to a gathering of mathematicians, I remembered
something that happened to Stephen Hawking. As he
was writing his famous book, A Brief History of Time,
he was told that every equation he included in the
book would cut sales in half. "I therefore resolved,"
Hawking said, "not to have any equations at all."
I have absorbed Hawking's lesson and I do not intend
to include any equations today. I would, however,
like to mention one significant number: 13.6 percent.
We are delighted that Congress has raised our budget
by this record amount. I can't think of a better anniversary
present during this, the 50^{th} year of NSF's
existence.
I would also like to express very deep thanks to all
of you for helping us to achieve this milestone. I
am convinced that we did it by uniting and speaking
with one voice for all of fundamental research. Every
one of you has my heartfelt gratitude. I am especially
glad that Sam Rankin has taken the helm at CNSFthe
Coalition for National Science Funding. It gives us
more to celebrate. [title
slide: Innumerable Connections] Use Back to Return
to Speech.
My first theme is the vital and growing role of the
mathematical sciences in all of science and engineering.
Then I would like to turn briefly to the interdisciplinary
initiatives that have taken shape as prominent features
on NSF's landscape. I will spend a bit more time on
the newest initiative we intend to propose, which
is of course of greatest interest to all of you: our
mathematical sciences initiative.
In fact, this is a kind of preview of how we might
present our case for the initiative, and we would
very much appreciate your advice on the best way to
do this beyond the mathematics community. [Roger
Bacon quote over mathematical image] Use Back
to Return to Speech.
Roger Bacon observed that "Mathematics is the door
and the key to the sciences." For us, seven centuries
later, his words ring with even deeper truth.
[MC Escher slide with
EO Wilson quote] Use Back to Return to Speech.
A more recent observation about mathematics comes from
E. O. Wilson. He writes,"...mathematics seems to point
arrowlike toward the ultimate goal of objective truth."
Given the accelerating crosspollination of mathematics
and bioscience, it's not a mere coincidence that Wilson
is a biologist.
Indeed, mathematics is the ultimate crosscutting discipline,
the springboard for advances across the board.
[a fractal image]
Use Back to Return to Speech.
Mathematics is both a powerful tool for insight and
a common language for science. Fundamental mathematics
engenders concepts and structures that often turn
out to be just the right framework for applications
in seemingly unrelated areas.
A good example, pictured here, is the fractal, a famous
as well as beautiful illustration of how inner principles
of mathematics enable us to model many natural structures.
[VLA at sunset slide]
Use Back to Return to Speech.
Cosmologists are beginning to draw an awesome portrait
of the structure of the universeusing mathematics
as the medium. On the other end of the scale, particle
physicists begin to sketch quantum phenomena, again
with mathematics as their brush and palette. Just
as telescopes probe outer space, the mathematical
sciences give us a platform to explore hidden universe
of the imagination, which mysteriously permeates our
real world. [rocket
and neuron] Use Back to Return to Speech.
Newton's invention of calculus inaugurated a new role
for mathematics: to enable mechanics to flourish and
the physical sciences to thrive. Today, we are watching
mathematics empower new areasbiology, neuroscience,
information technology, and nanotechnology, as represented
by this nerve cell. [weather
prediction] Use Back to Return to Speech.
As we take a quick trip across the disciplines, we
find mathematics as a full partner everywhere we alight.
Here is an example from meteorology. We find that
computing power at the terrascale, derived from mathematics,
gives us the ability to predict storms on a finer
scale. The new system reveals violent storms that
current prediction systems miss altogether. In this
map of Oklahoma, on the left the National Weather
Service has missed the storm. On the right the prototype
terrascale system predicts the storm. [El
Nino] Use Back to Return to Speech.
On a grander scale, our ability to predict El Ninothe
irregular shifts in ocean and atmospheric conditionsis
a superb example of where mathematics and computing
have brought us. It took the gathering of voluminous
amounts of data, and new mathematical techniques to
analyze it, to predict the onset of El Nino. [four
hearts] Use Back to Return to Speech.
The meeting of mathematics and medicine augurs well
for discovery on many fronts. Mathematics and complexity
theory, for instance, give insight into the human
heart. The top images are computer simulations of
the electrical activity in a normal heart. Below are
patterns of fibrillationuncoordinated electrical
activity that leads to heart attack.
This is the work of James Keenera University of Utah
mathematicianand his colleagues, but they go one
step further. They are investigating why some patterns
of electrical stimulus are better at eliminating fibrillation.
People with pacemakers and implantable defibrillators
will benefit. [Sethian
body scan] Use Back to Return to Speech.
Here J.A. Sethian of the University of CaliforniaBerkeley
uses mathematics to isolate and extract individual
components from a medical image. In this case we see
a twodimensional crosssection across the chest,
with the heart, liver and other features visible.
By clicking on the image one can automatically find
the outline of whatever region needed, such as the
outline of an organ. [new
monkey face graphic made of fractals] Use Back
to Return to Speech.
Fractal sets like we see here can be used in computer
graphics to build clouds, plants, or the surface of
the sea. They are also a goldmine for medical modeling,
of lungs or networks of blood vessels. [metabolic
rate graph] Use Back to Return to Speech.
If we look at metabolic rate across the scales of size,
we see the order that emerges from a comprehensive
view. The rate follows a hierarchy from mammals on
the upper right to eversmaller entities down through
a cell, a mitochondrion, and a respiratory complex.
We see a suggestion, perhaps, of a universal principle
underlying life at all scales.
In fact, Geoffrey West of Los Alamos National Laboratory,
who works on this problem, believes there may be two
or three hundred such scaling laws for biology. "Tree
trunks scale just as an aorta does," he says. "Nature
uses the same building blocks at every level."
[fantastic sea creatures
derived from knot theory] Use Back to Return to
Speech.
As a biologist I find the burgeoning twoway traffic
between biology and mathematics especially exciting.
I use these fanciful images, in which knot theory
gives form to fantastic sea creatures, to symbolize
this interchange. Not only is mathematics revolutionizing
biology, but biology begins to foster new paradigms
in mathematics. The information science of life edges
ever closer to electronic information science. Advances
in understanding life may lead to new algorithms and
new modes of computing, notably biological computing.
[knot theory and DNA
helix] Use Back to Return to Speech.
Another example is knot theory, which gives insight
into DNA replication and other molecular processes.
Knot theory also has applications to polymer sciencethe
creation of new materials. [cholera
genome] Use Back to Return to Speech.
Here is an application of mathematics to biology dear
to my own heart: the elucidation of the cholera genome.
I have studied this organism's relationship to its
environment for most of my research career. Modern
mathematics has helped us reach the brink of being
able to predict, for the first time, the onset of
cholera epidemics.
The sequencing of the human genome has also drawn upon
sophisticated mathematics, and illustrates the onslaught
of data we face not only in biology, but also in astronomy
and elsewhere. NSF's own math division director, Philippe
Tondeur, puts it this way: "Data acquisition used
to resemble drinking water from a tap, drop by drop.
Now it has become more like drinking from a firehose."
Our "postgenomic" eraas a recent Nature article
says"heralds an encyclopedic era of information
about the way biological cells and their genes and
proteins behave." [the
five initiatives] Use Back to Return to Speech.
Let's move now to how we implement this vision of "innumerable
connections" at NSF. Our mathematics effort really
does feed intoand complementall of the initiatives.
It provides the flow of fundamental mathematics essential
to the advance of information technology. It supplies
the understanding of complexity and uncertainty critical
to sorting out biocomplexity. It gives us some of
the tools we need to explore new frontiers at the
nanoscale. And math plays an indispensable role in
educating the scientific and technical workforce our
country needs. Let's take a quick look at each of
our initiatives in turn. [ITR
slide] Use Back to Return to Speech.
Our information technology initiative began at the
time the report by the President's Information Technology
Advisory Committee (PITAC for short) was being prepared.
The committee warned that without new federal investment,
the United States was in danger of losing its international
preeminence in computer science.
NSF is the lead agency in ITR, and we just announced
our first round of awards in September. These awards
stress "the science in computer science and the information
in information technology." Among advances we hope
for are software for critical applications like air
traffic control; IT to improve science and math education
in urban schools; robots to help the elderly at home;
and systems to manage massive data files. [biocomplexity]
Use Back to Return to Speech.
Our initiative on biocomplexity seeks to probe both
the physical and living realms of our world, and to
trace their interconnections. Biocomplexity is a timely
perspective because of the growing threats to our
environment and the expanding capabilities of our
science and technology.
Complexity gives us a perspective spanning all fields
and all scalesa richness across different orders
of magnitude. We know that many systems, such as ecosystems,
do not respond linearly to environmental change. Up
to now, we have sought understanding by taking things
apart into their components. Now, at last, we begin
to map out the interplay between parts of complex
systems. In October we awarded new grants in this
multiyear program. [nano:
three scales] Use Back to Return to Speech.
On still another front is our program at the Lilliputian
level of the nanoscale, with NSF at the lead of a
multiagency effort. These images help us to orient
ourselves to this perspective. At the left, you can
see an atom, just a few tenths of a nanometer in diameter.
In the middle, the DNA molecules are just 2.5 nanometers
wide. To the right are red blood cells a few thousands
of nanometers wide. At this magical point on the dimensional
scale, nanostructures are at the confluence of the
smallest of humanmade devices and the large molecules
of living systems.
We are beginning to manipulate individual atoms and
molecules. We're beginning to create materials and
structures from the bottom up, the way nature does
it. Nanotechnology could change the way almost everything
is designed, from medicine to computers to car tires.
NSF proposes to focus its nano investment on five
interrelated areas. They are: biosystems, nanoscale
structures, novel phenomena and quantum control, architecture
of devices and systems, nanoscale processes in the
environment, and the modeling of multiscale, multiphenomena.
[Knowledge the currency
of everyday life] Use Back to Return to Speech.
Another initiative is the 21^{st} century workforce.
In our new economy, information has moved to center
stage, and knowledge has become the currency of everyday
life. The longterm goals of this initiative are to
generate the knowledge, shape the people, and create
the tools needed to develop a workforce second to
none. Our workforce must fully reflect the strength
of our country's diversity. We will need individuals
educated to unprecedented levels of expertise in science,
mathematics, engineering and technology.
To date, we have managed quite comfortably by relying
on imported talent, but other nations have begun to
compete with us. For this new era, we need a highly
trainable workforceand retrainable workforce.
[Nature article headline:
"Recognition for mathematics is overdue"] Use
Back to Return to Speech.
I'll move now to the role of the mathematical sciences
initiative as complementary to the other NSFwide
efforts just described. You may have seen this headline
recently in the journal Nature: "Recognition for mathematics
is overdue." The editorial about our proposed initiative
said that "the whole of scienceand society at largewill
benefit" from boosting support for math. [Mathematical
Sciences Initiative: Why Now?] Use Back to Return
to Speech.
It makes eminent sense to replenish the wellspring
of fundamental mathematicswithout delay. I've already
discussed how mathematics has become interwoven with
all of science and engineering. However, before mathematical
concepts can be applied, they must first be developed.
That is why boosting support for fundamental mathematical
research is the first component of the initiative.
Fundamental mathematics is also critical to training
a mathematically literate workforce for the future.
Technologybased industries fuel the growth of our
economy, and we need welltrained graduates to fill
these jobs. More broadly, as our world grows increasingly
complex, the need for mathematical and statistical
literacy becomes ever more acute for making good decisions.
[mathematical sciences
in the U.S.] Use Back to Return to Speech.
It's not news to this crowd that our country's world
leadership of mathematics is fragile. We've been relying
on overseas talent and are not attracting enough U.S.
students.
I'll just cite a few figures that buttress the case:
 Between 1992 and 1999, fulltime graduate students
in math dropped by 21 percent, while U.S. citizens
in graduate math dropped by 27 percent.
 In 1997, only 12 percent of fulltime math grad
students had research assistantships.
[mathematical sciences
in the U.S.] Use Back to Return to Speech.
Between 1992 and 1999, upper level math majors dropped
by 23 percent. In the meantime, NSF's role in support
of mathematics is becoming even more important. We
provide about twothirds of federal academic research
support, and our share is growing. But our grants
in mathematics are smallmuch smaller than those
in other theoretical physical sciences. [MSI:
Three Frontiers] Use Back to Return to Speech.
Our new initiative in mathematics attacks this situation
on three fronts. We propose to advance the fundamental
mathematical sciences; accelerate mathematical interchange
between the disciplines; and equip our students with
mathematical skills and literacy. I'll add that the
program is still very much evolving, so the words
are subject to change. [Fundamental
mathematical sciences] Use Back to Return to Speech.
It all begins with strengthening fundamental mathematics
and statistics. Again, you know far better than I
do the incredible richness of your field. Examples
include research on dynamical systems, on advanced
statistical methodologies, and on geometry and topology.
The slide also indicates how this research would connect
with various other disciplines. [connections
to other science and engineering] Use Back to
Return to Speech.
Equally important is to deepen and create new connections
between math and other fields. Initially we will emphasize
research on:
 managing and analyzing large data sets;
 managing and modeling uncertainty;
 and modeling complex, interacting, nonlinear systems.
[mathematical sciences
education] Use Back to Return to Speech.
The third prong of our initiative is education. It
is vital to embed collaborative training in research
activities. We also want to step up the professional
development of mathematics teachers at every level,
and give them the tools they need to communicate the
excitement and power of mathematics. Finally, we need
research on how people learn mathematicsso we can
target our teaching to every student. [implementation]
Use Back to Return to Speech.
We have identified some mechanisms to reach these goals.
It's essential to increase both the size and duration
of grants, and expand our support for graduate student
and postdocs. Beyond that, we envision supporting
collaborative research groups, new institutes and
interdisciplinary centers, and other mechanisms. We
seek and we need your advice on these and other mechanisms.
[Jovean Bees] Use
Back to Return to Speech.
I will close now in anticipation of your questions
and comments. We have great hopes for our mathematical
sciences initiative, but we have a great challenge
before us and can only surmount it by working together.
My final slide gives a suggestion of how computing
enables us to share some of the beauty of the mathematical
world of the imaginationan illustration of how our
new tools accelerate the merger of the disciplines,
in this case, joining mathematics, computing and art.
The work, "Jovean Bees," is by artist Jean Constant,
and uses a program by mathematician Richard Palais.
To me the work embodies some of those "innumerable
connections."
Now I look forward to our discussion. Thank you.
