Dr. Rita R. Colwell
Director
National Science Foundation
Keynote Address: "Math Matters"
Society for Industrial and Applied Mathematics 50^{th}
Anniversary Meeting
Philadelphia, PA
July 10, 2002
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[title slide]
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Good evening to everyone and thank you for a very kind
introduction. It is truly an honor to deliver the
keynote address for SIAM's 50^{th} anniversary
meeting.
This is a golden occasion for all of you as well as
a golden opportunity for all of science and engineering
to celebrate and build upon the work of SIAM.
Both as an active researcher and as NSF director, I
am an unabashed supporter of SIAM's interdisciplinary
perspective and its achievements that bring such societal
benefit. I convey my heartfelt congratulations on
halfacentury of leadership.
This is an excellent occasion to recall physicist Eugene
Wigner's famous description of the unreasonable effectiveness
of mathematics. Wigner called it a "miracle" that
mathematics provides a natural language for science.
In the deepest sense, that's what we honor tonightthe
everevolving, miraculous lexicon and grammar of mathematics,
and you, its practitioners. For that same reason,
I have titled my remarks tonight and emphatically
so"Math Matters."
I intend to speak about why math matters at
NSF  and how math matters to our broader
society.
As a prelude to these themes, I would like to acknowledge
a person who mattersvery much. He is, of
course, the director of NSF's Division of Mathematical
Sciences, Philippe Tondeur.
Philippe is probably best known for presiding over
an increase in the math division's budget from $106
million in FY 2000 to more than $180 million this
coming fiscal year. As he recently told SIAM News,
the mathematics community needs to "take the money
and change the world..."
I understand that when Philippe was poised to come
to NSF three years ago, ready to leave the math chairmanship
at the University of Illinois, his department was
in the processliterallyof ripping out walls to
embrace change. Philippe brought this talentmetaphoricallyto
NSF, which helped him to surmount obstacles and overcome
the barriers between disciplines.
Philippe's arrival at NSF was foreshadowed by an elegant
yet substantial presence.
[photo of Ferguson
sculpture]
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One day, before he arrived, a golden mathematical sculpture
appeared at the entranceway to his office. This sculpture
by Helaman Fergusonanother of whose works was on
display in my own office for a whiledemonstrated
Philippe's own elegant appreciation for the deep connections
of mathematics to all of science, and beyond to the
world of art.
Yesterday, Philippe received SIAM's Frederick A. Howes
Commendation for Public Service. I would like to toast
you now, Philippe, for an honor much deserved.
[Math priority area
at NSF]
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In 1998, what we call the Odom reportnamed after
General William Odom who chaired the international
panel that assessed the U.S. mathematical scienceswarned
of disturbing trends that threatened to undermine
U.S. leadership in mathematics.
For one, support for math by federal agencies had been
declining. Today, more than twothirds of all federal
support for academic research comes from the National
Science Foundation. Given that NSF supports all of
science and engineering, and that mathematics is the
ultimate crosscutting discipline, vigorous support
for mathematics is one of our most vital responsibilities.
To strengthen the mathematical foundations of science
and society, NSF has established math as one of our
priority areas for focused investment. In the past
few years, we have made it a deliberate part of our
strategy to demarcate areas of converging discovery
for special support.
We select these priority areas based on their exceptional
promise to advance knowledge. Such convergent areasincluding
information technology and nanotechnologyhave been
called the "power tools" of the next economy. We highlight
mathematics as one such area.
In mathematics, we seek to advance frontiers in three
interlinked areas. The first is fundamental mathematical
and statistical sciencesbuilding and strengthening
a research community that is both intellectually distinguished
and relevant to society.
The second: interdisciplinary research involving the
mathematical sciences. Here we strive to explore and
nourish the connections between U.S. mathematics and
the rest of science and engineering. Third is mathematical
educationcreating a mathematically literate workforce
for the nation.
I will now move to three concrete examples of compelling
needs that can be metand indeed, are already beginning
to be metby the mathematics community.
[Business Week column
headline on math/ Natl. security]
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The first is a major current priority for our nation:
homeland security. Mathematics has tremendous potential
to help us deal with the threats to our nation and,
indeed, to the world that were brought into bold relief
by 9/11.
The public, however, may not grasp the link between
security and support for mathematicsanother challenge
for those of us who do: to explain it.
In April, the National Research Council sponsored a
workshop on the role of the mathematical sciences
in homeland security. The workshop was mindexpanding
for some, such as Howard Schmidt, from the President's
Critical Infrastructure Protection Board.
As he told Business Week, "When I got the email invitation,
I thought at first it was a joke." As the conference
proved, however, mathematics can provide deep insights
into many challenges of homeland security, from protecting
computer infrastructure to dealing with bioterrorist
threats.
[New Types of Problems:
word slide]
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The workshop recognized several new kinds of security
problems that mathematical solutions could alleviate.
These problems reverse older viewpoints and include:
searching for rare events instead of common patterns;
protecting systems from malicious attacks instead
of random failures; and combining data from many types
of sources.
[Math Research Challenges
in Homeland Security: word slide]
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As a next step, the workshop identified these four
major research challenges for mathematics related
to homeland security. They are: data mining for rare
events; computer, network and physical infrastructure
security; detection and epidemiology of bioterrorist
attacks; and voice and image recognition.
[graph analyzing
hands in different positions]
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Well before September 11 the National Science Foundation
identified information technology and mathematics
as priority areas for focused, interdisciplinary funding.
I will cite a few examples of NSFbacked research
that is already underway  mathematics research projects
that exemplify how we are already tackling some of
these security challenges.
In the realm of dealing with large data sets, here
is a graph analyzing images of hands in different
positions. These data are not amenable to classical
linear methods of analysis. How do weand how can
a computerrecognize all of these images as a hand,
even when rotated into many different positions?
Just so, how do we recognize a face when lighting and
expression change, and how can we tell a computer
to do that? How can the brain look at the many measurements
an object can possessand select only the dimensions
that vary, thereby zeroing in on what matters?
This work by Gunnar Carlsson and Joshua Tenenbaum at
Stanford University and their colleagues cut a problem
with many dimensions down to size.
[image processing
collage]
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Image restoration and recognition are making great
progress with insights from mathematics and computing.
As an example, a technique called "inpainting" borrows
techniques from classical fluid dynamics to use a
computer to fill in missing pieces of a digital image,
whether of a fine painting, an old movie or the blurry
face of a criminal suspect. There are many other such
techniques being developed, with representative results
shown here.
[Sir Martin Rees
and Dracula: two images side by side]
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Let's move to connectivity, as suggested by this unlikely
pair of images. "What do the Astronomer Royal and
Dracula have in common?" asked a headline in the British
newspaper Independent. (Sir Martin Rees, Britain's
astronomer royal, is on the left, as I hope you guess!)
A further question could be: what could they both
possibly have in common with epidemiology and tracking
bioterrorism?
The answer: connectivity. Both the astronomer royal
and the actor Christopher Lee, who has starred as
Dracula, are the most "connected" within their respective
communities. As discovered by Mark Newman of the Santa
Fe Institute, the astronomer has collaborated most
widely of anyone in astrophysics, while Lee is the
actor most linked to other actors.
Newman studies many sorts of networksmathematical
theory that applies to the World Wide Web, collaborations
among scientists, networks of company directors.
As he notes, "Networks of physical contact between
people also govern the way diseases spread. A proper
understanding of the nature and progress of epidemics
is impossible without good network models."
[two types of networks,
stylized; from Mark Newman]
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Here is an excellent illustration from Newman's work
that depicts how connected people are. On the left
we see one type of networkdepicting a core group
of highly connected people. On the right is another
type of network, less centrally organized.
Now, a strategy to control disease is to find highly
connected people and to treat them. It turns out that
this works exceptionally well with the case on the
rightbut not in the network on the left.
"Unfortunately," says Newman, "most social networksthe
networks over which diseases spreadseem to fall
into the category on the left. This suggests that
our current simple strategies for tackling the spread
of infection may not be effective. With new understanding,
however, we may be able to suggest effective targets
for immunization or education campaigns to slow disease
spread." What a timely application of mathematics
to current challenges.
[forest fire]
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Decisions that pit yield against risk are also important
in many sectors of society, from security to finance.
A timely example, given the nation's drought and the
forest fires in the Western U.S., is the problem of
forest management.
A complex system such as a managed forest may be very
susceptible to complete destruction by fire. Foresters
must weigh maximizing yieldthrough dense planting
of treesagainst the need for fire breaks. In fact,
a mathematical model that incorporates risk aversion
can predict how to eliminate a fire disasterwith
only a small loss in yield. Here, mathematics sheds
light on a critical societal need.
[nug30 illustration]
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When mathematicsthe language of science and engineeringconnects
to other disciplines, its own vocabulary is enriched
in the exchange. In fact, we cannot always be sure
where mathematics leaves off and computer science
beginsor vice versa. I see that as a superb example
of convergence.
There's the case of "nug30" (pronounced NEWG THIRTY)
 a mathematical problem in location theory that went
unsolved for decades. The problem was to assign 30
facilities to 30 fixed locations, yet to minimize
the cost of transferring material among the locations.
This applies to locating treatment areas in a hospital,
or laying out a computer chip. (Incidentally, there's
also the "nug26" problemhow to place the keys on
a keyboard for optimum performance. Of course, the
answer is different for every language!)
Although it sounds manageable, "nug30" is astonishingly
complex. We see the number of possible answers here265^{30th}.
As one of the researchers said, "The number of assignments
is so large that even if you could check a trillion
per second, this process would take over 100 times
the age of the universe."
Instead, it took seven days. The solution required
both a stateoftheart algorithmto reduce the complexity
of the problemand a distributed computational platform,
a sort of "protogrid," comprising about 2500 computers
in the United States and Italy.
[TeraGrid]
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Now we look toward a grander scale: the TeraGrid, a
distributed facility that will let computational resources
be shared among widely separated groups.
This will be the most advanced computing facility available
for all types of research in the United Statesexceptional
not just in computing power but also as an integrated
facility, offering access to researchers across the
country, merging of multiple data resources, and visualization
capability.
It is a step toward the vision of a cyberinfrastructure
that will give a broad range of disciplines access
to highperformance computing.
[aquaporin simulation]
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The Terascale system has already helped to study the
permeability of cells, as reported this April in Science.
The system simulated aquaporinthe channels that
conduct water through cells at up to a billion molecules
per second, yet block hydrogen ions from entering.
When impaired, aquaporins play a role in cataracts
and diabetes.
The simulation shows that the water molecules do a
midchannel flip, which we can see here. Simulation
was able to reveal what experiment could not.
[Richard Lenski:
digital and bacterial evolution]
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On quite another scale, mathematics, biology and computer
science intersect to bring surprising insights into
the process of evolution.
Richard Lenski at Michigan State has joined forces
with a computer scientist and a physicist to study
how biological complexity evolves, using two kinds
of organismsbacterial and digital.
Lenski's E. coli cultures are the oldest of
such laboratory experiments, spanning more than 20,000
generations. Here the two foreground graphs actually
show the family tree of digital organismsartificial
lifeevolving over time.
On the left, the digital organisms all compete for
the same resource, so they do not diversify and the
family tree does not branch out. On the right, the
digital organisms compete for a number of different
resources, and diversify.
In the background are round spotsactually laboratory
populations of the bacterium E. coli, which
also diversified over time when fed different resources.
In vivo derives insight from in silico.
[shuffling genes
of fruitflies]
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Mathematics is fundamental to advances in genomics,
yet each brings a different perspective. A statistician
might ask the questionhow many times must one shuffle
a brand new deck of cards to create random order?
A geneticist, on the other hand, compares chromosomes
of two fruitflies that diverged in evolution 50 million
years ago, and asks: What is the minimum number of
events needed to turn one arrangement into the other?
Understanding how genomes rearrangeand how quicklycan
help shed light on human diseases or improve agricultural
yields. This particular research is supported by a
joint program for mathematical biology between NSF
and the National Institutes of Health.
[Does Math Matter?]
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I have thus far explored how "math does matter" in
some challenges facing our nation and our world in
the realms of security, environment, and medicine.
All of these needs draw upon the final challenge I
wish to address: a mathematically literate workforce.
This poster, in fact, announced a panel discussion
held jointly by NSF and Discover Magazine
on Capitol Hill last month to explore this societal
need.
Does math matter? I am reminded of the opening scene
of the film, "A Beautiful Mind," which captures how
a mathematician might see the world: John Nash as
a young student becomes transfixed with the pattern
of sunlight glistening in a drinking glass, then sees
it repeated in the design of a tie worn by a fellow
student.
Mathematical literacy is becoming essential to our
ability to appreciate the world around us, perhaps
just as important as language literacy became when
printed mass media emerged.
Is innumeracy acceptable? We observe that many students
are less interested in math and more interested in
toys and technologies based on mathcomputers, video
games, cell phones and credit cards.
We must all ponder what level of mathematical knowledge
is needed for an individual or a society to thrive.
Mathematical literacy exists at different levels,
and the dialogue should extend to who needs to know
what.
Today, people are bombarded with risk assessmentsfrom
the probability of contracting disease, to the likelihood
of terrorist attacks, to the chances of winning the
lottery or making money in stocks. The debate about
the use of calculators and the like should extend
beyond basic skills and into such subjects as fractals,
differential equations, and probability.
Mathematical literacy is also vitally needed on quite
another front, and that front is a bottleneck. This
country graduates about a thousand math and statistics
PhDs per year. Of these, 500only about halfhold
U.S. passports. Compare this to what's needed by the
National Security Agencyabout 60 new staff per year.
NSA is actually able to hire only half that numberabout
30. No more are available. That equation simply does
not work.
[
New math institutes]
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We hope that NSF's recent announcement of three new
math research institutes is a start toward strengthening
fundamental mathematics and its connections to science
and engineering, as well as another reason to celebrate
as SIAM embarks on a new halfcentury.
 The Mathematical Biosciences Institute at Ohio
State University in Columbus will support interdisciplinary
work on problems such as neuroscience and cell
processes. The institute will foster the "quantitative
culture" in the life sciences by drawing together
biologists and mathematicians. Postdoctoral scientists
will be mentored by both a bioscientist and a
mathematician.
 The Statistical and Applied Mathematical Institute
in Research Triangle Park ties together statistics,
applied math, and other disciplines to attack
challenges that involve models and massive data
sets. Initial projects include largescale models
for environmental systems.
Duke University leads the consortium, which includes
North Carolina State University, the University of
North Carolina at Chapel Hill, and the National Institute
of Statistical Sciences.
 Third is the Research Conference Center of the
American Institute of Mathematics in Palo Alto,
which will host workshops on fundamental and interdisciplinary
mathematics. This format will spawn novel approaches
to stubborn scientific challenges.
The collaborations will include mathematicians from
underrepresented groups and junior researchers. These
three new centers bring to a total of six such institutes
supported by NSF.
In addition, an award is renewed to the School of Mathematics
at the Institute for Advanced Study in Princeton,
which integrates education with research.
Two thousand years ago, the ancient library of Alexandria
Egypt housed hundreds of thousands of scrolls, perhaps
the closest to a universal library for its time. Here,
Ptolemy's famous map shows the "Egyptian Sea"of
course today's Mediterranean Sea upon whose shore
Alexandria still resides.
Legends surround the fate of the Alexandria Library,
yet its memory haunts us with a great dream of universal
scholarship.
Today, NSF envisions the creation of a digital mathematics
library that would house the entire scholarly literature
of the mathematical sciences.
At the end of this month, an international workshop
will be held at NSF with participation by at least
eight nations to begin discussing technical issues
related to the library.
Currently a dream, the library is a vision for an international
resource that could symbolize the future of science
and engineering in our electronically interconnected
world.
What a fantastic vision for the "wonderful gift" as
Eugene Wigner put itpresented to us in the form
of mathematics. A vision for a wonderful gift on a
50th anniversary. My congratulations to SIAM. Thank
you.
