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Dr. Colwell's Remarks


Dr. Rita R. Colwell
National Science Foundation
Keynote Address: "Math Matters"
Society for Industrial and Applied Mathematics 50th Anniversary Meeting
Philadelphia, PA

July 10, 2002

See also slide presentation.

If you're interested in reproducing any of the slides, please contact
The Office of Legislative and Public Affairs: (703) 292-8070.

[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 50th 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 half-a-century 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 tonight--the ever-evolving, 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 matters--very 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 process--literally--of ripping out walls to embrace change. Philippe brought this talent--metaphorically--to 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 Ferguson--another of whose works was on display in my own office for a while--demonstrated 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 report--named after General William Odom who chaired the international panel that assessed the U.S. mathematical sciences--warned 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 two-thirds 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 cross-cutting 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 areas--including information technology and nanotechnology--have 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 sciences--building 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 education--creating a mathematically literate workforce for the nation.

I will now move to three concrete examples of compelling needs that can be met--and indeed, are already beginning to be met--by 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 mathematics--another 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 mind-expanding for some, such as Howard Schmidt, from the President's Critical Infrastructure Protection Board.

As he told Business Week, "When I got the e-mail 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 NSF-backed 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 we--and how can a computer--recognize 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 possess--and 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 networks--mathematical 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 network--depicting 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 right--but not in the network on the left.

"Unfortunately," says Newman, "most social networks--the networks over which diseases spread--seem 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 yield--through dense planting of trees--against the need for fire breaks. In fact, a mathematical model that incorporates risk aversion can predict how to eliminate a fire disaster--with only a small loss in yield. Here, mathematics sheds light on a critical societal need.

[nug30 illustration]
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When mathematics--the language of science and engineering--connects 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 begins--or 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" problem--how 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 here--26530th. 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 state-of-the-art algorithm--to reduce the complexity of the problem--and a distributed computational platform, a sort of "proto-grid," comprising about 2500 computers in the United States and Italy.

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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 States--exceptional 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 cyber-infrastructure that will give a broad range of disciplines access to high-performance 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 aquaporin--the 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 mid-channel 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 organisms--bacterial 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 organisms--artificial life--evolving 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 spots--actually 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 question--how 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 rearrange--and how quickly--can 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 math--computers, 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 assessments--from 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, 500--only about half--hold U.S. passports. Compare this to what's needed by the National Security Agency--about 60 new staff per year. NSA is actually able to hire only half that number--about 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 half-century.

  • 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 large-scale 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 it--presented to us in the form of mathematics. A vision for a wonderful gift on a 50th anniversary. My congratulations to SIAM. Thank you.



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