Devlin's Angle

April 2002

Mathematics and Homeland Security

During the 1950s and 60s, the United States poured millions of dollars into mathematics research as part of the national effort to fight (or at least to avoid losing) the Cold War. This came on the heels of the crucial, and successful, role mathematicians played during the Second World War.

Today the United States finds itself in a new war, an international War on Terror. Since the opening salvo in this new war was launched on the continental USA, and because the next attack could likewise take place in America, Homeland Security is a high priority in the new struggle. And once again, the US is looking to the mathematical community to assist in the conflict.

As part of the mathematical profession's initial response, later this month (on April 26-27) the National Academies' Board on Mathematical Sciences and their Applications (BMSA) is holding a two-day, invitational workshop on The Mathematical Sciences' Role in Homeland Security, hosted by the National Research Council in Washington, D.C. The aim is to bring together leading experts in the various areas of mathematics that are likely to be required in fighting international terrorist organizations, with a view to setting a national research agenda to aid the country in combating this new kind of warfare.

Mixing with mathematicians from universities, industry, and national laboratories at the workshop will be senior representatives from the Defense Advanced Research Projects Agency (DARPA), the National Security Agency (NSA), the Centers for Disease Control and Prevention (CDCP), the Directorate of Defense Research and Engineering, and of course the Office of Homeland Security.

The topics to be discussed fall into five general (and overlapping) areas: Data Mining and Pattern Recognition, Detection and Epidemiology of BioTerrorist Attacks, Voice and Image Recognition, Communications and Computer Security, and Data Integration/Fusion.

Many if not all of these areas are unfamiliar to most mathematicians, and they are quite different from the kinds of mathematics that were required to fight wars in the past, hot or cold. Statistical and computational techniques figure heavily in this new kind of strategic mathematics.

Data Mining and Pattern Recognition looks for ways to discover patterns, structure, or associations in large bodies of empirical data, such as financial or travel records. Much of the early research in this area was developed for industrial and commercial purposes, for instance, by banks to detect credit card fraud, by telephone companies to spot unauthorized use of the phone system, and by supermarket chains to identify purchasing patterns. (Why do you think they have those electronically readable "store membership cards"?) The relevance of this area of research to homeland security is obvious.

Detection and Epidemiology of BioTerrorist Attacks involves a number of lines of mathematical research. The development of mathematical models of how diseases spread is perhaps one of the most well known examples - well known in part because simple scenarios form standard examples in calculus classes. In fact, within days of the September 11 attacks on the World Trade Center towers and the Pentagon, researchers at Los Alamos National Laboratories had taken a mathematical model of traffic flow they had been developing and applied it to predict the likely spread of disease following a possible bioterrorist attack. There is significant scope for further research into the mathematics of how biological and chemical agents spread.

Another area where mathematics will be important in countering a biological or chemical attack is in early detection that such an attack has in fact taken place. In the early stages, it can be hard to differentiate between a malicious attack with a dangerous weapon and a naturally occurring outbreak of a common agent. The available data is almost always noisy, creating a need for better techniques to integrate and fuse data to identify patterns, determine sources, increase confidence, and predict the spread of infectious or chemical agents, in order that the available counter agents of containment methods may be brought to bear in the most timely and efficient fashion. As the science of patterns, mathematics may turn out to be one of the main weapons in the nation's arsenal in fighting this new kind of war.

Voice and image recognition: Today's terrorists operate globally, maintaining contact by telephone and the Internet. Identifying the occasional key telephone conversation among the millions that take place daily can only be done (if it can be done at all) using sophisticated automation, with monitoring systems that are able to break down voices and words into digital patterns that can be scanned for keywords. This requires the development of new algorithms to monitor communications channels in real time to provide the nation's defense authorities with early warnings of a potential threat. Similarly, methods need to be developed for the automated screening of images sent over the Internet, to look for messages embedded in pictures (steganography), a technique believed to have been used by the September 11 terrorists.

New and more sophisticated mathematical techniques for image processing and recognition will also be required to identify potential terrorists involved in suspicious activities and to improve screening at airports and other checkpoints.

Communications and Computer Security: Most mathematicians are familiar with the basics of cryptography. This, after all, is one of the areas where mathematics played a major role in the Second World War. But with secure encryption systems now widely available to security forces and terrorist alike, the focus has shifted elsewhere, to the overall integrity of communication and computer systems. A secure cryptosystem becomes worthless if an enemy can break into your computer or disrupt the network. There is thus a pressing need for taking a broad look at computers and computer networks to examine their vulnerabilities and develop ways to defend them, including early detection of an attack. New methods for analyzing Internet traffic are likely to be important in this new area of cyber warfare.

Data Integration/Fusion is the process of synthesizing information from diverse sources in order to make prudent decisions. At present there is little by way of a reliable mathematical framework to support this kind of activity. Current practitioners make largely ad hoc use of statistics, probability, decision theory, graph theory, and tools from artificial intelligence and expert systems design. The relevant parts of these disciplines need to be merged into at least a compatible toolkit, if not a coherent theory. I know first hand from my own attempts over the past twenty years to come to grips with information representation that there are enormous theoretical challenges to be overcome in order to make progress in this now crucial area.

The Washington workshop is not going to provide answers to any of the pressing questions that need to be answered. That is not the purpose. As with the war on terrorism itself, we are in the early days of what will certainly be a long haul. The workshop is intended merely to draw up a roadmap of where we want to go and how we might get there.

Much of the work that has to be done will not be "hard, elegant" mathematics of the kind that many mathematicians (myself included) view as a thing of beauty. (Although history tells us that there is a high probability that this effort will lead to such mathematics as an unintended side-effect.) Consequently, there are likely to be few public rewards or accolades for those who choose to engage in such projects. But it is work that can only be done by mathematicians. Such was the case with the part played by mathematicians in previous conflicts. Now, as then, I doubt there will be any shortage of willing volunteers.

NOTE: The April workshop is by invitation only.

Devlin's Angle is updated at the beginning of each month.
Mathematician Keith Devlin ( is the Executive Director of the Center for the Study of Language and Information at Stanford University and "The Math Guy" on NPR's Weekend Edition. His latest book is The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip, published by Basic Books.