In his State of the Union address in January, President Bush stressed the importance of improving math education. He proposed to "train 70,000 high school teachers to lead advanced placement courses in math and science, bring 30,000 math and science professionals to teach in classrooms, and give early help to students who struggle with math."

But where will these teachers come from? And will the training of teachers be sufficient to increase the number of students choosing math and science careers? And why does all this matter?

Because mathematics is the foundation of the natural sciences. It is no coincidence that Isaac Newton, the man who formulated the law of gravitational attraction that revolutionized our understanding of the universe, was also the man who popularized the calculus. And the natural sciences, however pure, are what give us airplanes, cable TV and the Internet.

In the 2003 Program for International Student Assessment, a test that measures math literacy, American 15-year-olds performed worse than their peers in 23 countries, as well as those in Hong Kong. It's not hard to see why. According to the National Council of Teachers of Mathematics, 40 percent of the nation's middle school math teachers do not have the equivalent of an undergraduate minor in math. The average starting salary of a teacher is only $30,000, whereas the average starting salary for a recent college graduate in computer science or engineering is $50,000.

Short of following the British, who have proposed paying experienced math teachers more than $100,000, with a guaranteed minimum of $70,000, where will we find a way to attract the thousands of teachers George Bush wants?

New York State initiated an innovative program to bring teachers from Jamaica for two or four years to teach in New York schools. Jamaica, a developing nation where one U.S. dollar equals 65 Jamaican dollars, is nonetheless a stable, English-speaking nation with an unbroken democratic tradition; it stands poised to beat the United States in establishing the world's first Institute for Mathematical Methods in Counterterrorism. When teachers for the New York program were recruited on the campus of the University of the West Indies, recruiters found more experienced math and science teachers than they ever dreamed they would.

But you can have all the teachers in the world and still not inspire kids to learn math. My friend Autumn e-mailed me about her nephew, Joshua: "He's upset because he's asked several of the math teachers why math is important or what are certain formulas used for -- there has to be a use, correct?"

Autumn told her nephew about my work in counterterrorism and for the television crime drama "Numb3rs." Autumn reported, "He's told his math teachers about you as well, and about the show 'Numb3rs.' He's informing them that through something called lattice theory you are managing to fight terrorists -- all with math."

Mathematics is art, and should be appreciated for its beauty, not simply for its utility. But we cannot expect 11 year-olds to cherish totally order-disconnected topological spaces as much as professional mathematicians do.

As I first proposed in January 2005, television shows like "Numb3rs" (or "Medium") -- where the main characters are mathematicians -- could work with the National Council of Teachers of Mathematics to show kids how math is really used; the council and Texas Instruments are now working together to use "Numb3rs" to promote math literacy in schools.

Another way to inspire kids is to relate mathematics to something they see every day. In order to excite students and draw funding to his school, school superintendent Ronald Ross of Roosevelt, N.Y., has begun looking into the idea of creating a curriculum involving math and counterterrorism. What kinds of topics would students learn?

The opening line of the Oscar-winning movie "A Beautiful Mind" is "Mathematicians won the war." During World War II, the mathematics underlying cryptography played an important role in military planning. Winston Churchill admired Alan Turing, the mathematician who had mastered the German codes, recognizing him as the man who had perhaps made the single greatest individual contribution to defeating Hitler.

At Los Alamos, the lab that built the atomic bomb, Cliff Joslyn uses lattice theory to mine data drawn from thousands of reports of terrorist-related activity to discover patterns and relationships that were previously in shadow.

Lattice theoretical methods developed at MIT tell us the probability that we have disabled a terrorist cell, based on how many men we have taken out and what rank they hold in the organization. Lauren McGough, a Massachusetts high school student, tested the accuracy of this model by getting her classmates to pretend they were terrorists, passing orders down a fictitious chain of command, essentially confirming what the theory predicts.

High school students could learn algebra, trigonometry, calculus and logic while also learning concrete applications involving homeland security. No longer would students yawn and ask, "What is math good for?" Beauty could defeat both terror and boredom.

Whatever you may think of the State of the Union address, when it comes to supporting math education, we should all see pi to pi. President Bush is correct when he says that mathematics education in America must improve if the United States is to stay economically competitive, but the stakes are much higher than that. During the Cold War, the United States would not have tolerated a military gap between itself and its adversaries. Yet today, with 61 percent of all U.S. doctorates in math going to foreigners (15 percent to Chinese), we readily accept a "math gap."

Dollar for dollar, the best defense against our adversaries' weapons of mass destruction may be our allies in the Americas, armed with weapons of math instruction.

Improving math education is not merely a smart idea. It is a matter of national security. Algebra is one revolutionary Islamic concept we cannot afford to neglect or ignore.

This study, conducted by the faculty and research fellows of the Combating Terrorism Center (CTC) at West Point, serves multiple purposes, the most important of which is contributing to the depth of knowledge about the al-Qa'ida movement. Evidence supporting the conclusions and recommendations provided in this report is drawn from a collection of newly-released al-Qa'ida documents captured during recent operations in support of the Global War on Terror and maintained in the Department of Defense's Harmony database. In the text of these documents, readers will see how explicit al-Qa'ida has been in its internal discussions covering a range of organizational issues, particularly regarding the internal structure and functioning of the movement as well as with tensions that emerged within the leadership.

In the first part of the report, we provide a theoretical framework, drawing on scholarly approaches including organization and agency theory, to predict where we should expect terrorist groups to face their greatest challenges in conducting operations. The framework is informed as much as possible by the captured documents, and provides a foundation upon which scholars can build as more of these documents are declassified and released to the public.

Our analysis stresses that, by their nature, terrorist organizations such as al-Qa'ida face difficulties in almost any operational environment, particularly in terms of maintaining situational awareness, controlling the use of violence to achieve specified political ends, and of course, preventing local authorities from degrading the group's capabilities. But they also face problems common to other types of organizations, including private firms, political parties, and traditional insurgencies. For example, political and ideological leaders--the principals--must delegate certain duties to middlemen or low-level operatives, their agents. However, differences in personal preferences between the leadership and their operatives in areas such as finances and tactics make this difficult and give rise to classic agency problems.

Agency problems created by the divergent preferences among terrorist group members present operational challenges for these organizations, challenges which can be exploited as part of a comprehensive counterterrorism strategy. Thus, the theoretical framework described in this report helps us identify where and under what conditions organizations can expect the greatest challenges in pursuing their goals and interests. Understanding a terrorist organization's internal challenges and vulnerabilities is key to developing effective--and efficient--responses to the threats they pose and to degrade these groups' ability to kill. The captured al Qa'ida documents contribute significantly to this type of understanding.

Our analysis emphasizes that effective strategies to combat threats posed by al-Qa'ida will create and exacerbate schisms within its membership. Members have different goals and objectives, and preferred strategies for achieving these ends. Preferences and commitment level vary across specific roles performed within the organization and among sub-group leaders. Defining and exploiting existing fissures within al-Qa'ida as a broadly defined organization must reflect this intra-organizational variation in preferences and commitment in order to efficiently bring all available resources to bear in degrading its potential threat. While capture-kill options may be most effective for certain individuals--e.g., operational commanders--we identify a number of non-lethal prescriptions that take into account differences in al-Qa'ida members' preferences and commitment to the cause. Many of our prescriptions are intended to induce debilitating agency problems that increase existing organizational dysfunction and reduce al-Qa'ida's potential for political impact.

To achieve long-term success in degrading the broader movement driving terrorist violence, however, the CTC believes the United States must begin aggressively digesting the body of work that comprises jihadi macro-strategy. We therefore also seek to apply our model to the ideological dimension of al-Qa'ida revealed in numerous instances in these documents, the goal being to identify ways to facilitate the ideational collapse of this body of thought. The included documents provide insights into the points of strategic dissonance and intersection among senior leaders that must be better understood in order to be exploited.

In sum, this theoretically informed analysis, along with assessments of the individual captured documents themselves, contributes to existing bodies of research on al-Qa'ida. It provides several tools for identifying and exacerbating existing fissures as well as locating new insertion points for counterterrorism operations. It presents an analytical model that we hope lays the foundation for a more intellectually informed approach to counterterrorism. And perhaps, most importantly, this assessment demonstrates the integral role that scholars can play in understanding the nature of this movement and in generating smarter, more effective ways to impede its growth and nurture the means for its eventual disintegration.

You burst into the room. Sitting on a chair, blindfolded, his hands tied behind his back, is your prisoner. The room is dark, except for a lonely naked bulb hanging from the ceiling. He is sweating. He is afraid.

"Tell me where it is!" you scream. "Now!" You know there is little time left. Somewhere in your city, a time bomb is ticking. Whether it spits serin into the air, uranium into the water or atomic fire into the heavens, you do not know.

He does. But he is not talking. Involuntarily, you raise your hand as if to strike. What you are about to do violates the law and your conscience. And yet. ...

In peacetime, torture ranks next to murder as a primal sin. But during war, the debate begins over whether this evil can ever be justified to combat the seemingly greater evil of the enemy. Harvard law Professor Alan Dershowitz has said torture should be legalized.

In early October, the U.S. Senate voted 90-9 to ban it. Although Secretary of State Condoleezza Rice and President Bush have both recently asserted that "We do not torture," five U.S. Army Rangers were charged in November for punching and kicking detainees in Iraq, secret U.S. prisons have caused anxiety in Europe, and Vice President Dick Cheney has battled to win the CIA an exemption from the torture ban. As late as December, the U.S. House of Representatives stood poised to defeat the White House.

Few of us will ever be asked to torture. But, indirectly, all of us have to make a choice: to support, as citizens, those politicians who back torture, or those who seek its prohibition.

The decision of an individual to support, or reject, torture seems at first to be a purely moral question. But what would be the long-term consequences to society if we were to make this radical break with the past?

One cannot do experiments with societies, or predict the future, but, it turns out, one can attempt to address this issue using the cold, hard tools of mathematics and logic. This story begins in 1963.

The United States and the Soviet Union are on the perpetual brink of war, balanced like two sides of an equation. On the American side are "game theorists" like Thomas Schelling, recently awarded the Nobel Prize for his work on the strategy of conflict. On the Soviet side, there is the solitary mathematical psychologist Vladimir Lefebvre.

Just as mathematics could be used to describe logical reasoning, Lefebvre saw that mathematics could be used to describe ethical reasoning. If something was good -- for example, "church," "democracy," "prosperity," "kindness" -- it had value "1."

If something was evil -- "earthquake," "famine," "military defeat," "murder" -- it had value "0." But rarely were ethical situations so simple. For instance, "killing" is bad (0) but protecting one's country is good (1) -- so is war 1 or 0?

Lefebvre saw that, at the crudest level, there were essentially two types of ethical systems. Those that held that employing evil means to attain just ends was good, and those that saw that employing evil means to attain good ends was wrong.

There were also, crudely put, two types of relations between individuals: those entailing compromise (or cooperation) and those entailing confrontation.

Of course, evil people rarely see themselves as evil. So Lefebvre had to incorporate in his model of human nature the capacity of human beings to judge -- correctly or incorrectly -- the goodness or evil of their own acts, and to reflect upon their own judgments, and others'. "Reflexive Theory" was born.

It quickly became a paradigm within the Soviet defense establishment, with the publication of books such as "Mathematics and Armed Conflict." Nothing like it was known in the West.

With very simple assumptions -- for instance, that an individual who correctly sees his actions to be good when they are good, and evil if they are evil, is more highly regarded by society than an individual who incorrectly sees himself -- Lefebvre showed that in a society that accepted the compromise of good with evil, individuals would more often seek the path of confrontation with each other.

Lefebvre's insights were called upon by the State Department during negotiations with Mikhail Gorbachev in Reykjavik, Iceland. (And perhaps Lefebvre's model could be re-enlisted to help U.S. officials understand and negotiate with Arab and Muslim heads of state, who must also negotiate with their people.)

In support of Lefebvre's revolutionary new theory, a survey of Soviet émigrés and Americans was conducted in the 1970s. They were asked questions like, "Should a doctor conceal from a patient that he has cancer in order to diminish his suffering?" Overwhelmingly, the Americans would say no, and overwhelmingly, the Soviets yes. The Soviets accepted the compromise of good with evil; the Americans rejected it.

What does this mean? If Americans begin to accept the use of torture, American society might turn into a society of individuals in conflict.

Not uniformly, thanks to something called free will, but generally, with harmful consequences for society: Imagine two roads, with a stream of cars moving along each one. Each driver wants to reach his destination as quickly as possible; on occasion, drivers will impede each other.

On the first road, drivers rise in their own, and in other drivers', estimation if they yield. Drivers on the second road lose face when they yield. It is clear that traffic will move faster on the first road than on the second.

It can be argued that repressive states like Saudi Arabia, which bred most of the Sept. 11 hijackers, are on the second road. If the United States moved to accept torture, it could veer toward the second road, too -- the road of the Soviet Union.

And we know where that road ends. The Soviet Union no longer exists.

This article adopts a two-tiered approach: it provides a detailed, historical account of anti-terrorist finance initiatives in the United Kingdom and United States--two states driving global norms in this area. It then proceeds to a critique of these laws. The analysis assumes--and accepts--the goals of the two states in adopting these provisions. It questions how well the measures achieve their aim. Specifically, it highlights how the transfer of money laundering tools undermines the effectiveness of the states' counterterrorist efforts--flooding the systems with suspicious activity reports, driving money out of the regulated sector, and using inappropriate metrics to gauge success. This article recognizes that both states consider the fight against terrorism to be partly military but also a matter of bringing certain democratic principles to bear. Critics have been quick to condemn some of the measures for their encroachments into civil liberties. My goal is not to measure the success of the laws according to any particular ideology but rather, accepting the governments' democracy-promoting goals, and the role these play in generating domestic and international support, to clarify which components do not appear to serve the states' aims.

This article won Stanford Law School's Carl Mason Franklin Prize for 2005-2006, for most distinguished written work in international law.

A net assessment of the benefits/losses of arms control treaties in terms of military significance was required in response to the START Resolution of Ratification. The response by the Executive Branch belabored smaller issues, avoided accomplishments and didn't carry out the net assessment.