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.

Noah Feldman

In looking at the brewing civil war between the two groups in Iraq, it's easy to assume that the cause is ancient hatred. Nothing could be further from the truth. For the overwhelming majority of Iraqi history, Sunnis and Shi'ites have lived peacefully side by side, and numerous Iraqis are the children of mixed marriages. Instead we are witnessing in Iraq what occurs when government collapses and there is no state around capable of guaranteeing personal security.

What do you do when your family is in peril and you cannot turn to the government for protection? The answer is that you will take security wherever you can get it. You need to find some group that will be capable of keeping you safe, and that group had better be one that can count on your loyalty just as you can count on its protection. If you are a member of my ethnic, racial or religious group, then we share at least some basic bond, which may be enough to ensure our loyalty to one another. I need some assurance that you will have my back, and identity is better than nothing.

Sunnis and Shi'ites may find themselves joining militias or supporting denomination-based political parties even if they are not particularly pious and would much prefer not to. Something similar happened in the former Yugoslavia when its government collapsed with the fall of communism and nothing replaced it. Ethnic activists - call them identity entrepreneurs - will always form the core of the new militia. These radicals will emphasize symbols, like al-Askari mosque that was blown up last week in Iraq, and hope that followers will react by strengthening their commitments to the group itself.

Is it possible to break the cycle of violence that gets under way when identity groups move toward civil war? One answer is for an outside force to impose a solution. The killing did not stop in Bosnia or Kosovo until Western powers showed they were willing to bomb. But this approach is not viable in Iraq, where U.S. bombs came first and civil strife has followed. Instead the only way out of the violence is for Iraqis to realize that they have more to gain by negotiating a settlement between their groups than they do by allowing a full-blown brothers' war to break out.

Vali Nasr Author The Shia Revival (forthcoming)

What lies at the heart of the sectarian violence in Iraq is not so much religious dispute as it is a very secular competition for power and prominence in the new Iraq. Iraq is not all that different from Northern Ireland or Bosnia, where religion paraded as ethnicity and became a vehicle for communal rivalries. In the vacuum of power left by the fall of Saddam Hussein, the game of numbers has favored Shi'as, who are 60% of the population. It is for this reason that they wholeheartedly embraced democracy. Disgruntled Sunnis, on the other hand, vested their fortunes in boycott and violence, hoping that as spoilers, they would gain leverage in negotiating over the future.

Few in the West recognized the depth of either the Shi'a anger at the Saddam regime or the Sunni rage born of loss of power. There is a strong sense of Iraqi identity among both Shi'as and Sunnis, but as strong allegiance to sect and ethnicity in every election has shown, a shared notion of what Iraqi identity means and how each community sees the future of Iraq is fast disappearing. As happened in Bosnia, in Iraq mixed marriages and shared memory of coexistence will not be enough to stop internecine violence.

Shi'as embraced the political process that the U.S. set in place in 2003 in the hope that it would guarantee their security and serve their interests. There is indication now that many Shi'as are having second thoughts. Already overstretched in facing the Sunni insurgency, the U.S. can hardly afford losing the Shi'a as well. If tensions escalate to a full-blown civil war, Iran, Saudi Arabia, Jordan and Syria may all join the war to protect their co-sectarians and to scramble for pieces of a failed Iraq.

Pulling Iraq back from the brink will be difficult. Building a strong central government and an effective security force will help. The challenge is to get them up and running before events on the ground pass a point of no return.

James D. Fearon

By any reasonable definition, there has been a civil war in progress in Iraq at least since the Coalition Provisional Authority formally handed over authority to the Iraqis in 2004. A civil war is a violent conflict within a country fought between organized groups seeking to compel a major change in government policies or to take control of the center or a region. The insurgents in Iraq target the U.S. military, but they are also fighting against the Shi'ite-dominated Iraqi government and killing large numbers of Iraqis. There is little reason to think that if the U.S. suddenly withdrew, the insurgents would not continue to fight to control or shape the government.

When we hear talk about incipient civil war in Iraq, the fear is of an escalation of the current insurgency into a much bigger war. Analysts may have in mind something like the U.S. Civil War, with Sunni and Shi'ite armies fighting each other across well-defined fronts. Or they may imagine a sudden spasm of massive communal conflict and ethnic cleansing along the lines of Bosnia or Rwanda. Neither scenario is all that likely, although bouts of violent ethnic cleansing are certainly possible in a few parts of the country, especially Kirkuk.

My guess would be that as the insurgency continues to create insecurity, sectarian militias will continue to grow in power and influence. They will increasingly supply local security, but in the form of protection rackets that extort as they protect. They will clash with each other over territory and control of revenue sources. Since the Sunnis remain highly disorganized, some of these local fights may initially be intra-Shi'ite. But in the absence of effective political incorporation and protection from national police and army units - which are heavily infiltrated by Shi'ite militias - Sunnis will gradually form a patchwork of militias. Neighborhood-by-neighborhood conflict and violence will increase. Think Lebanon.

Juan Cole

If you look at the ethnic conflicts and street demonstrations during Iraq's modern history, it is remarkable how few have involved Shi'ites fighting Sunnis. During the colonial era, Iraqis were united by their opposition to the British occupation. Sunni and Shi'ite tribes cooperated in rebelling against British rule, and were only put down with a bombing campaign in 1920 that killed 9,000. In 1941 mobs targeted Iraq's small Jewish population; Jews had been a valued part of the Iraqi national fabric but were accused, unfairly, of being pro-colonial. After World War II, much of the violence in Iraq was fueled by issues of class. In 1948 slum dwellers and railway and oil workers revolted against a government treaty with Britain. In 1959, Arab nationalists assassinated Communist Party members, while mobs in Mosul and Kirkuk attacked and killed rich businessmen and landowners.

Iraqi Muslims have not all along been severely divided by religious sect. There have been many instances of strong cooperation between Sunnis and Shi'ites. Other social divides have led to mob violence in the past, but Iraqis have overcome them to re-establish national unity. It remains to be seen whether they can accomplish this feat again.

Since the controversy over cartoons of the Prophet Muhammad erupted, Europe's leaders have shown remarkable--and uncharacteristic--courage under fire. Refusing to apologize for the alleged slight to religious Muslims, a chorus of Continental voices has instead risen to the cartoons' defense, citing freedom of expression as the very essence of liberty, democracy and the European Way.

Unfortunately, free speech is about the weakest card in Europe's hand these days. An Austrian court's conviction and sentencing of the British historian David Irving to three years imprisonment for Holocaust denial is merely the most recent footnote to European hypocrisy on freedom of expression over the past decade.

The European Convention on Human Rights, which legally binds all EU states and supersedes domestic law, explicitly guarantees "the right to freedom of expression" including "the freedom to hold opinions and to receive and impart information and ideas without interference by public authority."

This provision is in keeping not only with the U.S. Bill of Rights, but with the central instruments of international human rights law to which Europe and America claim adherence. Yet Europe's interpretation of free expression has diverged markedly from America's broad deference to First Amendment freedoms of speech, assembly and religion.

American courts have upheld the publication of false, even racist materials, the right of neo-Nazis to rally in Jewish neighborhoods, and the objections of some citizens to the Pledge of Allegiance and to school dress codes on religious grounds.

European governments, on the other hand, have consistently trampled analogous rights, outlawing publication of hate speech, trade in Nazi paraphernalia, and the wearing of distinctive religious clothing, to name but a few recent examples.

According to the Austrian court that convicted him on Monday, David Irving's offense was to have "denied, grossly played down, approved, or tried to excuse" the Holocaust in print or other media, in violation of a 1992 statute. Although he has not been tried at home in Britain, Irving was convicted and fined in Germany in 1995 for "inciting race hatred."

At best, Irving is a monumentally terrible historian, who, only after publishing dozens of books on World War II, read the notes of the Holocaust mastermind Adolf Eichmann and came around to admitting that the Nazi genocide might actually have occurred. At worst, he is an artless but unrepentant bigot, on the model of America's David Duke or Austria's own Jörg Haider, but without any independent political power.

Why, then, is Irving's Holocaust denial, like other minority and extremist views in European society, of such great concern to lawmakers? If European governments want to guard against the repetition of genocide, they should actively educate their citizens in tolerance and respect for different cultures and beliefs, not gag those who express conflicting ideas.

Europe's suppression of free speech is guaranteed to spawn and incubate precisely the kind of bigotry and sectarian violence it is intended to prevent. Hounded for the unthinkable crime of publishing false history, David Irving appears almost heroic as he stands up to censorship, fines and imprisonment, making him a kind of martyr for neo-fascist groups.

Likewise, suppression of young Muslims' rights to dress or worship as their religion requires lends government sanction to already widespread anti- Muslim attitudes. This official xenophobia in turn breeds simmering resentment that has already exploded into mass violence and been manipulated by radical Islamists to recruit willing terrorist agents from within European society.

While European leaders should be praised for their belated conversion to the cause of free speech, outraged Muslims around the world are right to allege a double standard. Until Europe consistently respects its own guarantees of free expression, and actively promotes tolerance instead of clumsily stifling dissent, its brave rhetoric will ring disappointingly false.

His Excellency Sir David Manning, British Ambassador to the United States, delivered the 2006 Frank E. and Arthur W. Payne Distinguished Lecture: "Energy: A Burning Issue for Foreign Policy," on Monday, March 13, 2006 at 4:30 p.m. in the Bechtel Conference Center at Encina Hall.

Sir David Manning has been Her Majesty's Ambassador to the United States of America since September 2, 2003.

Sir David Manning's Biography:

2003 - present: Washington, USA (Ambassador)

2001 - 2003: Foreign Policy Adviser to the Prime Minister

2001: UK Delegation NATO Brussels (Ambassador)

1998 - 2000: Foreign and Commonwealth Office (Deputy Under-Secretary)

1995 - 1998: Tel Aviv, Israel (Ambassador)

1994 - 1995: Foreign and Commonwealth Office (Head of Policy Planning Staff)

1994:UK member of Contact Group on Bosnia (International Conference on Former Yugoslavia)

1993 - 1994: Foreign and Commonwealth Office (Head of Eastern Department)

1990 - 1993: Moscow, Russia (Counselor, Head of Political Department)

1988 - 1990: Counselor on loan to Cabinet Office

1984 - 1988: Paris, France (1st Secretary)

1982 - 1984: Foreign and Commonwealth Office (Deputy Head of Policy Planning Staff)

1980 - 1982: Foreign and Commonwealth Office (Soviet Department, later Eastern Department)

1977 - 1980: New Delhi, India (2nd later 1st Secretary)

1974 - 1977: Warsaw, Poland (3rd later 2nd Secretary)

1972 - 1974: Foreign and Commonwealth Office (Mexico/Central America Department)

1972: Entered Foreign and Commonwealth Office