Does the conflict in Iraq amount to a civil war? In many ways, the public debate over this question is largely political. Calling Iraq a "civil war" implies yet another failure for the Bush administration and adds force to the question of whether U.S. troops still have a constructive role to play.

Politics aside, however, the definition of civil war is not arbitrary. For some -- and perhaps especially Americans -- the term brings to mind all-out historical conflicts along the lines of the U.S. or Spanish civil wars. According to this notion, there will not be civil war in Iraq until we see mass mobilization of sectarian communities behind more or less conventional armies.

But a more standard definition is common today:

1) Civil war refers to a violent conflict between organized groups within a country that are fighting over control of the government, one side's separatist goals, or some divisive government policy.

By this measure, the war in Iraq has been a civil war not simply since the escalation of internecine killings following the bombing of a Shiite shrine in Samarra in February, but at least since the United States handed over formal control to an interim Iraqi government in June 2004.

Here's why: Although the insurgents target the U.S. military, they are also fighting the Shiite-dominated Iraqi government and killing large numbers of Iraqis. There is little reason to believe that if the United States were suddenly to withdraw its forces, they would not continue their battle to control or shape the government.

Political scientists who study civil war have proposed various refinements to this rough definition to deal with borderline cases. One issue concerns how much killing has to occur -- and at what rate.

2) For a conflict to qualify as a civil war, most academics use the threshold of 1,000 dead, which leads to the inclusion of a good number of low-intensity rural insurgencies.

Current estimates suggest that more than 25,000 Iraqis have been killed in fighting since the U.S.-led invasion in March 2003 -- a level and rate of killing that is comparable to numerous other conflicts that are commonly described as civil wars, such as those in Lebanon (1975-1990) and Sri Lanka (beginning in 1983).

The organization -- or rather, disorganization -- of the warring communities in Iraq means that a large-scale conventional conflict along the lines of the U.S. Civil War is unlikely to develop. More probable is a gradual escalation of the current "dirty war" between neighborhood militias that have loose ties to national political factions and are fighting almost as much within sectarian lines as across them.

This is roughly what happened in Lebanon and at a lower level in Turkish cities in the late 1970s. Ethnic cleansing will occur not as a systematic, centrally directed campaign (as in Bosnia), but as a result of people moving to escape danger.

And there's another twist to the terminology:

3) If the conflict in Iraq becomes purely a matter of violence between Sunni and Shiite communities driven by revenge and hatred rather than by political goals, many political scientists would say that it is something other than civil war.

Almost no one, for example, calls the Hindu-Muslim violence in India a civil war.

A civil war has to involve attempts to grab power at the center of government or in a given region, or to use violence to change some major government policy.

In Iraq's case, however, the vacuum of power at the center means that communal violence will inevitably be tied to struggles for political power and control.

A final complication concerns the nature of international involvement. Some argue, for example, that the war in Bosnia should be seen as an interstate war rather than a civil war, since the Bosnian Serb forces were armed and directed largely by Belgrade. Post-Mobutu violence in Congo is often termed a civil war, even though fighters have been closely tied to armies from neighboring states.

4) A conflict may be both a civil and an interstate war at the same time.

The Vietnam War, for instance, clearly comprised both a civil war in the South and an interstate war involving the North, the South and the United States.

Iraq may be moving in this direction. The United States and Britain are already openly involved, and such neighboring countries as Iran and Syria are more covertly involved. Not that it matters to the people dying there, but the next debate here may turn on whether what is already a civil war in Iraq should be viewed as an interstate war as well.

The Middle East seems to occupy all the attention of our foreign-policymakers these days. But there are other parts of this globe that are probably more important, and potentially no less dangerous.

One of these is the Taiwan Strait. That narrow passage of water separates China from Taiwan, in Chinese minds a renegade province that must eventually be returned to its control.

The Chinese communist leadership dreads the prospect that Taiwan's democratically elected government might make the island's de facto independence a legal reality. China's heated military buildup in recent years is largely focused on creating the muscle to intimidate Taiwan and to seize the island if that fails.

A war across the Taiwan Strait makes the American top-five list of security dangers. The U.S. commitment to defend Taiwan is ambiguous, but it is not hard to imagine us being drawn into a conflict. And a war in the strait could easily expand to include Japan.

That is why the mayor of Taipei, Taiwan's capital city, got such a rousing welcome last week in Washington. Ma Ying-Jeou, or Mayor Ma as he is popularly known, does not threaten to upset the apple cart of cross-strait relations by pushing Chinese buttons with talk of independence, as the Taiwanese government loves to do.

Sitting down with Ma for breakfast as he made his way home to Taiwan, I could see why he was received with open arms at senior levels of the Bush administration. Ma, the leader of the opposition Kuomintang (KMT) party, is the front-runner in polls to win the 2008 presidential elections. He is articulate, a Harvard Law School graduate with movie-star looks and a reassuring message for Americans.

"We support maintenance of the status quo, which is also U.S. policy,'' he told me.

A KMT-led government would not waver from the "Five Nos,'' a pledge made by President Chen Shui-bian not to take steps toward a declaration of independence. He offers in addition a program of ``Five Dos'' should it return to power.

First, the KMT hopes to resume negotiations with the mainland, based on a 1992 agreement that while there is one China, there are different interpretations of what that means. Second, it will try to reach a peace agreement, lasting from 30 to 50 years. Third, the KMT would expand the already massive economic ties between Taiwan and the mainland into a possible cross-strait common market. Fourth, the KMT would try to create a formula to allow Taiwan to participate in international affairs, including global organizations, short of being an independent state. Last, it would expand cross-strait cultural and education exchanges.

Ma downplays the threat from Beijing these days. "Their goal is no trouble,'' he told me. "They are not interested in unification right now.'' But, he said, the Chinese do worry about "the further drifting away of Taiwan.'' That drift, he fears, could inadvertently force a conflict that might drag in the United States.

That charge is aimed at the government in Taipei. And it is a concern shared by U.S. officials who are visibly unhappy these days with Chen. The warm reception for Ma was intended to send that message to Taipei -- and also to Beijing, ahead of the visit next month of Chinese leader Hu Jintao.

Reassuring as Ma's words may be, there are reasons to be cautious about his message and his prospects.

Taiwanese nationalism may rattle the status quo, but so does China's military buildup. As does the failure of Taiwan to adopt a significant U.S. defense package, offered five years ago, to counter that buildup. The KMT blames the current government for this impasse but the party, which now controls the legislature, has blocked passage of the budget.

Deepening economic ties with China are a market reality, as Taiwan's electronics industry shifts production to low-wage China. But ultimately that could make them another Hong Kong, a satellite of Beijing that must bend to its political will.

Taiwanese are deeply divided. The KMT, the party of mainlanders who fled to the island after the communist victory in 1949, ruled Taiwan for decades as the exiled government of China. But democracy, which came in the 1990s, brought to power native Taiwanese who want to preserve their separate identity.

Ma may prove to be a political leader who plays better in Washington than back home. But if Taiwanese embrace his vision of the status quo at the ballot box, all the better. Ultimately, his mandate must come from Taiwanese, not Americans.

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.