The Brazilian government is declaring victory in its decades-long struggle to become self-sufficient in the supply of oil. The milestone is cause for celebration in a country that has long paid a high price for imported energy.

It will also reverberate here in the United States where policy-makers, too, are trying to wean the nation from costly imports, jittery markets and the foreign spigot. But we must learn the right lessons. Brazil's success came not from treating oil as an addiction but by producing even more of the stuff and by becoming even more dependent on world markets

Here in the United States, most attention to Brazil's fuel supply has focused on the country's aggressive program to replace oil with ethanol that is made by fermenting homegrown sugar. American newspapers are filled with stories about Brazil's famous "flex fuel" vehicles that make it easy to switch between ethanol and conventional gasoline.

Guided partly by Brazil's apparent success, American policy-makers are crafting new mandates for ethanol, and flex fuel vehicles are now taking shape. We have the impression that ethanol is king.

In reality, ethanol is a minor player in Brazilian energy supply. It accounts for less than one-tenth of all the country's energy liquids.

The real source of Brazil's self-sufficiency is the country's extraordinary success in producing more oil. After the 1970s oil shocks, when Brazil's fuel import bill soared, the government pushed Petrobras, the state-controlled oil company, to look asunder for new energy sources.

Petrobras delivered, especially at home, where the firm pioneered the technologies that make it possible to extract oil locked in sediments under the seabed in extremely deep water. In the middle 1970s Brazil struggled to produce just 180,000 barrels of oil per day while importing four times that amount. Today it produces about 2 million and is self-sufficient. Indeed, the current milestone of self-sufficiency arrives with the inauguration of Brazil's newest deep water platform, the "P50." When P50 reaches its full output later this year, that one platform will deliver more liquid to Brazil than the country's entire ethanol program.

Brazil's self-sufficiency offers three lessons for U.S. energy policy:

-First is that ethanol, with current technology, will do little to sever our dependence on imported energy. Today's approach involves growing a crop - sugar in Brazil, corn in the United States - and then fermenting the fruits to yield fuel. Sugar plants in Brazil's climate are a lot more efficient at converting sunlight to biomass than is corn in the Midwest, but U.S. policy nonetheless favors corn (and imposes tariffs on imported sugar) because the program is really a scheme to deliver heartland votes rather than a commercially viable fuel.

Yet, even with Brazil's favorable climate and sugar's inviting biology, ethanol is already reaching the limit. That's because the land and other resources devoted to ethanol can be put to other uses such as growing food and cash crops.

Indeed, today the Brazilian government is actually reducing the share of ethanol that must be blended into gasoline because sugar growers prefer to make even more money by selling their product as sugar on the world market rather than fermenting it into alcohol.

New technologies - notably "cellulosic biomass"- could breathe fresh life into ethanol and replace still more oil. Cellulosic biomass is intriguing because it cuts costs by allowing the entire plant - the cellulose in the stalks, as well as the prized grain or sugar - to be fermented into fuel.

Advocates for this technology, including President Bush in his State of the Union address, have wrongly confused the sexy promise of this new-fangled approach to making ethanol with the practical realities of fuel markets. Schemes to produce cellulosic biomass, today, work only under special circumstances and nobody has delivered the fuel at the industrial scale that would be required for the technology to become commercially viable.

-Second, we should learn that, for now, the greatest force to loosen the world's oil markets lies with oil itself. We can use oil more efficiently, as would occur with a gasoline tax or wise fuel economy standards. But we can also find ways to produce more of the stuff - as Brazil did with Petrobras.

The problem for U.S. policy-makers is that the richest veins for new production lie mainly outside the United States and beyond our direct control.

Indeed, the Brazilian government made Petrobras more efficient by putting the firm partly beyond its control as well. When the government sold part of the company on international stock exchanges, it accepted Western accounting procedures and other strictures that have given Petrobras the autonomy and accountability to its shareholders that, in turn, helped make it an efficient company.

We have a stake in seeing other countries do the same - from Algeria to Mexico to Iran and even Russia. But we must remember that Brazil did this on its own, in response to internal pressures for reform, with little leverage from foreign governments.

-Third, we should learn from Brazil not to confuse the goal of greater self-sufficiency with the illusion of independence. Even as Brazil has become self-sufficient it has also, ironically, become more dependent on world markets. That's because the Brazilian government has wisely relaxed price controls so that the prices of fuels within the country are set to the world market. Thus Brazilians see real world prices when they fill up at the pump, and the decisions about which cars to buy and how much to drive reflect real costs and benefits of the fuel they consume. That is why, even as the country becomes self-sufficient, Brazilians are working ever harder to be more frugal with oil - because the price at the pump is high and rising.

Dependence on oil is a liability that must be managed. But it is not an addiction.

Efficiency, sober policies toward modest alternatives such as ethanol, and more production - all tools of the manager, not the addict - are required. Brazil helps show the way, but only if we learn the right lessons.

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.

A recent report from Duke University that critiques the supposed gap between the number of American science and engineering (S&E) graduates and those of merging economies -- especially China's -- has led to false reassurance that the U.S. lead in science and technology is not under threat from China. It would be a grave mistake to drop our concerns about China's competitive challenge.

First, the Duke report simply claimed that China's true number of science and engineering bachelor degrees was 351,000, rather than the widely reported 600,000. Coupling this with an upward adjustment for American graduates still left China producing 214,000 more such degrees than the United States.

Moreover, undergraduates are only part of the concern. China's production of those with doctorates has increased rapidly. By 2003, China's homegrown science and engineering doctorates numbered almost half of the U.S. total.

Chinese were also earning large numbers of doctorates abroad. In 2001, the number of Chinese S&E doctorates earned in Japan, the United Kingdom and the United States equaled 72 percent of the total of S&E doctorates earned by American citizens and permanent residents.

Since 1975, China has increased its global share of S&E doctorates from zero (courtesy of the Cultural Revolution) to 11 percent, not counting doctorates earned overseas. During the same three decades, the U.S. global share has fallen from half to roughly 22 percent.

More worrisome than the aggregate numbers is American universities' reliance on foreigners who earn doctorates. In engineering, foreigners account for over half of America's doctorates, and in computer science just under half.

If foreign-born holders of doctorates continued to stay in the United States, we wouldn't have to worry. Unfortunately, there are many signs that it is becoming much harder to retain them.

One need only look at the flow from Taiwan, one of the former main sources of American S&E doctoral degrees, to see what could happen. Up until 1994, Taiwanese earned more science and engineering doctorates in the United States than members of any other foreign nationality. By 2000, their numbers had plummeted because economic and educational opportunities at home were more appealing.

The Taiwanese didn't just stop coming to America. They also began to leave. As Taiwan's tech sector boomed in the 1990s, huge numbers of Taiwanese technologists (estimates range as high as 100,000) left America for home and took their technical skills with them.

Our two current biggest foreign sources of technologists, China and India, appear to be following Taiwan's path. China has begun to lure back large numbers of technologists. China's central and local governments offer free office space and other benefits to attract technologists home. These inducements are working. A 2005 survey of the Chinese American Semiconductor Professionals Association's members showed that the vast majority regard China as the most likely future work destination, and they rated Shanghai higher than even Silicon Valley on career potential. India's recruitment efforts have also started to bear fruit.

The challenge is not simply keeping up the numbers of technologists in America. China by many measures has improved its technological capabilities. On the Georgia Institute of Technology's Index of Technological Capability, China has more than doubled its index score over the past decade. China now ranks fourth behind the United States, Japan and Germany.

This rapid ascent is not surprising given China's increasing investments. China's research and development spending as a percentage of gross domestic product has tripled to 1.3 percent in the last decade, even while its GDP has ballooned. Few emerging economies spend even 1 percent of their GDP on research.

U.S. patents invented in China are also on the rise. Information-technology patents from corporations' Chinese technologists have risen from 134 in 1997-2001 to 482 during 2002-04. As a first step to meet this challenge, we should increase federal spending on basic and exploratory research. Our R&D spending has been flat at 2.6 percent of GDP for four decades, but the share of federal spending has declined from two-thirds to one-quarter.

Given that corporations now de-emphasize basic scientific research, the federal government should further support the basic research that could maintain our lead at the cutting edge of technology.

Increased federal funding would also address the issue of the falling share of investment in certain disciplines. With spending flat, the rising share commanded by biomedicine has meant a falling share spent on engineering and physics.

Federal support may also play a direct role in increasing interest in pursuing a science education. Since the 1950s, the number of undergraduate S&E majors in America has risen and fallen in line with federal research funding, as Professor Henry Rowen of Stanford University has pointed out.

Before meeting China's challenge, we first must recognize it. Complacency in reaction to "good'' news that China is producing fewer S&E graduates than commonly thought is not the answer.

Three months ago the Russian energy giant Gazprom forced Ukraine to pay sharply higher prices for natural gas. At the time, the story was portrayed as a political struggle for control in Kiev. But last week Gazprom announced it was tripling gas prices in Belarus, a country that is politically close to the Kremlin. Moldova has been forced to accept a doubling of prices over the next three to four years, and the other former Soviet republics are already paying market prices for Russian gas.

The truth is that these price increases are not political. Rather, they reflect worrisome economic and geological facts about Russian gas fields. The Kremlin is not simply trying to use Gazprom to reassert authority in Belarus, Ukraine or anywhere else. There are in fact deep problems with Gazprom -- problems created by its inefficient management and a looming decline in gas production.

Russia controls over a quarter of the world's gas reserves -- more than any other country. Most of the known Russian reserves (about 80 percent) are in west Siberia and concentrated in a handful of giant and super-giant gas fields. Since the early 1970s the rate of discovery for these new fields has been declining. Moreover, output from the country's mainstay super-giant fields is also steadily falling.

Huge investments are needed to replace this dwindling supply, and all the options for new production will prove costly and difficult. New fields in the far north and east of the country are distant from most of Russia's people and export markets, requiring wholly new transport systems such as pipelines. Moreover, most of these fields are found in extremely harsh environments where it is technically and financially difficult to operate.

Gazprom controls neither the capital nor the technology that will be needed. The state-controlled company is already deeply in debt and burdened by many expensive obligations, such as supplying Russia's population and friends with cheap gas. The company has to work with foreign partners.

So far Gazprom has been able to forestall crisis. Economic stagnation across the former Soviet Union and Eastern Europe since 1990 dampened gas demand. Russia, which had a surplus at the time, sharply increased its gas exports and made contractual commitments that will remain in force for many years.

But following the long stagnation, Russia's internal gas consumption is rising again as the economy expands. And new Russian policies to promote development of the country's eastern regions will, in the next few years, require large new commitments to supply gas to that region (along with spending on railroads, airports and other infrastructure).

Even when the Russian economy was in the doldrums the country was notable as a large gas consumer because of its extremely inefficient energy system. Today Russia is the world's second-largest gas user, after the United States, although its economy is only one-twentieth the size of the U.S. economy.

Electricity in Russia is produced for the most part by gas, but the country's gas-fired electric generators work at 33 percent efficiency on average, compared with 50 to 55 percent in Europe. More than 90 percent of residential and industrial gas consumers don't have meters. Gas is even cheaper than coal -- Russia is the only large country where that is true -- so incentives to switch to an abundant fuel are weak.

In recent years Russia has boosted gas supplies by squeezing Turkmenistan to sell gas to Russia at a deep discount. But Turkmen gas production is poised to decline, and Turkmenistan's gas industry is barely functional because the country's political environment is scary for long-term investors. Other Central Asian suppliers, notably Kazakhstan, are unlikely to be able to bridge the gap.

Caught between growing internal consumption of gas, continued inefficiency and mounting external obligations, Russia's gas industry faces a looming crisis. Given the country's vast resources, it seems that many producers could fill the void. But a series of policy decisions created two roadblocks that Gazprom has been happy to reinforce. One is the lack of access to the Gazprom-controlled pipeline network, which explains why few companies even bother to look for gas: They know they can't get what they find to market. The other barrier to investment is the low internal prices, which make gas production uneconomic except for companies that can sell their products outside.

Gazprom needs cash -- much more cash -- for investment. At the same time, it needs a strong incentive for former Soviet republics to cut their own very inefficient consumption.

Analysts have ignored the risk that Russia's supplies could fall short because they focus on Russia's vast gas resources and the new Western investors who are -- albeit cautiously -- entering into joint ventures with Gazprom. But those resources and ventures are for the long term, and the looming crisis of supply is unfolding now.

The gas shortage is likely to become most acute over the next few years. If there is an unusually cold winter in 2008, the year of Russia's presidential election, then Gazprom will face a politically unpleasant choice: whether to cut off internal customers (voters) or the Western customers who are the firm's main source of hard cash.

The writer is a research fellow at the Program on Energy and Sustainable Development at Stanford University. She is co-author of "Axis of Oil" and of a forthcoming comprehensive review of Russia's gas pipelines.

The fierce debate on immigration ignores a crucial reality -- what is happening to the United States is only one piece, although a big one, of a much larger global picture.

That hit me a couple of weeks ago when I was in Singapore. The Southeast Asian island nation has long been hailed as an economic model, the business capital for the entire region.

But it is an economy facing demographic peril. Its small population of 4 million is shrinking, thanks to a very low fertility rate. Prosperous Singaporean couples work hard, have fewer children and worry about how to take care of their aging parents. By 2050, Singapore will have a median age of over 52, one of the oldest in the world.

Singapore's answer is to import labor. A third of its workforce are migrants, from construction workers to maids. One out of seven households employs a domestic worker -- low-paid women mostly from neighboring Philippines and Indonesia.

Singapore tries to lure "talents'' -- highly skilled and affluent migrants -- to stay permanently. But the men hauling bricks and the maids washing laundry are in a separate class of temporary guest workers, with no chance to join Singaporean society. If a maid becomes pregnant, she is shipped out within seven days. Employers have to post bonds that must be paid should their servants break the rules and try to stay, putting them in the role of migrant police.

Problems of abuse of domestic workers, including physical and sexual violence and confinement, are serious enough to have prompted a report last December by Human Rights Watch.

Singapore's dependence on migrant labor and its guest-worker policy may be at the extreme end but it's very much on the global spectrum. Labor, like capital and goods before it, is part of a global market. The movement of people across borders in search of wages and work, most of it from developing countries to developed, is growing at a phenomenal pace.

The numbers are staggering. From 1980 to 2000, the number of migrants living in the developed world more than doubled from 48 million to 110 million. Migrants make up an average 12 percent of the workforce in high-income countries. About 4 million migrants cross borders illegally every year.

The demand for labor is driven in part by a demographic disaster -- the falling birth rates of developed countries. Almost all of those countries now have fertility rates that are well below 2.1, the level at which a population replaces itself. At the very low end are Hong Kong (0.94), Korea (1.22) and Singapore in Asia (1.24), along with much of Eastern Europe.

Low fertility means shrinking workforces and aging populations. Without migration, according to a recent study, Europe's population would have declined by 4.4 million from 1995 to 2000. Immigration accounted for 75 percent of U.S. population growth during the same period.

This movement of people cannot be stopped, certainly not by hundreds of miles of fences or even by tens of thousands of border guards. It is an issue that cries out for global cooperation, for common policies that cut across national boundaries. Already, we can benefit from looking at what has worked -- and not worked -- elsewhere.

A Global Commission on International Migration, formed in 2003 by the United Nations secretary-general, has taken an initial stab. Their report, issued last winter, supports the growth of guest-worker programs.

The Senate immigration bill now up for debate includes a provision for a guest-worker program. The bill is clearly preferable to the punitive and ineffective approach of the House version. But the Singapore experience -- and previous guest-worker programs like the German import of Turks -- should prompt second thoughts about going down this road.

One problem is that the guests don't leave. The United States has its own experience with this in the bracero program to import farmworkers, and more recently with the supposedly temporary H1-B visas used so extensively by the high-tech industry here in Silicon Valley.

Most troubling to me, these programs create an underclass of migrants who are never assimilated, as happened in Germany. It sets us on the Singapore road, encouraging inhumane policing mechanisms. And it is a gilded invitation to employers to depress the wages and incomes of American workers, and not just in the dirty jobs that are supposedly so hard to fill.

The United States has been rightfully proud of a tradition that treats all immigrants as citizens in the making. Rather than guest workers, isn't it more American to set realistic immigration quotas and enforce them fairly?

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.