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.

Divorce proceedings bring out the worst in people. When Abdul Rahman tried to get custody of his daughters in Kabul, Afghanistan, his wife's family told the court that he was unfit to care for his children because he had converted from Islam to Christianity some 16 years ago. A zealous prosecutor, hearing of the case, charged Mr. Rahman with apostasy, a crime punishable by death under some interpretations of Islamic law. If Mr. Rahman does not repudiate Christianity, the judge in the case has said, he will get the death penalty.

Mr. Rahman's case is a discouraging illustration of the uneasy balance between the democratic norms Afghanistan's Constitution enshrines and the conservative Islamic values its judiciary upholds. On the one hand, the Afghan Constitution states that "followers of other religions are free to exercise their faith and perform their religious rites within the limits of the provisions of the law," and it requires the state to adhere to the Universal Declaration of Human Rights, which clearly protects freedom of conscience and the right to change one's religion.

On the other hand, the Constitution also says that no law can be "contrary to the beliefs and provisions of Islam," and it gives judges broad power to interpret and apply Islamic law. Several schools of Islam do indeed prescribe the ultimate punishment for those who abandon the faith. And so Mr. Rahman's case may well come down to the interpretive leanings of the court.

Moderate Islamic jurists in some countries have attempted to balance or reconcile these often-conflicting interests. In Egypt, for instance, the Islamic Research Center decreed that although apostasy may be a crime, the time period for redemption is limitless - in other words, it is up to the individual, not the state, to adhere to divine will. The former chief justice of Pakistan, which has explicit anti-blasphemy laws, has written that the death penalty for apostasy is not required by the Koran and conflicts with other Islamic values.

Afghanistan's post-Taliban judiciary, however, has shown a propensity to use Islam as a political weapon. The country's chief justice, Fazil Hadi Shinwari, is a hard-line conservative associated with the Islamist parties of Abdul Rasul Sayyaf and Burhanuddin Rabbani. He has used the court as a bully-pulpit, issuing fatwas on a variety of issues outside his jurisdiction.

For instance, under Justice Shinwari's leadership the Supreme Court has variously attempted to ban co-education; tried to eliminate a rival to President Hamid Karzai from the 2004 elections; and jailed newspaper editors, all in the name of Islam.

In other words, the court has overstepped its bounds and contributed to the radicalization of Afghan politics in the process. To further his aims, Justice Shinwari has packed the lower courts with judges who have Islamic educations but no foundation in Afghan law or experience in the judiciary.

President Karzai has a unique opportunity to change this. Under the Constitution, Mr. Karzai must appoint a new Supreme Court this month, and he sent his slate of nine justices to Parliament for approval last week. Although the current chief justice has retained his position, there are some very promising choices among the eight other justices. They include known moderates, like the former chairman of the Judicial Reform Commission, Bahauddin Baha, and the deputy minister of justice, Qasim Hashimzai, who led a major corruption investigation involving members of President Karzai's cabinet.

These appointments mark President Karzai's first opportunity to compose Afghanistan's Supreme Court under a fully constitutional government. They are of momentous importance to the country's stabilization and the consolidation of its nascent democracy.

By creating a competent, professional and moderate judiciary, President Karzai will help to establish the rule of law. If, however, the court remains in the thrall of ideology and factionalism, Afghanistan's experiment in democracy will be compromised.

But the new judges will be powerless to reform the system unless they are given the political support and resources to do so. International involvement in Afghanistan's justice sector since 2001 has been inadequate. Both the Afghan government and its donors need a strategic vision for the judiciary's future and the political focus to make it a reality.

The new judiciary will need support to review the qualifications of the lower court judges, facilities to train new judges and functioning courthouses in the provinces. It will need to be able to share information, laws and legal decisions among officials throughout the country and to pay judges a living wage.

We must do more than simply react loudly to the most extreme cases, like that of Mr. Rahman. Instead, we must partner with the Afghans and other democratic governments in the Islamic world as they struggle to promote modernity and the rule of law. This means working with judicial systems on less controversial, bread-and-butter issues like criminal law and property disputes.

We have seen throughout the world, and in our own history, that competent and independent judges will stand up for the rule of law even when their decisions indict the powerful and defend the unpopular. Mr. Rahman's case should remind us of how important it is to help Afghanistan develop such judges if we want its democracy to succeed.

Before attacking Iraq in March 2003, the United States told the world that Saddam Hussein had reconstituted his nuclear weapons program in defiance of the United Nations. That claim, used to justify the war, was based on assessments provided by the United States intelligence community. But as everyone now knows, those assessments were wrong. So Jeffrey T. Richelson's history of American nuclear intelligence, including our attempts to learn about Iraq's nuclear program, could hardly be more timely.

In "Spying on the Bomb," Richelson, the author of several books on American intelligence, has brought together a huge amount of information about Washington's efforts to track the nuclear weapons projects of other countries. He examines the nuclear projects of Nazi Germany, the Soviet Union, China, France, Israel, India, South Africa, Taiwan, Libya, Pakistan, Iran and North Korea, as well as Iraq. Through interviews and declassified documents as well as secondary works, he sets out briefly what we currently know about those projects and compares that with assessments of the time.

This may sound like heavy going, but Richelson writes with admirable clarity. And along the way he has fascinating stories to tell: about plans to assassinate the German physicist Werner Heisenberg during World War II; about discussions in the Kennedy and Johnson administrations on the possibility of attacking Chinese nuclear installations; about Indian measures to evade the gaze of American reconnaissance satellites; and about the bureaucratic infighting over the estimates on Iraq.

The United States has put an enormous effort into gathering information about the nuclear projects of other countries. After World War II it equipped aircraft with special filters to pick up radioactive debris from nuclear tests for isotopic analysis. It created a network of stations around the world to register the seismic effects of nuclear explosions. Most important, in 1960 it began to launch reconnaissance satellites that could take detailed photographs of nuclear sites in the Soviet Union and China. Richelson occasionally speculates about the role of communications intercepts and of spies, but these appear from his account to have been much less important than the other methods of collecting information.

Through these means the United States has gathered a vast quantity of data, sometimes to surprising effect. Intelligence played a crucial role in the cold war, for instance, by reducing uncertainty about Soviet nuclear forces. Alongside such successes, however, there have been failures. One notable example concerned the first Soviet test, which took place in August 1949, much sooner than the C.I.A. had predicted. Another was the failure to detect Indian preparations for tests in May 1998, even though at an earlier time the United States, with the help of satellite intelligence, had managed to learn about preparations the Indians were making and to head off their tests.

But the most serious failure of all was in Iraq in 2003, because in no other case did the intelligence assessments serve as justification for the use of military force. The information needed for avoiding political surprise is one thing. That needed for preventive war is quite another, if only because of the consequences of making a mistake.

Beyond making the uncontroversial recommendation that "aggressive and inventive intelligence collection and analysis" should continue, Richelson draws no general conclusions. That is a pity, because his rich material points to issues that cry out for further analysis. He suggests in one or two cases that failures sprang from the mind-set of the intelligence community, but he does not elaborate on this point. He has little to say about relations between policy makers and the intelligence community, even though the quality of intelligence and the use made of it depend heavily on that relationship.

His focus is no less narrow in his discussion of foreign nuclear projects. He concentrates on the programs themselves, paying very little attention to their political context. Does that reflect a technological bias in nuclear intelligence? Would, for example, the prewar assessment of Iraqi nuclear capabilities have been more accurate if it had paid more attention to the broader political and economic circumstances of Hussein's regime?

The task of intelligence has become more complex than it was during the cold war. A single dominant nuclear opponent has now been replaced by a number of nuclear states, along with states and stateless terrorists that are aiming to get their hands on nuclear weapons. Meanwhile, the technology needed for producing nuclear weapons has become easier to acquire.

Many critics believe the recent performance of the intelligence community shows it has not responded adequately to this new situation. Richelson does not have much to say on this question; nor does he discuss the likely impact of the current reforms, initiated in response to the Iraq war, on the quality of intelligence. His reticence may imply that he does not think reform is necessary. Still, it is disappointing that he does not draw on his historical survey to discuss whether new approaches are needed for dealing with nuclear threats, and, if so, what those new approaches might be.

Stanford, California - If the deal to supply India with nuclear technologies goes through, future generations may remember it for quite different reasons than the debate over nuclear proliferation.

Nuclear power emits no carbon dioxide, the leading cause of global warming. And India, like most developing countries, has not been anxious to spend money to control its emissions of this and other so- called greenhouse gases.

India is embracing nuclear power for other reasons - because it can help the country solve its chronic failure to supply the electricity needed for a burgeoning economy. But in effect, the deal would marry their interest in power with ours in protecting the planet.

India is growing rapidly. In recent years its economy has swelled at more than 7 percent per year, and many analysts believe it is poised to grow even faster in the coming decade.

The economic growth is feeding a voracious appetite for electricity that India's bankrupt utilities are unable to satisfy. Blackouts are commonplace. Farmers, who account for about two-fifths of all the power consumed, can barely rely on getting power for half of every day. In industrial zones, the lifeblood of India's vibrant economy, unstable power supplies are such trouble that the biggest companies usually build their own power plants.

So most analysts expect that the demand for electricity will rise at about 10 percent a year. (For comparison, U.S. power demand notches up at just 2 percent annually.)

Over the past decade, about one third of India's new power supplies came from natural gas and hydro electricity. Both those sources have been good news for global warming - natural gas is the least carbon- intensive of all the fossil fuels, and most of India's hydroelectric dams probably emit almost no greenhouse gases.

However, the bloom is coming off those greenhouse-friendly roses. New supplies of natural gas cost about twice what Indians are used to paying, and environmental objections are likely to scupper the government's grand plans for new hydro dams.

That leaves coal - the most carbon-intensive of all fossil fuels. Already more than half of India's new power supplies come from coal, and that could grow rapidly.

Traditionally, the coal sector was plagued by inefficiencies. State coal mines were notoriously dangerous and inefficient. Coal-fired plants in western provinces, far from the coal fields and vulnerable to the dysfunctional rail network, often came within days of shutting operations due to lack of coal.

All that is changing. Private and highly efficient coal mines are grabbing growing shares of the coal market. Upgrades to the nation's high-tension power grid is making it feasible to generate electricity with new plants installed right at the coal mines.

These improvements make coal the fuel to beat.

So the deal struck with President George W. Bush matters. At the moment, India has just 3 gigawatts of nuclear plants connected to the grid. Government planners envision that nuclear supply will grow to 30 GW over the next generation, but that will remain a fantasy without access to advanced nuclear technologies and, especially, nuclear fuels - such as those offered under the deal with the Bush administration.

By 2020, even after discounting for the government's normal exuberance in its forecasts, a fresh start for nuclear power could increase nuclear generating capacity nearly ten-fold.

By displacing coal, that would avoid about 130 million tons of carbon dioxide per year (for comparison, the full range of emission cuts planned by the European Union under the Kyoto Protocol will total just 200 million tons per year).

The effort, if successful, would eclipse the scheme under the Kyoto Protocol, known as the Clean Development Mechanism, that was designed to reward developing countries that implement projects to reduce their emissions of greenhouse gases. The largest 100 of these CDM projects, in total, won't reduce emissions as much as a successful effort to help India embrace safe nuclear power.

The benefits in slowing global warming are not enough to make the deal a winner. Care is needed to tame the risks of proliferation, especially those connected from India's system of breeder reactors that make more weapons-capable fuel than they consume. And complementary efforts, led by Indians, are needed to fix the trouble in India's electricity sector that have so far discouraged private investors.

None of this will be easy. There are no silver bullets in cooling the greenhouse.

What is important is that the deal is not just a one-off venture, as the administration's backers, on the defensive, have suggested. It could frame a new approach to technology sharing and managing a more proliferation proof fuel cycle that, in turn, will multiply the benefits of a cooler climate.

Coal-rich China is among the many other countries that would welcome more nuclear power and whose emissions of carbon dioxide are growing fast - even faster than India's.

Quite accidentally, it seems, the Bush administration has stumbled on part of an effective strategy to slow global warming. Now it should marry that clever scheme overseas with an effective plan here at home.