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.

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.

Congress will soon hold hearings on the National Security Agency's domestic spying program, secretly authorized by President Bush in 2002. But that program is just the tip of the iceberg.

Since 9/11, the expansion of efforts to gather and analyze information on U.S. citizens is nothing short of staggering. The government collects vast troves of data, including consumer credit histories and medical and travel records. Databases track Americans' networks of friends, family and associates, not just to identify who is a terrorist but to try to predict who might become one.

Remember Total Information Awareness, retired Adm. John Poindexter's effort to harness all government and commercial databases to preempt national security threats? The idea was that disparate, seemingly mundane behaviors can reveal criminal intent when viewed together. More disturbing, it assumed that deviance from social norms can be an early indicator of terrorism. Congress killed that program in 2003, but according to the Associated Press, many related projects continued.

The Defense Advanced Research Projects Agency runs a data-mining program called Evidence Extraction and Link Discovery, which connects pieces of information from vast amounts of data sources. The Defense Intelligence Agency trawls intelligence records and the Internet to identify Americans connected to foreign terrorists. The CIA reportedly runs Quantum Leap, which gathers personal information on individuals from private and public sources. In 2002, Congress authorized $500 million for the Homeland Security Department to develop "data mining and other advanced analytical tools." In 2004, the General Accounting Office surveyed 128 federal departments and agencies to determine the extent of data mining. It found 199 operations, 14 of which related to counterterrorism.

What type of information could these mine? Your tax, education, vehicle, criminal and welfare records for starters. But also other digital data, such as your travel, medical and insurance records--and DNA tests. Section 505 of the Patriot Act (innocuously titled "Miscellaneous National Security Authorities") extends the type of information the government can obtain without a warrant to include credit card records, bank account numbers and information on Internet use.

Your checking account may tell which charities or political causes you support. Your credit card statements show where you shop, and your supermarket frequent-buyer-card records may indicate whether you keep kosher or follow an Islamic halal diet. Internet searches record your interests, down to what, exactly, you read. Faith forums or chat rooms offer a window into your thoughts and beliefs. E-mail and telephone conversations contain intimate details of your life.

A University of Illinois study found that in the 12 months following 9/11, federal agents made at least 545 visits to libraries to obtain information about patrons. This isn't just data surveillance. It's psychological surveillance.

Many Americans might approve of data mining to find terrorists. But not all of the inquiries necessarily relate to terrorism. The Patriot Act allows law enforcement officers to get "sneak and peek" warrants to search a home for any suspected crime--and to wait months or even years to tell the owner they were there. Last July, the Justice Department told the House Judiciary Committee that only 12% of the 153 "sneak and peek" warrants it received were related to terrorism investigations.

The FBI has used Patriot Act powers to break into a judge's chambers and to procure records from medical clinics. Documents obtained by the American Civil Liberties Union recently revealed that the FBI used other new powers to eavesdrop on environmental, political and religious organizations.

When Congress looks into domestic spying in the "war on terror," it should ask a series of questions:

First, what information, exactly, is being collected? Are other programs besides the president's NSA initiative ignoring traditional warrant requirements? Are federal agencies dodging weak privacy laws by outsourcing the job to private contractors?

Second, who has access to the data once it is collected, and what legal restrictions are set on how it can be used or shared?

Third, who authorized data mining, and is its use restricted to identifying terrorists?

Fourth, what is the collective effect of these programs on citizens' rights? Privacy certainly suffers, but as individuals begin to feel inhibited in what they say and do, free speech and freedom of assembly also erode.

Fifth, how do these data collection and mining operations deal with error? As anyone who's tried to dispute an erroneous credit report can attest, once computer networks exchange data, it may be difficult to verify its accuracy or where it entered the system. Citizens who do not know they are under surveillance cannot challenge inaccurate information that may become part of their secret digital dossier.

What will Congress do to ensure that the innocent remain so?

In today's increasingly interconnected world, weak and failed states pose an acute risk to U.S. and global security. Indeed, they present one of the most important foreign policy challenges of the contemporary era. States are most vulnerable to collapse in the time immediately before, during, and after conflict. When chaos prevails, terrorism, narcotics trade, weapons proliferation, and other forms of organized crime can flourish. Left in dire straits, subject to depredation, and denied access to basic services, people become susceptible to the exhortations of demagogues and hatemongers. It was in such circumstances that in 2001 one of the poorest countries in the world, Afghanistan, became the base for the deadliest attack ever on the U.S. homeland, graphically and tragically illustrating that the problems of other countries often do not affect them alone.