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.

Analysis of the Indian-U.S. nuclear agreement, as well as substituting natural gas for coal in fueling the Chinese electricity sector, reveals that side agreements between developed and developing countries could result in massive greenhouse gas emission reductions.

As part of its ongoing series of "Studies of the Walter H. Shorenstein Asia-Pacific Research Center", Shorenstein APARC announces two major new titles on the Chinese Cultural Revolution and the genealogy, politics, and legacy of ethnic nationalism in Korea.

The first, The Chinese Cultural Revolution as History, edited by Joseph W. Esherick, Paul G. Pickowicz, and Andrew G. Walder, shows how the Cultural Revolution was experienced by ordinary Chinese at the base of urban and rural society. The second title, by Shorenstein APARC director Gi-Wook Shin, examines the blood-based notion of Korean identity that has come to override other forms of identity in the modern era.

Both books are available for purchase from the Stanford University Press website, through the links given below.

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.

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.