In an age where you need to be numerate to do almost anything else (from building bridges to conquering disease), governments anxiously compare their performance in mathematics with that of competitor nations. This month a new cry of alarm came from America, where a National Mathematics Advisory Panel, established by George Bush in 2006, reported that “without substantial and sustained changes” the country was doomed to “relinquish its leadership” in the world of numbers as the century wears on.
America has long masked its difficulty in educating enough mathematicians by importing lots of ready-made talent, especially from East Asia and the former Soviet Union. But the problems are real enough. As the panel noted, the share of American students doing degrees in maths or related areas fell from 32% in 1994-95 to 27% in 2003-04. And the share of maths-related doctorates at American universities that went to American citizens or residents fell over the past four decades from 80% of the total to less than 60%. The panel concluded that America's problems become apparent when students start to study algebra—for most, their first encounter with genuinely abstract thinking.
The Economist reports on scarcity in native mathematicians in the US.
From an economic point of view, gearing up the American educational system to produce more capable mathematicians might be far more expensive than simply offering fast-track visas to mathematicians of proven ability who have had the bad luck to be born in countries with nasty political systems (I say 'nasty'; OK, 'nastiER'), underfunded universities, poor infrastructure, a scarcity of malls, fast-food outlets, first-class orchestras - WHATEVER it is that makes one place look less appealing than another to a mathematician of proven ability.
From a nationalistic point of view, um, isn't there something a bit fishy about this soul-searching? 'We're not producing enough second-generation, third-generation, fourth-generation, fifth-generation, n+1th-generation American mathematicians!!!!! We've had to fall back on first-generation Americans!!!!!!! The country is doomed!!!!!!!' If a State of Emergency has been declared because we are not producing enough Cherokee, Navajo, and other certifiably aboriginal American mathematicians, it has passed without comment by the Economist. Fact is, it's a country of immigrants. Today's Chinese math whiz, freed from the one-child-family rule, is tomorrow's parent of a gaggle of Chinese-Americans, some of whom may be math whizzes, all of whom will be American.
The real objection to America's poor showing in mathematical education is not a matter of economics, it's a matter of human rights. For reasons that are never entirely clear to me, religious beliefs, however loopy, are generally treated with respect even by those who don't share them. Mathematicians, however, are drawn to something that has no church and no tax-exemptions: a world outside this world of accidents, waiting to be discovered, a world of beauty, elegance and wit. Because of the strongly utilitarian bent of our educational system, because of the assumption that EVERYONE, regardless of aptitude or inclination, must achieve a certain level of competence, those drawn to mathematics are often forced to study it in a social group consisting primarily of contemporaries who regard it with unqualified loathing. We don't require Jews to study the Talmud in a class of bored, resentful Christians; we don't require Muslims to study the Qur'an in a class of bored, resentful Jews; we don't require Christians to study the Gospel in a class where they are outnumbered by Jews and Muslims 10 to 1. We do throw young mathematicans to the, ahem, unenlightened, with the result that too many end up unqualified to engage with those who should have been their peers.
A few years ago I gatecrashed a class on partial integration given by a Chinese lecturer at Columbia; the thing that stays with me is the wit he brought to the business of converting the seemingly unintegrable to something more tractable. If every American schoolchild could be taught by someone with his gifts we could count ourselves lucky.
