There's an old joke about the French: A guy gives a plan to a Frenchman. He looks at it, shakes his head and says, "Well, that probably works fine in practice, but how does it work in theory?"
It's a jab at France's deep-seated preference for the abstract over the concrete, which can make the French a bit frustrating to deal with if you're, say, trying to get a cup of coffee in a café or watching a French art-house film. But it makes them second to none if you're doing complex math or trading obscure financial instruments.
France, the birthplace of storied math geniuses like René Descartes and Evariste Galois, has long punched above its weight in the study of numbers. The steady stream of math students cranked out by French universities each year gives the country an edge among rich nations struggling to keep up with math-savvy emerging powers like China and India. Although most kids don't emerge from France's abstract-math education any better at number crunching than other Western students in the Organisation for Economic Co-operation and Development's Program for International Student Assessment, French students score little better than average at math the best of them are math killers. "It's something like what the Soviet system was for sports," says the Courant Institute's Ben Arous. In France 27% of college students earn a degree in math, science, technology or engineering, compared with only 17% in the U.S., according to the U.S.'s National Science Foundation. And French math whizzes dominate the lucrative business of quantitative finance, a field that accounts for roughly half of all financial trades and requires analysts well versed in advanced forms of calculus, probability and statistics. "When you go into any trading floor in the world, you hear people speaking French," says Michel Crouhy, head of quantitative research and development for Natixis, a French investment bank. France's 18 master's programs have grown to 500 to 600 graduates a year in what is known as financial engineering, up from about 300 a decade ago.
Crouhy started the first master of financial engineering program at Paris' Ecole des Hautes Etudes Commerciales in 1986. The Financial Times rated it No. 1 in finance in 2011, with another French business school, Essec, at No. 3. Many of Crouhy's students arrive from France's rigorous math-oriented grandes écoles, such as the Ecole Polytechnique and Ecole Nationale des Ponts et Chaussées. "I said, 'Look, we can't just hire M.B.A.s. They're not good enough at math.'"
According to Jean-Pierre Bourguignon, director of the Institut des Hautes Etudes Scientifiques, roughly a quarter of the world's high-level quants are French. "We're not terribly good at shopkeeping, but we're very good at models and paradigms," says a former derivatives trader at French banking giant BNP Paribas. "When you had open-outcry trading, the world belonged to the truck drivers of finance. Now you've got algorithms and models. I'm trying to be Cartesian about the world."
Cartesian meaning dispassionate, logical and unsentimental is the adjective the French believe expresses their deepest selves. It is derived from Descartes, the 17th century French philosopher and mathematician widely known for the exceedingly Gallic proposition "I think, therefore I am." It was Descartes who first applied the abstract rules of algebra to physical shapes. The result was analytic geometry.
In the centuries since, France has developed a powerful math tradition and a fearsome teaching apparatus that has made its mathematicians, pound for pound, the best in the world. Of the 52 winners of the Fields Medal, often called the Nobel Prize of math, 11 have been French. Only the U.S., a country five times the size of France, has had more: 13. But unlike in France, many of America's medal winners have come from elsewhere. The great French mathematician Jean-Pierre Serre, the youngest Fields winner, at age 27, also won the first Abel Prize, awarded by Norway in 2003, for outstanding achievement in math for his work on number theory. Of that prestigious prize's 11 winners, three have been French.
"We've been really good at math for several hundred years," says Cédric Villani, who won the Fields Medal in 2010 for his work on the Boltzmann equation and optimal transport. He now runs the high-powered math- and physics-based Institut Henri Poincaré in Paris. "Math is an abstract way of looking at the world, which fits well with the French mentality. We apply algebra to everything."
Tourists sipping coffee along Paris' leafy boulevards can't hear it, but the city is alive with the scratchy sound of chalk on blackboards. There are roughly 2,000 full-time academics at Paris' great centers of math learning. "You don't have that in Boston, Berkeley or Beijing," says Bourguignon. "The Paris area has the largest concentration of mathematicians in the world."