Quotes of the Day

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."

As with so many things French, Napoleon gets much of the credit and blame for this. It was Napoleon who set up the grandes écoles to train the nation's elite administrators in critical math and engineering skills. He was a pretty fair mathematician, not to mention an artilleryman by training. He surmised that the correct angle of cannon elevation counted for as much as, if not more than, skill with a saber. Ever since, two of the grandes écoles, the Ecole Normale Supérieure and the Ecole Polytechnique, have been cranking out many of the world's best mathematicians.

"I never said to myself that I wanted to do math research, but being good in math is the best way to get into the grandes écoles, and that's the entry stamp to French society," says Wendelin Werner, who won the Fields Medal in 2006 and now teaches at Normale Sup, as everybody calls the Ecole Normale Supérieure.

To Werner, it's all about being, well, Cartesian. "When you're young in France, you get graded all the time, and you experience figure-skating-judging trauma — you have no idea why you got the grades you got. You can be a brilliant philosophy student and get bad marks. Math is different. If you solve the problem, you solve the problem, so the smartest kids choose the discipline that seems the most fair."

And in their Cartesian way, some of the most gifted graduates of these grandes écoles take the lucrative exit to quantitative finance. "It's clear that we get very good students who could have made a solid career in pure math," says Gilles Pagès, director the Polytechnique master's program in probability and finance, perhaps the most prestigious financial-engineering master's in France. Each year, 70 to 100 Polytechnique students apply to his program, which selects about a fifth of them. Most graduates start as quantitative analysts in bank research, and by their third or fourth year out of the program, they're often structuring or trading exotic derivatives.

In a funny way, the French quants never leave the classroom. "In France we're suspicious of markets, and we believe that because we have mathematical models, we don't need to understand markets to make money," says Eugene Durenard, who studied math at Polytechnique and now runs a financial-consulting firm in Bermuda.

This attitude doesn't win the French quants any popularity contests. When the markets blew up in 2008, French black-box financial wizardry got something of a black eye. Former French Prime Minister Michel Rocard went so far as to charge math professors with "a crime against humanity." It didn't help that Fabrice Tourre, a 31-year-old Goldman Sachs vice president accused by the U.S. Securities and Exchange Commission of fraud in 2010, graduated from one of France's oldest and best-known engineering schools, the Ecole Centrale de Paris, with a bachelor's in mathematics.

Even Jacques Olivier, who runs the international-finance master's program at Hautes Etudes Commerciales, worries that too much math and too little economics can have dangerous consequences. "The crisis is due in part to all the people who know how to count marbles but have no idea what those marbles mean," he says. Others, like Natixis' Crouhy, feel different. "It's totally unfair to make the quants the scapegoat. People are criticizing the models and the quants, but the quants are hardly responsible for data that is b.s."

Responsible or not, the quants and the programs that train them are feeling the fallout from the crisis. "People are thinking twice before applying for a master's in finance," says Crouhy. Pagès says his financial-engineering program has seen a drop-off in applications, particularly from the grandes écoles, to about 65 a year.

And there are regulatory threats looming. France's top market regulator wants to impose speed limits on high-frequency trading, a form of quant finance that uses computer algorithms to trade in huge volumes at lightning speed. Thierry Francq, secretary general of France's market regulator, recently said, "You have some active retail investors who have quit the market because they feel very uncomfortable since they have no level playing field." Investors and banks are also shying away from exotic derivatives, says Pagès. "It will take a long time before they come back."

The challenge for French quants will be proving that their work benefits everyone, not just an elite few, before that comeback happens.

• Josh Levine
• Investment banks are filled with graduates of Paris' math academies. What makes them so special?