The City of London and Wall Street are full of men and women from France who pass for geniuses, and sometimes they are. The key to their success is the language they speak, but not necessarily that of Camus or Molière. They know how to talk mathematics of a very rarefied kind that most of us find quite impossible to understand. And as the market for derivatives, the exotic financial instruments based on that math, exploded over the last decade, so too did the demand for the skills of those who could master the relevant equations. (And if they couldn’t, who among us could tell?)

The reason that so many came from France is that basic French education puts a strong emphasis on pure mathematics, and many French universities have developed programs specializing in “the very, very complex modeling of derivatives,” says one young French veteran of the City.

Another reason is that bright young French men and women who are not afraid of risk often prefer to work in “Anglo-Saxon” environments like New York and London where their payoffs won’t be taxed so heavily and the culture admires success rather than envies it, as often happens in France.

Oh, and there’s the Eurostar train, which makes it so easy to get from the Champs Élysées to the City and back.

“I worked for five years in London,” says Mr. Gaul, who preferred that we not use his real name. His team at a major British bank eventually had about 40 people on it, he said, and of those, at least 75 percent were either French or had a French educational background. Among the elite schools they attended: Paris VI at Jussieu, which has a one-year intensive course in financial math; the ESSEC international business school; and the University of Paris Dauphine. But there are many more where formal mathematics is a strong suit.

Jérôme Kerviel, whose supposed “rogue” trades brought Société Général to its knees in early 2008, was a graduate in finance from the University of Lyon. “Fabulous” Fabrice Tourre, allegedly the bane of Goldman Sachs, which paid out half a billion dollars in fines related to his work, went to the École Centrale Paris, a top-flight engineering school. Bruno Iksil, the latest Frenchman to be partially but publicly implicated in disaster, this time at JPMorgan Chase, also reportedly attended the École Centrale. He was known as “The Whale” because he took such huge positions in the markets where he operated. He was also called “Voldemort,” after the nemesis of Harry Potter.

So, what are these math wizards actually doing? Gaul walked me through it.

Let’s say you want to develop a financial product that will protect investors with huge amounts of money against various movements in the market. “The people who build the models are the technical guys, and those are called the ‘quants,’” says Gaul, “quant” being short for quantitative analyst, although the math may be reminiscent of quantum physics in its incomprehensibility. “Everything is very mathematical in derivatives, and it is pure math, even though we say it is applied mathematics,” says Gaul.

Then you have “the structure guys,” as Gaul calls them. They actually put together financial products based on the models developed by the quants, and Gaul was one of them. Traders buy and sell the various elements in the package based on the models and structures they have to work with. “The traders manage the risk,” says Gaul, “and they tend to have similar backgrounds to the quants.” As the quants develop their models in the financial equivalent of an ivory tower and the traders provide their input from the financial trenches, the structure guys design solutions and improvements. And finally there are the salespeople, who may not know that much about the math, but know how to talk a persuasive bottom line.

Most of us can see in hindsight how dangerous this juxtaposition of mathematical theory and multiple billions of dollars might be if something goes wrong, but for the traders in the middle of the action following the model and counting on it working out, that may not be so obvious. They’ve seen the numbers sort out before, and maybe they will now. The outside world hears only about the derivatives that go wrong, while careers are built on the ones that go right. Or, at least, they were.

Given the extent to which teams are involved in the work, refining and improving the products, the idea that a “rogue trader” can make billion-dollar bets all on his own is, to say the least, improbable. One notes that other heads besides Iksil’s are rolling already at JPMorgan Chase and they’re not French.

As for Gaul? He shrugs: “As the derivatives market is declining, you have less interest in these French mathematicians,” he says. For his part, he’s moved back to Paris.