Two women of different cultures, generations, and specialties have both chosen a field that remains one of the most heavily male-dominated: mathematics. Far from evoking the rote memorization of inflexible formulae that many associate with high school math class, Nicole El Karoui and Carolina Canales describe a world of creativity and freedom. Certain realities for women in the field may translate into extra challenges, but, passionate for their subject, they remain undaunted.
They can’t share much in the way of similar backgrounds. One, a distinguished professor at a French university. The other, a young Chilean student pursuing her Master’s degree in Paris. But their experience coincides on one fundamental point: the two women’s passion for math. It’s rich, it sparks the imagination, it’s liberating. Listening to them, one begins to suspect the rest of us are missing out.
Professor Nicole El Karoui is a member of the Probabilities and Random Models Laboratory at the University of Pierre and Marie Curie (UPMC). Although it was the last thing she would ever have expected, El Karoui became a pioneer in the world of mathematical finance. In 1987, a six-month sabbatical in the research center of a bank marked the beginning of “an adventure that never stopped,” she says. This experience revealed to her the role that her probability work could play in modeling risk on the markets. El Karoui went on to create a training program for quantitative analysts, which has ranked among the most prestigious in the world.
Her former students can be found in the most important investment banks, helping to create and determine the value of financial derivative products. Following the crisis of 2008, these mathematical models, their wranglers, the quantitative analysts, and even their creators, El Karoui and colleagues, came under fire for exposing the market to unnecessary risk. It was said that they had allowed the belief to take hold that the predictive ability of their models had effectively negated the risk. Professor El Karoui calls this ridiculous: No one expects a model to be 100% accurate. She admits that she and her team were naïve, perhaps, but their models were being used in ways they had never imagined, such as for speculation. The profits to be made, she feels, were just too tempting, and the academics’ warnings were ignored.
The cascade of consequences is all too well known, and the responsibility of mathematicians has been debated—El Karoui has even heard accusations of crimes against humanity—but the fact remains that this theoretician from the east of France unexpectedly revolutionized the financial world. On a student’s CV, her name alone has practically been a ticket to success in finance. But Professor El Karoui explains her appreciation for mathematics in less practical terms.
“The richness of math is in the abstraction. It allows you to take a step back from reality, and that gives us the freedom to think the way we want. Mathematicians display a great deal of imagination”"
Imagination and math may seem an unlikely pair, but Carolina Canales, a Master’s student at the University of Paris Sud, readily agrees. “To do research in math, you need creativity. And a bit of madness!” she adds with a laugh. The role of imagination becomes clear as diagrams of Carolina’s subject of study, complex geometry, take shape on the page before her. Never mind placing ordinary numbers on your simple X and Y axes; Canales plots imaginary numbers—baffling square roots of negative numbers—on coordinate planes that roll up into cylinders, doughnuts, and spring-like shapes. Quite reserved at first meeting, she can no longer contain her enthusiasm for the “really nice properties” of her imaginary numbers, which “behave so well” in her hands.
Carolina’s mother is a math teacher, back in her native Chile, but, due to the limited job prospects, her parents initially discouraged her from pursuing studies in the field. After a year of architecture courses, though, Carolina could not resist the lure and switched to a Bachelor’s program in mathematics. In Chile, she was one of two girls in a class of 15. In the first year of her Master’s in France, the proportion was two out of 50. This year, at her new university, she says there are lots of girls: a grand total of six.
Asked why she doesn’t have more female classmates—whether it is a choice on their part, or whether girls are discouraged from studying math—Carolina responds that they probably see the field as “cold”.
“They imagine that math is too rational, too cut-and-dried, too closed, because at school we’re given formulas and told ‘This is what you have to do.’ But in reality, math isn’t rigid. It’s flexible and diverse”"
The geometry student seems unperturbed by her own rare state of being a woman in math. Nicole El Karoui’s experience was slightly more dire. In the 1960s, in her classe préparatoire, a year of demanding preparatory study, often undertaken in France before entering higher education, the message for even the top girls on the course was that they couldn’t hope to be as good as the boys. Later, too, at the prestigious women’s Ecole Normale Supérieure at Sèvres, the promising young mathematicians were met with a condescending attitude, their skills considered “decent, but…” El Karoui remembers.
Once the initial educational hurdles are cleared, women entering the professional world of mathematics face further challenges, but ones that are familiar to their counterparts in other fields. In the famous “El Karoui Master’s”, as it is simply, but reverently, known, about 30% of the quantitative engineers she trains are women. However, those “quants” who go on to model risk for investment banks work closely with the traders on the floor. “It’s a very fast-paced, macho environment. It’s about being the best.” In this world, it’s about 80 or 90% percent male.
Women in the field frequently find themselves drawn to regulatory positions, providing oversight of the high-speed activity taking place among traders. Nicole El Karoui explains that
“there are a lot of women here because it’s less stressful than on the floor. These positions are less technical and less specialized. It’s the nature of the job that makes [women move in this direction], but it’s also the fault of the system: Can a woman leave the trading room for three months to start a family? No. Or if she does, will she get her old job back?”"
Even in the comparatively tranquil world of academia, the numbers are not much more balanced. Among assistant professors in mathematics, El Karoui sees about 30 or 40% women. “But at the level of full, tenured professor? There are almost no women, the higher you go.” She describes challenges faced by female researchers in every field when they decide to start a family, from needing to travel and work abroad in order to advance one’s career, to having to leave work early to pick the kids up from school. “The men never did that!” Professor El Karoui insists. The knowledge that the male colleagues on her team would always be there, pushing the research forward, was a factor that motivated her to keep juggling her many commitments.
Carolina Canales, from her position on an early rung of the mathematics career ladder, is not intimidated by these potential obstacles. “There are more challenges for women in every field,” she feels. “But it’s not the biological fact of being a woman that matters. The men should help out, too!” Nicole El Karoui, too, speaks of the importance of one’s family and husband for a successful career in research: this psychological support sometimes had a greater impact on her classmates’ professional success than their math skills did. She also underlines the need for credible examples for girls to follow. Before her time, for example, the preparatory school she attended had never sent a student on to the Ecole Normale. Once three girls were accepted from El Karoui’s class, however, the school sent a student every year for the next ten years. They had just needed to see their peers succeed: “It’s the fact of believing it’s possible.”
Very little, it turns out, is not possible in mathematics. (Carolina Canales will tell you why 1+1=0) Nicole El Karoui, who declares her loathing for closed-minded worlds and suffers from an “allergy to certainties”, finds in mathematics a liberating openness and endless possibility. While acknowledging that she will always find vitally important elements of life outside of her research, math remains her great passion. “It lets us think with a new kind of freedom, and benefit from all the consequences of that.” The result is an enormously enriched world, which more women would likely appreciate. But, first, they must also think differently about the field of mathematics itself, and believe that all its possibility is open to them, as well.
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To find out more: "Why Students Of Prof. El Karoui Are In Demand", Wall Street Journal, March, 9, 2006. http://online.wsj.com/article/SB114187184703793317-search.html?KEYWORDS=%22Carnegie%2BMellon%22&COLLECTION=wsjie/6month "The Blame Game : Will Maths Apologize to Finance? Well, Maybe Not", ParisTech Review, June 7th 2010. http://www.paristechreview.com/2010/06/07/the-blame-game-will-maths-apologize-to-finance-well-maybe-not/ Association for Women in Mathematics http://sites.google.com/site/awmmath/ Biographies of Women Mathematicians, sponsored by Agnes Scott College http://www.agnesscott.edu/lriddle/women/women.html Women in Math Project, University of Oregon http://darkwing.uoregon.edu/~wmnmath/ A Visual, Intuitive Guide to Imaginary Numbers http://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/ Widgets Amazon.fr