A few years back, a prospective doctoral student sought out Sylvia Serfaty with some existential questions about the apparent uselessness of pure math. Serfaty, then newly decorated with the prestigious Henri Poincaré Prize, won him over simply by being honest and nice. “She was very warm and understanding and human,” said Thomas Leblé, now an instructor at the Courant Institute of Mathematical Sciences at New York University. “She made me feel that even if at times it might seem futile, at least it would be friendly. The intellectual and human adventure would be worth it.” For Serfaty, mathematics is about building scientific and human connections. But as Leblé recalled, Serfaty also emphasized that a mathematician has to find satisfaction in “weaving one’s own rug,” alluding to the patient, solitary work that comes first.

Born and raised in Paris, Serfaty first became intrigued by mathematics in high school. Ultimately she gravitated toward physics problems, constructing mathematical tools to forecast what should happen in physical systems. For her doctoral research in the late-1990s, she focused on the Ginzburg-Landau equations, which describe superconductors and their vortices that turn like little whirlwinds. The problem she tackled was to determine when, where and how the vortices appear in the static (time-independent) ground state. She solved this problem with increasing detail over the course of more than a decade, together with Étienne Sandier of the University of Paris-East, with whom she co-authored the book Vortices in the Magnetic Ginzburg-Landau Model.

In 1998, Serfaty discovered an irresistibly puzzling problem about how these vortices evolve in time. She decided that this was the problem she really wanted to solve. Thinking about it initially, she got stuck and abandoned it, but now and then she circled back. For years, with collaborators, she built tools that she hoped might eventually provide pathways to the desired destination. In 2015, after almost 18 years, she finally hit upon the right point of view and arrived at the solution.

“First you start from a vision that something should be true,” Serfaty said. “I think we have software, so to speak, in our brain that allows us to judge that moral quality, that truthful quality to a statement.”

And, she noted, “you cannot be cheated, you cannot be lied to. A thing is true or not true, and there is this notion of clarity on which you can base yourself.”

In 2004, at age 28, she won the European Mathematical Society prize for her work analyzing the Ginzburg-Landau model; this was followed by the Poincaré Prize in 2012. Last September, the piano-playing, bicycle-riding mother of two returned as a fulltime faculty member to the Courant Institute, where she had held various positions since 2001. By her count, she is one of five women among about 60 full-time faculty members in the math department, a ratio she figures is unlikely to balance itself out anytime soon.

Quanta Magazine talked with Serfaty in January at the Courant Institute. An edited and condensed version of the conversation follows.

QUANTA MAGAZINE: When did you find mathematics?

SYLVIA SERFATY: In high school, there was one episode that crystallized it for me: We had assignments, little problems to solve at home, and one of them seemed very difficult. I had been thinking about it and thinking about it, and wandering around trying to find a solution. And in the end I came up with a solution that was not the one that was expected — it was more general than the problem was calling for, making it more abstract. So when the teacher gave the solutions, I proposed mine as an alternative, and I think everybody was surprised, including the teacher herself.

I was happy that I’d found a creative solution. I was a teenager, and a little bit idealistic. I wanted to have a creative impact, and research seemed like a beautiful profession. I knew I was not an artist. My dad is an architect and he’s really an artist, in the full sense of the word. I always compared myself to that image: the guy who has talent, has a gift. That played a role in building my self-perception of what I could do and what I wanted to achieve.

So you don’t think of yourself as having a gift — you weren’t a prodigy.

No. We do a disservice to the profession by giving this image of little geniuses and prodigies. These Hollywood movies about scientists can be somewhat counterproductive, too. They are telling children that there are geniuses out there that do really cool stuff, and kids may think, “Oh, that’s not me.” Maybe 5 percent of the profession fits that stereotype, but 95 percent doesn’t. You don’t have to be among the 5 percent to do interesting math.

For me, it took a lot of faith and believing in my little dream. My parents told me, “You can do anything, you should go for it” — my mother is a teacher and she always told me I was at the top of my cohort and that if I didn’t succeed, who will? My first university math teacher played a big role and really believed in my potential, and then as I pursued my studies, my intuition was confirmed that I really liked math — I liked the beauty of it, and I liked the challenge.