In mathematics, ‘you cannot be lied to’

Siobhan Roberts writes: 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.” [Continue reading…]

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