teaching machines

Mathematician Grapples

Laurent Schwartz was a French mathematician and human rights activist. He’s not the Schwarz of the Cauchy-Schwarz inequality. In fact, I don’t know if I’m familiar with any of his math work, which was way over my head. Nevertheless, I just finished his biography, A Mathematician Grapples with His Century.

His life was fascinating. He was Jewish, and he remained in occupied France during World War II, narrowly averting many roundups and mass executions. Rarely did he take notes, relying instead on an excellent memory. He also spent a considerable portion of his life involved in politics and pacifism, helping end wars and free dissidents in repressed countries.

Schwartz had a strong love for Vietnam and visited often. On one of these trips, he met a model student:

Vietnamese students are generally very studious. Once, in a large deserted street of Hanoi, towards midnight, I was passing in a car and I saw a student installed in the middle of the sidewalk, sitting on a chair in front of a table covered with papers, under the light of a big street lamp; he had chosen this unusual spot because he had no electricity at home.

His research was on distributions, not the statistical ones but the ones that generalize functions. He speaks at length on the ups and downs he encountered in his research, and laments that the history of science is not taught more. Without a historical perspective, young folks get the false impression that knowledge comes quickly and easily:

This alternation of joy and suffering is at the heart of research. Young people need to get used to it. High school students all too often think that it isn’t normal to think about a problem for more than an hour, whereas to find something really important, it’s necessary to think for several days, if not months, and even years… When you read a well-written book, you don’t think about the joys and suffering of the author who wrote it. It can be quite instructive to learn about them.

In his youth, he didn’t think his mind was particularly special. His thoughts remind me of my own education:

In spite of my success, I was always deeply uncertain about my own intellectual capacity; I thought I was unintelligent. And it is true that I was, and still am, rather slow. I need time to seize things because I always need to understand them fully. Even when I was the first to answer the teacher’s questions, I knew it was because they happened to be questions to which I already knew the answer. But if a new question arose, usually students who weren’t as good as I was answered before me.

Schwartz goes on:

Towards the end of the eleventh grade, I secretly thought of myself as stupid. I worried about this for a long time. Not only did I believe I was stupid, but I couldn’t understand the connection between this stupidity and my good grades. I never talked about this to anyone, but I always felt convinced that my imposture would someday be revealed: the whole world and myself would finally see that what looked like intelligence was really just an illusion. If this ever happened, apparently no one noticed it, and I’m still just as slow.

Like Schwartz, I’ve got a nagging case of impostor syndrome.

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