Andrew Wiles: Obsession, Proof of Fermat’s Last Theorem

Fermat’s Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. This theorem was first conjectured by Pierre de Fermat in 1637, and it remained unsolved for over three hundred years. Andrew Wiles proved the theorem in 1994.

What’s fascinating is how long Andrew Wiles spent working on this theorem (answer: seven years). In a great interview with NOVA, Andrew Wiles explains his obsession:

I used to come up to my study, and start trying to find patterns. I tried doing calculations which explain some little piece of mathematics. I tried to fit it in with some previous broad conceptual understanding of some part of mathematics that would clarify the particular problem I was thinking about. Sometimes that would involve going and looking it up in a book to see how it’s done there. Sometimes it was a question of modifying things a bit, doing a little extra calculation. And sometimes I realized that nothing that had ever been done before was any use at all. Then I just had to find something completely new; it’s a mystery where that comes from. I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction, I would have the same thing going round and round in my mind.

Have your ever been consumed by anything on this scale?


Italo Calvino on Photography

I always find it fascinating when authors incorporate their academic thoughts into works of fiction.

I came across this this story by Italo Calvino titled “The Adventures of a Photographer,” found in his novel Difficult Loves. In it, we follow Antonino Paraggi, who is described as a non-photographer. Feeling isolated, he picks up the camera and begins to shoot. The story is short, and perhaps unrealistic (what of finding love through a model shoot?), but I wanted to highlight a couple of noteworthy passages.

Is it possible to use an extracurricular endeavor, such as photography, to discover ones faults, misgivings, and dissatisfactions in life? Calvino makes the case that it is so:

It must be said that his examination of photography to discover the causes of a private dissatisfaction—as of someone who feels excluded from something—was to a certain extent a trick Antonino played on himself, to avoid having to consider another, more evident, process that was separating him from his friends. What was happening was this: his acquaintances, of his age, were all getting married, one after another, and starting families, while Antonino remained a bachelor.

Have you encountered parents who become obsessed with photography because they think that if there’s a moment of their child’s life that they don’t capture, it will be lost forever?

Given the speed of growth, it becomes necessary to photograph the child often, because nothing is more fleeting and unmemorable than a six-month-old infant, soon deleted and replaced by one of eight months, and then one of a year; and all the perfection that, to the eyes of parents, a child of three may have reached cannot prevent its being destroyed by that of the four-year-old. The photograph album remains the only place where all these fleeting perfections are saved and juxtaposed, each aspiring to an incomparable absoluteness of its own.

Antonino’s argument here is interesting, but flawed:

For the person who wants to capture everything that passes before his eyes, the only coherent way to act is to snap at least one picture a minute, from the instant he opens his eyes in the morning to when he goes to sleep. This is the only way that the rolls of exposed film will represent a faithful diary of our days, with nothing left out. If I were to start taking pictures, I’d see this thing through, even if it meant losing my mind. But the rest of you still insist on making a choice. What sort of choice? A choice in the idyllic sense, apologetic, consolatory, at peace with nature, the fatherland, the family. Your choice isn’t only photographic; it is a choice of life, which leads you to exclude dramatic conflicts, the knots of contradiction, the great tensions of will, passion, aversion. So you think you are saving yourselves from madness, but you are falling into mediocrity, into hebetude.

I find it hard to believe that there is a person who wants to capture “everything” — that is impossible. Secondly, one would not use a still camera in this instance, but would shoot a film. On this topic, I highly suggest reading “While the Women Are Sleeping,” which I previously discussed here. The central obsession of shooting continuously in the two stories is very, perhaps eerily, similar.

And this is probably the best passage in the story. Can the photographed reality be better (i.e., more visually appealing, more engrossing, more ethereal, more subjective, etc.) than reality itself? I’ve previously noted, with my photography, that it’s often the case (because I sometimes envision a scene as I would like it to look, and complete my mental image in post-processing).

Photographed reality immediately takes on a nostalgic character, of joy fled on the wings of time, a commemorative quality, even if the picture was taken the day before yesterday. And the life that you live in order to photograph it is already, at the outset, a commemoration of itself. To believe that the snapshot is more true than the posed portrait is a prejudice…

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Hat tip to @escapeintolife for posting a link to this story on Twitter.

While the Women Are Sleeping

The best thing I read today was a short story in The New Yorker titled “While the Women Are Sleeping.” The story is by an author I haven’t heard of before: Javier Marías.

The story starts out with more questions than answers…

For three weeks, I saw them every day, and now I don’t know what has become of them. I’ll probably never see them again—at least, not her. Summer conversations, and even confidences, rarely lead anywhere.

It’s kind of an intriguing opening: who is them? What have they become? And summer conversations rarely lead to anywhere?

The story concerns a couple from Madrid vacationing on an island. While there, they observe another couple; the beautiful Inés, described as so:

She was beautiful, indolent, passive, and, by nature, languid. Throughout the three hours a day that we spent at the beach (they stayed longer, perhaps taking their siesta there and, who knows, staying until sunset), she barely moved and was, of course, concerned only with her own beautification

and her older, less attractive male companion named Alberto Viana. What the observing couple find remarkable (and so does the reader, no doubt) is that Alberto constantly, without interruption records Ines on video camera. The video camera has become an extension of him…

The story, admittedly, starts out slowly (I had to step away from reading it in the evening, and came back to it the following day)… But then it picks up and absolutely sucks you in. At least, it did for me. What could be so interesting about a guy videotaping his girlfriend? The answer is explained in the story, which begins with this conversation between the narrator and Alberto:

“I’ve noticed that you’re very keen on video cameras,” I said after that pause, that hesitation.

“Video cameras?” he said, slightly surprised or as if to gain time. “Ah, I see. No, not really, I’m not a collector. It isn’t the camera itself that interests me, although I do use it a lot. It’s my girlfriend, whom you’ve seen, I’m sure. I film only her, nothing else. I don’t experiment with it at all. That’s fairly obvious, I suppose.”

And the conversation picks up from there. What I find fascinating is our abilities to remember things; some go about life, cruising. Others write things down. Others photograph the world around them. This was an intriguing conversation between the narrator and Alberto Viana:

“You don’t have a camera? Don’t you like to be able to remember things?” Viana asked me this with genuine confusion.

“Yes, of course I do, but you can remember things in other ways, don’t you think? Memory is a kind of camera, except that we don’t always remember what we want to remember or forget what we want to forget.”

And still others prefer to record things on video, as Alberto explains to the narrator:

“How can you compare what you can remember with what you can see, with what you can see again, just as it happened? With what you can watch over and over, ad infinitum, and even freeze?

But there is something sinister (though arguably honest) in Alberto’s declaration…

I won’t say much more except that this is an incredible story of obsession, vision (literally and figuratively), memory, human misconceptions, life, and death. Shortly put, it is one of the best works of fiction I have read in 2010, so I highly recommend reading it.

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A hat tip to @etherielmusings for pointing out this story via Twitter.