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DFW on Cantor and Mathematical Insanity

October 11, 2008

Susan at Intrinsically Knotted is talking about a frustrating documentary about — among other things — Cantor being driven insane by the continuum hypothesis. It reminded me that David Foster Wallace wrote about just this sort of treatment of Cantor in his book Everything and More.

In relevant part:

Here is a quote from G. K. Chesterton: “Poets do not go mad; but chess players do. Mathematicians go mad, and cashiers; but creative artists very seldom. I am not attacking logic: I only say that this danger does lie in logic, not in imagination.” Here also is a snippet from the flap copy for a recent pop bio of Cantor: “In the late nineteenth century, an extraordinary mathematician languished in an asylum. . . . The closer he came to the answers he sought, the further away they seemed. Eventually it drove him mad, as it had mathematicians before him.”

The cases of great mathematicians with mental illness have enormous resonance for modern pop writers and filmmakers. This has mostly to do with writers’/directors’ own prejudices and receptivities, which are in turn functions of what you could call our era’s particular archetypal template. It goes without saying that these templates change over time. The Mentally Ill Mathematician seems now in some ways to be what the Knight Errant, Mortified Saint, Tortured Artist, and Mad Scientist have been for other eras: sort of our Prometheus, the one who goes to forbidden places and returns with gifts we can all use but he alone pays for. That’s probably a bit overblown, at least in most cases (Although so is the other, antipodal stereotype of mathematicians as nerdy little bowtied fissiparous creatures. In today’s archetypology, the two stereotypes seem to play off each other in important ways.). But Cantor fits the template better than most. And the reasons for this are a lot more interesting than whatever his problems or symptoms were.

In modern medical terms, it’s fairly clear that G. F. L. P. Cantor suffered from manic-depressive illness at a time when nobody knew what this was, and that his polar cycles were aggravated by professional stresses and disappointments, of which Cantor had more than his share. Of course this makes for less interesting lap copy than Genius Driven Mad By Attempts To Grapple With ∞. The truth, though, is that Cantor’s work and its context are so totally interesting and beautiful that there’s no need for breathless Prometheusizing of the poor guy’s life. The real irony is that the view of ∞ as some forbidden zone or road to insanity—which view was very old and powerful and haunted math for 2000+ years—is precisely what Cantor’s own work overturned. Saying that ∞ drove Cantor mad is sort of like mourning St. George’s loss to the dragon: it’s not only wrong, but insulting.

Of course, I’ve had to adjust things a bit, because it’s hard to add footnotes to a weblog post in general, let alone within a block quote.

6 Comments leave one →
  1. October 11, 2008 16:26

    Yeah, he put it waaaayyyy better than I could. I really need to reread that book.

  2. October 11, 2008 21:04

    Over on my LiveJournal blog, I had many quotes on Mathematics and Madness.

  3. Avery Andrews permalink
    October 12, 2008 05:57

    Hmm, poets don’t go mad? thinking of Ezra Pound.

  4. October 12, 2008 06:00

    Chesterton was never one to let the facts get in the way of a good story. See: Orthodoxy.

  5. nzrc permalink
    October 12, 2008 18:21

    cantor was the best

  6. Greg Friedman permalink
    October 13, 2008 05:50

    The best what?

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