Opinion 34: We Should Confess to Our Dumb Mistakes, in Order that Our Students should not feel bad about their Mistakes

By Doron Zeilberger

Written: Feb. 18, 1999

I have asked lots of dumb questions in my life, and, of course, have been asked lots of dumb questions, not only by students, but sometimes even by permanent members of the Institute for Advanced Study, and members of the National Academy of Science.

Of course, it is not appropriate to publicize, even anonymously, the latter kind, but, I believe that it is desirable, if nothing else for my own sake, (as the Catholic Church knows so well, confession is the best therapy), to advertise some of MY dumb questions.

It would be very boring to tell you about all the stupid questions that I have ever asked, and all the inane and dumb remarks, so let me pick my two favorites.

When I have met Per Enflo, of Banach fame, for the first time, I wanted very eagerly to make a good impression, and asked him what he was working on. He told me that he is trying to find the maximum of a certain analytic function on the unit disc. I then asked him: do you mean the maximum over the disc, or only over its boundary? He grinned, ever so slightly, and very politely and tactfully reminded me of the maximum principle.

But this is nothing compared to how I made a fool of myself in front of Gordon Slade, the great Self-Avoiding-Walker, about eight years ago.

I had a method that I was very fond of, to compute the so-called finite-memory generating functions for SAWs. It had many variables, but when I did lots of specializations, I obtained an incredibly elegant corollary: the number of n-step non-retracing walks, on the square-lattice, equals 4*3^(n-1). I was very excited about this beautiful new result, and made a quick literature search, and convinced myself that it is apparently new. Then I wrote Gordon Slade, asking him about the novelty of this amazing result. In his reply, he pointed out, very politely, that my `new result' is not terribly deep. I am leaving this as an exercise to the reader.

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