Written: Sept. 24, 1998
Now that Yom Kippur is coming up again, it is about time that I atone, in public, to a sin that I committed a few years ago of being a Colloquium wise-guy and making a remark of the format: ``Your major result follows immediately from well-known classical results''.
Luckily, in this case, the damage was minimal, since the speaker was no other than the great Hyman Bass. I expected not to understand a word of his talk. Imagine my pleasant surprise when his talk turned out to be a clear and lucid combinatorics talk. Then he mentioned all the familiar stuff: graphs, paths, and the matrix-tree-theorem. Then he stated his major result: a certain relationship between Eulerian paths and spanning trees. This `rang a bell'. That's exactly the classical and famous BEST theorem, that can be found. e.g., in Knuth's ACP, v. 1. As soon as I `realized' that Bass's result was `essentially a rediscovery' I raised my hands and announced it out loud.
My colleagues were very impressed. One even said, after the talk: `One should not dare give a combinatorics talk when you are in the audience'. And I felt very proud and superior. These fancy K-theorists are finally discovering combinatorics, but instead of looking things up, or asking the experts, they re-invent the wheel.
Then, later that day, I looked at my notes again, and realized that the assumptions were NOT EXACTLY the same as in the BEST theorem. Big deal, I said, it is a minor variation, that should be done in five minutes. Well, these five minutes dragged on and became two years. Finally, Dominique Foata and I were able to prove, that indeed, Bass's result is a `trivial consequence' of well-known combinatorics. So what if it took us two summers and twenty pages ( if you wish, you can look at Dominique Foata and Doron Zeilberger's article on Bass's Theorem ).
But don't worry, G-d has already punished me seven-fold for my wise-guyness. Quite a few times, people made sage remarks during my talks, that I was unable to rebut on the spot, that turned out to be nonsense.
As recently as last July, during the IWOP98 conference that was held in Madrid, Spain, I gave a talk on evaluating determinants using orthogonal polynomials. I described my technique of evaluating determinants of matrices obtained from the Hilbert matrix by changing one row. It so happened that in the audience was one Gene Golub, who happens to be a member of the NAS, and who is considered a matrix guru. Hearing his favorite key-words: Hilbert matrix, determinant, etc. he felt at home, and made a wise-guy comment: `What you are doing is NOTHING BUT inverting a rank-1 change of the Hilbert matrix' . I am sure that quite a few at the audience believed that my stuff was old hat.
Only after the talk, when I asked him for clarification, it turned out that while most of the key-words are the same, not all of them mean the same. When he talks about inverting a matrix, he thinks about it numerically, whereas, for me, as a combinatorialist, I mean that I want the entries to be in CLOSED FORM. So his comment was useless. But the impression that the comment has made on he audience stayed on.
But most colloquium comments are made in good faith. More irritating is to get referee reports that are complete nonsense, that, while rebuttable, are annoying, since they are anonymous. Even worse are stupid and unfounded comments in grant reviews, that are not even rebuttable.
But, in spite of all our sins, we mathematicians are tzadiks next to politicians and lawyers, and real angels compared to media people.