Wednesday, November 18, 2015

"Mathematicians" and the Law

Mark Tushnet

I just finished reading "Mathematicians," a book of really striking photographs (by Mariana Cook) of world-class mathematicians. Each photo comes with a one-page statement by the subject about his or her life, mathematical interests, and the like. The descriptions of the mathematics are of course largely unintelligible to me; John Tate observes,"It is next to impossible to describe to a non-mathematician in any but the vaguest terms the solutions we have found and the puzzles we are trying to solve." But I did notice one thing that led me to think about academic law as a discipline.

A fair number of the mathematicians say that in the course of their work they have made more than a few mistakes -- pursued lines of analysis that didn't pan out, thought they had proved something when they hadn't, and the like. (The thought here is clearly stronger than the one Andrew Wiles articulates in connection with his proof of Fermat's Last Theorem, which in its initial version had a mistake that forced Wiles to do quite a bit more work before he eliminated the error.)

That led me to wonder whether academic law really has a category of "mistakes." One test that occurred to me was this: What's your estimate of the number of papers presented at workshops that are never published, just put back in the drawer, because the author[s] concluded that the paper was just wrong? My own estimate is "not many at all" (I don't exempt myself from this -- I do have a handful of papers in my "drawer" that I'm never going to publish because they didn't work out, but not many).

The self-defensive reaction is that the papers are published after they've been revised in light of criticisms made at workshops. Maybe so. And maybe, more important, academic law is fundamentally a rhetorical discipline, in the sense that the measure of an argument's "goodness" is whether it gets itself accepted in some segment of the academic community. If that's so, academic law really isn't going to have a category of "mistake," and the number of wrong arguments is going to be vanishingly small.

Still, honestly, do you think that no one has ever come up with an idea so bad that it shouldn't be published? Or an argument that just doesn't work? I don't. (In my field, there's major recent work about which the old snarky line is applicable: "This fills a much needed gap in the literature.")

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