Newsletter #55     Nicolas Balachef and Proofs

Actually, this is more like a newspointer than a newsletter. Nicolas Balacheff, who gave a colloquium on Proof here in spring of '96, now has a web page on Proof on which he invites a debate. This month's letter of invitation I find highly intriguing and provocative because it directly contradicts something I had always considered obvious. The title of the invitation is "L'argumentation est-elle un obstacle?" ("Argumentation: is it an obstacle?") and I shall translate the beginning of the thumbnail sketch which appears below it. On the other hand, if you get to that title box and click on the word English you will get a (slightly free) translation of the considerably longer article in which he backs up his basic thesis. Myself I'm still more or less at the "But gee whiz, guys!" stage, but my bet is that some of you will have something considerably more articulate to say on the subject--and that would be great!

So here's the beginning of the introduction (the latter portions come straight from the text that's already translated):

Does argumentation have a place in the teaching of mathematics? Some people respond positively, and we even see argumentation appearing explicitly as an object of teaching in some curricula. I would like to propose here for debate the thesis that between argumentation and mathematical proof (or proof in mathematics) there is neither continuity not rupture, but a complex relationship which helps create the meaning of both: argumentation constitutes an epistemological obstacle to the learning of mathematical proof and more generally proof in mathematics.

NOTE: There's an on-going verbal snafu that needs clarifying. The French have two words, "preuve" and "demonstration" both of which translate to "proof". The latter is definitely what would be used in the case of a theorem, and the former has a good many sub-meanings along the lines of "evidence", and some relatively informal uses. So we have opted to translate "demonstration" consistently as "mathematical proof" and "preuve" as "proof". But I'd say that the last sentence of the introduction above is clear evidence (preuve) that this solution is not flawless.

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