## 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.

[Back to index]