Re: [HM] History of Mathematics: to whom?
Ken Pledger (Ken.Pledger@vuw.ac.nz)
Thu, 15 Apr 1999 09:18:41 +1200
At 3.35 am +1200 15-4-99, John Conway wrote:
> ....
> The reason is that for the history to be at all worth while it
> should be more than that of elementary mathematics. It should contain
> a discussion of evolution of the subtle concepts the students are
> learning in their mathematical courses. But for most of these, a
> course specifically on mathematical history is not the most appropriate
> place, because its teacher can seldom be sure that all the students
> really are familiar with the modern versions of these concepts: there's
> no point in teaching how we got to X to students who don't really
> understand the point of X itself.
>
> So the best place to say something about this kind of X will usually
> be in the courses where X is taught. Of course this requires that the
> teacher of mathematics must also be the teacher of mathematical history,
> and doesn't work too well nowadays because too many mathematicians are
> unfamiliar with mathematical history. But the reason above isn't the
> only why the specialist courses don't work too well - another is that
> nowadays many specialist mathematical historians don't know too much
> mathematics!
> ....
I'm currently teaching introductory group theory. I began with the
16th century Italian solutions of the cubic and quartic equations, then
used the Lagrange resolvents to illustrate permutations of the roots.
After some elementary work on permutation groups in the style of Cauchy
(but no Galois theory), we reached modern group axioms in the seventh
lecture.
My knowledge of this history is imperfect, and the purpose of the
course is not history but algebra. Was I wrong to do it?
Ken Pledger.