> > 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?
No of course not - indeed you make my point, which as I said in
the paragraph I've left "upstairs", is that the best place to teach
the history of many mathematical concepts X is in the courses
where X is being taught. Specialized courses in the history
of mathematics cannot do this, since it cannot be guaranteed that
their students will actually understand the concept X.
John Conway