>
> In substance, my correspondent disagrees completely with the current fad
> that encourages teaching of the (so-called) History of Mathematics either
> to undergraduates or to normal mathematics graduates when both his/her
> eneral historical background and or intellectual maturity are below a
> reasonable (whatever the term means) threshold:
>
> "Of course, a lecturer should make the occasional historical
> remark, and it should be well founded. But it is not possible to
> acquire historical knowledge about the Renaissance authors without
> reading Italian, about the Baroque authors without Latin, about
> the 18th/19th century authors without French. And even for Peano
> we also need latine sine flexione. Every translation is already
> an interpretation. Second hand clothes may be acceptable; second
> hand knowledge is not."
>
> Reactions?...
>
> Julio Gonzalez Cabillon
I have kept out of this before now, but found myself feeling so
sympathetic to the remarks of this correspondent (almost despite
myself) that I now feel I should say why.
I feel that with most students, time spent teaching mathematical
history would almost always be better spent teaching mathematics.
This holds even in very good universities like the ones I've taught
in; Cambridge and Princeton, in each of which I've taught courses in
mathematical history.
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 think that there IS a place for courses on mathematical history -
namely ones aimed at the best mathematical students, but only after
they've learned a lot of mathematics, and taught by teachers who
know both the modern mathematics and its history. In other words,
such courses should come AFTER the students learn the mathematics
rather than BEFORE or WHILE they do so, and with both the teacher and the
students knowing the consequential mathematics.
I believe this used to be the way it was done, but nowadays there are
many mathematical history courses that are taught to students who don't
know much mathematics, and which therefore consist of a few tidbits
about number-systems and the like, which are quite interesting but
mathematically trivial, and better displaced by teaching real mathematics.
John Conway