> I've read this discussion with interest also. Not being in a "lofty"
> academic position as many of you, but responsible for the students you
> get in the university, I realize after 36 years that math history does
> more to inspire students than anything else I do. And, I'm a darn good
> mathematics teacher! I can teach algebra to high school students. Yet,
> they savour the subject when I talk about AlKorizmi or Hypatia. They
> remember the class when I tell stories about Descartes. Geometry is not
> the same without background about Euclid and the origins of non-Euclidian
> Geometry.
>
> Of course, my discourse is not on the level of a undergraduate or
> graduate mathematics course. But it is factual; it is interesting; and
> it is inspiring. In recent years my student who received a silver medal,
> then a gold medal in the International Mathematics Olympiads when asked
> what inspired him to university work in mathematics, he replied that
> Mrs. Michalowicz and her mathematics history stories.
>
> No one should be deprived of the beauty of mathematics history just
> because his/her level of mathematics understanding is not sophisticated.
To my mind, there's a big difference between teaching history of
mathematics, and using history of mathematics in teaching mathematics --
especially using history of mathematics as motivation and entertainment
(yes, entertainment!) in getting students to learn some mathematics. I
heartily support the latter even when a teacher using this technique has
only a modicum of knowledge about the history of mathematics.
I will go so far as to suggest that historical accuracy in teaching
mathematics from kindergarden up through about sophomore university level
(in the USA system) is less important than telling good stories about what
one thinks happened, based perhaps only on reading, say, E. T. Bell's *Men
of Mathematics*. I choose this example because Bell's book has often been
criticized, and rightly I think, for its, shall we say, mildly,
questionable judgments. However, I for one was much inspired by it when I
read it about 60 years ago, and I've heard numerous other people say they
too were inspired by it when they were young. I believe it's still in print.
When I spoke in an earlier message about teaching history of mathematics
to beginning graduate students, I was referring to teaching a course which
assumed, perhaps too hopefully, that one was talking to students who were
beyond needing motivation of the kind one wants to give in teaching
mathematics under numerous other circumstances. I suppose I was also
assuming that in a course in history of mathematics at graduate level, one
should try to be as historically accurate as is within one's means, and
also to give some idea of how one can try, in the instructor's view, to
attain an acceptable level of accuracy.
Which brings us to historiography, the subject Julio tried to get us going
about earlier. One thing I noticed long ago is that mathematicians who try
to learn something about the history of mathematics for whatever purpose
customarily find that learning or doing history is a quite different
enterprise from learning or doing mathematics as far as accuracy is
concerned. I remember an historian of science whose seminars I attended
years ago saying that in his view an historian might well being doing good
even though 20% of his or her statements of alleged fact in a book or
article were partly or wholly incorrect. If a mathematician published an
article or book with this kind of accuracy, what would people think?
Gordon Fisher gfisher@shentel.net