I'm a relatively new member of this list, so forgive
me if I'm stating what is already obvious.
It is becoming apparent to me that we have at least two
substantially different groups of people on this list,
who are thinking about how to achieve different objectives --
Some of the people in this list are very learned historians
of math, in many cases engaged in writing books or research
papers about the subject.
Others (like me) are newcomers to the subject -- I'm presently
teaching History of Math for my first time, because the
fellow who used to teach it here has just retired.
So the question "What should we do in the history of math"
really refers to at least two different things: (i) What
should we do in our research on that subject, and (ii) What
should we do in that subject when we teach it to undergraduates?
There may be other meanings too.
> >Did Grattan-Guiness
> >mean we just stick to the records of an epoch when we are describing
> >mathematical work of that epoch, and not be guided by a current state of
> >mathematics, as we see it? If the latter, we are faced with vexing
> >historiographical questions about how we can sufficiently eliminate
> >relevant parts of ourselves and our cultures from our historical
> >interpretations,
It is my experience that my undergraduate students have very
little knowledge of the mathematics of our own modern culture.
I find that in order to make any sense out of the history,
I first have to teach them some of the more recent stuff.
For instance, in order to explain what infinitesimals are
and what Dedekind's definition of the reals meant and
why angles can't be trisected and several
other historical topics, I first have to give a modern definition
of a "field." I suppose things could be taught in chronological
order, but I think it would take much much longer that way.
The modern, abstract definition gives us a framework in which
we can talk about all these older topics, skipping over the
old confusions and misunderstandings -- or perhaps discussing
some of the confusions and misunderstandings *after* we've
considered the correct explanations.
I guess this makes me a "Whig" historian. Can someone recommend
one or two elementary things I should read, to begin to reduce
my Whigginess?