>> The difference between these two questions is worth pondering.
>> Answers to the second one draw _only_ on those parts of the
>> past that have led to our present situation; while a perfectly
>> respectable form of research, they can give quite mistaken
>> impressions about the aims and purposes of historical figures,
>> and the priorities they saw in their own work."
Gordon Fisher posted a terrific reply, and the main point
I got from it was: This distinction is obviously attractive when
you first hear it, but it just gets more and more difficult to
understand (if not impossible) when you try to use it.
I want to add a little bit about one possible interpretation
that Gordon offered:
>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,
Such an effort is insane in history of math. Take Dedekind's
algebraic number theory. Few mathematicians in Dedekind's time saw
even a good fraction of what Dedekind had done (Weber, Frobenius,
maybe Kronecker but he disliked much of it). Emmy Noether later showed
there was much more already in Dedekind.
So, even if you are a peer of Frobenius, willing to work as
long and hard on it as he did, if you study Dedekind just from the
work of his epoch you will miss most of what Dedekind himself saw.
Only if you are a peer of Dedekind, or Emmy Noether, can you hope ....