Different questions are naturally intertwined, such as:
1) What do I as a mathematician learn by studying "the" history of
mathematics?
2) are there not in fact many different histories of mathematics?
3) would all mathematicians profit from studying the history of their
own subject?
4) how do these questions change if I am (a) not teaching a course, vs
(b) constrained by the artificial structures known as courses to the
kinds of students whom we have to teach whether we like it or not?
Let me introduce a couple of new questions and a new distinction.
5) what do I as a historian learn from studying histories of
mathematics?
6) what price do HISTORIANS pay for NOT studying histories of
mathematics?
The new distinction I propose for your consideration is between
historiography and hagiography -- i.e. between "history" and "the
lives of the saints". Like many mathematicians I was moved, indeed
converted, as a child by reading E T Bell, and I too wanted to be a
"Man of Mathematics". But ET Bell is hagiographic -- I am speaking in
terms of literary genres right now. Hagiography is not necessarily a
bad thing, it has its low and its high versions; E T Bell is "high";
anecdotes about Archimedes in the bath tub and Gauss adding the
numbers from 1 to 100 are "low" hagiography.
The religious analogy has already been introduced into this thread:
one could thus ask whether priests of a religion should learn (and
teach -- to whom?) the history of their own "dogma"? And in what
form?
My main point (for now) is this: historians today are well aware of
the many different literary devices they use to give their stories a
plot. Plotting the history of mathematics as the story of a group of
saints whose virtues we sinners can all draw on (if we believe) is
only one method. There are others, such as the method used by
Lakatos.
May this suffice for my "maiden speech" to this august body of
colleagues.
Su humilde servidor
Tomas Kalmar