As many friends in the network have already pointed out, there
are a number of issues involved in the discussion : (1) doing research
in history of mathematics, (2) teaching history of mathematics as a
subject, (3) integrating history of mathematics in teaching
mathematics. These are closely related and yet are separate issues.
One can further subdivide (3) into : (3a) for studying a certain
subject area in mathematics, (3b) for general motivation and
enjoyment, (3c) for an even more general awareness of human culture.
Ever since I began teaching mathematics in 1972 I got interested in
(3), the enthusiasm for which grows with time. I cannot claim
myself to be a historian of mathematics as I am brought up as a
mathematician rather than as a historian of mathematics, but I do
proclaim myself to be a "friend of history of mathematics". Enough
has been said by many friends in the stream of emails to clarify the
argument. I benefit from reading all of them. There are two points I
like to add ( or echo ).
(1) At one point in the plenary talk mentioned above, I played the
devil's advocate in proposing a list of "cons" on the use of history
of mathematics in the classroom. Among those "cons" one item happens
to strike the same chord raised by your friend, viz. "both his/her
[the student's] general historical background and or intellectual
maturity are below a reasonable (whatever the term means) threshold".
However, an answer to turn this "con" into "pro" is : we can make use
of this opportunity to let students see something about history and
more generally about culture, and to generate a regard for learning. I
find that many students do appreciate it and begin to feel how
mathematics forms part of the cultural heritage of the human race,
even though they may have mistaken history for a dry and dead subject
in their school years.
(2) I am thankful to the listmember who brought up the point on
history of mathematics for non-mathematicians [ the term
"mathematician" is used here in a rather wide sense to include anybody
who studies mathematics, e.g. a school pupil in the mathematics
classroom ]. It leads me to think about a related question : In the
ancient world, who were the mathematicians? Unlike in the modern
world, the mathematicians in the ancient world did not really comprise
a well-defined group. I do not know enough to speak about what the
situation was like in the Western world. Let me say a few words about
what it was like in ancient China to illustrate my point. For the
past few months I was studying the state curriculum and examination
in mathematics in the Tang Dynasty (618- 907) in ancient China. In
connection with this I look into the question : Who were the
mathematicians? It seems that, besides those "official" mathematicians
who were employed as imperial astronomers or officials in charge of
engineering works, or those "unofficial" mathematicians who left us
with written mathematical classics or commentaries on earlier
mathematical classics, mathematical activities were also carried out
among others such as buddhist monks, taoist priests, craftsmen,
merchants, or even hermits. In this sense, mathematics appeared in the
full social web. Maybe that is why your friend maintains that history
of mathematics is closely tied up with the history of the time.
I am sorry to have written this long to take up much of your
time ( and that of others in the network ). I left the MATH-HIST-LIST
network in July 1997 and do not join your network until recently
precisely because I feel that I cannot cope with the bulk of incoming
emails from the network. I should have therefore kept my email short!
Anyway, thanks for the discussion you help to generate, and all the
best!
Man-Keung
SIU Man-Keung
Department of Mathematics
University of Hong Kong
Hong Kong SAR, CHINA