The contempt I sense can be indicated as follows: "Why worry," someone
says, "over what actually happened in mathematical developments, when
what's important is to get students interested in mathematics, and
entertain them between the harder parts with some nice little anecdotes
which often have little relationship, or a false relationship, to what
actually happened. And, anyway, what good is knowing what actually
happened to someone who is interested in the timeless activity known as
doing mathematics? Why, look at me, I'm good at mathematics, and I don't
know much about what actually happened!" Truth is essential in
mathematics, but truth in history be damned!
Of course, in creating mathematics which is allegedly new, one would like
to know what's already been done in a chosen specialty. However, lots of
mathematians, what with pressures of one sort or another, have to content
themselves with whatever they can become acquainted with that's been done
in the 10 or 20 years before they start working, and hope they've absorbed
enough to guide them into new and interesting paths. (Cf statements of the
sort "by a classic theorem of XXX, so-and-so", where XXX turns out to have
proved the theorem ten years before, and the fact that the genesis of the
theorem is traceable to Euler or Lagrange or the like, or to some lesser
known mathematician, lies hidden.)
Often what happens is that a dissertation director is relied on to guide a
person starting out on creative mathematics, and some dissertation
directors have had good dissertation directors, and so on, back to Gauss or
Erdos or someone like that. And some mathematicians, especially as they
get older, become curious about the significance and relevance of what
they've been doing, and turn to genuine history of mathematics, which they
can pass on to younger people who have the time and temperament to listen.
And there are those rare individuals who are deep and good in doing both
mathematics and history of mathematics -- two relatively recent names that
come to mind are Jean Dieudonne and B L van der Waerden, but there are others.
As I see it, one problem with a high-handed attitude to what actually
happened in mathematical developments is that mathematicians become separated
from their roots. For example, in my experience, many teachers of calculus
and differential equations really are teachers of foundations of calculus
and differential equations who sometimes have contempt -- that word again!
-- for physicists and chemists and engineers, and so on, who frequently
view calculus and differential equations quite differently from such
mathematicians.
Now that I think about it, I would like to suggest that, mathematicians
aside, contempts of these kinds are endemic in the human race, and often
originate as defense mechanisms. "I don't know much about that stuff, and
I don't have the time or inclination to learn about that stuff" one says,
"so it must not be important." Persons of this persuasion may then signal
the non-importance to them of pursuit of such stuff by showing contempt for
it, often enough without realizing that they are being contemptuous.
Gordon Fisher gfisher@shentel.net