"All philosophical advances had a great charm for
him [Gauss], although he often disapproved of the
means by which they had been attained".
The HUMAN means by which advances (and not just philosophical ones)
get attained give strong reasons for the study of the history of
academic fields, mathematics strongly among them.
I came upon the following argument for historical work in science and
mathematics, not only for its own sake, but for the sake of safety and
solid progress. I hoped it might interest some of you, as well. P.W.
Bridgman spoke of physics here, but I believe that some of what he says
applies to the human enterprise of mathematics, as well.
*****************
The introduction to THE THERMODYNAMICS OF ELECTRICAL PHENOMENA IN METALS
by Percy W. Bridgman (McMillan Co, 1934) starts as follows.
(Bridgman was Hollis Professor of Mathematics and Natural Philosophy,
Harvard University, winner of the Nobel Prize in Physics, and "patron
saint" of engineering measurement theory.)
"The progress of physics is unsystematic. The activities of the moment
are determined by the most compelling interests of physicists at that
moment, and into this enter many complex and human elements. There is a
little of the element of sheer fashion, for most physicists are gregarious,
and enjoy talking over common activities with their fellows; there is the
strategical element, for it is only human prudence to cultivate the fields
in which success is most probable, and this usually means a new field; and
there is the economic element, which demands that an experiment shall not
involve to costly an apparatus. The development of physics is thus not
always in that direction which would be taken by a competent dictator,
charged with the task of getting intellectual mastery of the physical
world as rapidly as possible, nor, indeed, is it in the direction which
would be chosen by the majority of physicists themselves, if they could be
freed from ulterior considerations. The result is that physics sometimes
passes on to new territory before sufficiently consolidating territory
already entered; it assumes sometimes too easily that results are secure
and bases further advance on them, thereby laying itself open to further
possible retreat. This is easy to understand in a subject in which
development of the great fundamental concepts is often slow; a new
generation appears before the concept has been really salted down, and
assumes in the uncritical enthusiasm of youth that everything taught it in
school is gospel truth, and forgets the doubts and tentative gropings of
the great founders in its eagerness to make applications of the concepts
and pass on to the next triumph.
"In particular has all this been true of the development of our theories
of the electrical properties of matter. The historical development of
the fundamental ideas spread over a long time, sixty years from Poisson
to the formulation of the field equations for stationary bodies by Maxwell,
to pick out two important landmarks. It is true that the expression for
the mechanical action of an electrical current was formulated at once by
Amp\ere in its final form "leaping, full grown and full armed, from the
brain of the 'Newton of electricity'," to quote Maxwell, but this was
only an episode and a rare exception. The ideas of the proper way to
measure the strength of an electrical current, the equivalence of static
and current electricity, the conception of resistance and the proper way
of measuring it, the conception of electromotive force were all of slow
growth, and involved continual rumination and chewing of the cud of
contemplation to determine whether the picture that was forming itself was
a consistent picture and capable of including new facts as they were
discovered. But each new physicist, as he enters the lists, is in danger
of forgetting all the past rumination and the present uncertainty, and
of starting with an uncritical acceptance of the concepts in the stage
of development in which he finds them."
**********
Work to soften that danger seems worthwhile, and fascinating as well.
Bob.