Indeed, how can we understand what the 'important' did without
understanding the 'normal' mathematics of their time? True, they read
and corresponded with other high flyers: but they began by reading the
same things that were available to other students. They performed the
routine calculations of their times, as well as inventing new ones.
They taught the elementary mathematics of their times. They swam in it,
even if leaping like dolphins.
The problem is even worse in the study of literature. That field is now
better at recognizing important women, but it is even worse at noticing
the context of the great. The 'canonical' writers of each period read
far more of the 'unimportant' books, pamphlets and broadsides of their
time than present scholars do, and refer to them (by theme, structure or
allusion) as often as to their now-considered equals. Study of only the
canon guarantees the canon will be understood.
We don't do the history of technology this way. From flint spearpoints
to aircraft, we carefully record what was regularly done in the
workshops of the time, and used by the mass of the people. Sure, there
are names associated with the steam engine and the cotton gin, but our
books notice the people picking and spinning and weaving and driving and
laying track.
Why do we teach the history of mathematics and literature as though they
were irrelevant to the people they served, and unresponsive to them? To
make the subjects seem irrelevant to our students? Is the nine-point
circle really more important than the management of numerical records?
Double-entry book-keeping, invented independently around the world, is
quite as important a handling of consistency issues as the independence
of the Axiom of Choice. Logical and numerical consistency history both
flow into the development of modern control software, which requires
modules such as a 'truth maintenance engine'. Should truth tables be
taught only to prove the consistency of the propositional calculus?
Where are the histories of working mathematics?
Tim Poston
_________________________________________________________________________
"Sure, it was written by dead white males,
but most of them weren't dead when they wrote it."