My view of scholarly debate considers the modern
aspects of a discipline, at best, as a secondary judge
to deciding history of math issues. That is, looking
back through time, through the prism of modern pedagogies
and modern break-throughs, even simple ones like base 10
decimals, a 400 year old practice, often confuses the
history of math's acutal roots. The history of math needs
light shed on its origins by the full reading of primary
sources, read from as many mathematical disciplines
that are reported in each document.
Another way to state my view is, to study the history of
mathematics in a scholarly manner is to read its original
texts in its historical context, separate and not muddled
in any way by modern developments. For example, neither the
math of Plato nor Pythagoras nor Euclid can be fairly read
from the well known Platonic and Pythagorean revisionist efforts
of 200AD-500 AD, nor the views of Classical scholars in the
1920's, that often only considered the geometric aspects of
Plato and Pythagoras as fully explaining Euclid and The
Elements. Plato and Pythagoras, as well as Euclid, wrote a
great deal about arithmetic and algebra within exact
systems of numeration, that are often skipped over
by well meaning scholars that write only from an
infinite series point of view.
To make my point generally, to fairly read any culture's
mathematics at any time, like reading other Greek mathe-
maticians like Archimedes, must be based on the confirmed
earlier work of Eudoxus and others from primary documents.
When only secondary documents, like Islamic sources, are
available less than a clear view of the past should be
reported (as sadly is not the case).
Touching upon your alchemy and astrology points, clearly to
read Aristotle and many other Greeks, for example, in
historical context, an odd mix of mysticism and science is
seen, even taking modern science of chemistry and astronomy
principles into account. Simply ignoring those 'odd' aspects
of original historical documents, or worse, pretending that
they do not exist, offers very poor scholarly techniques.
I hope that my points add something to your discussion.
Regards,
Milo Gardner