<<I said that axiomatization led to non-Euclidean geometry.>>
Might one not also argue that axiomatization and a concern for it leads to the
production of "more" mathematics because it inspires a search for as many of
the most specific consequences of a general statement as possible?
In a later message the same day, Roger Cooke wrote:
<<All the most important things needed for human survival are low-tech things
that don't require any particular intelligence. The human race would never
have survived if they weren't.>>
I don't think it can be assumed without argument that <<all the most important
things needed for human survival are low-tech things that don't require any
particular intelligence>>. "Low-tech" is a term more cultural than scientific
and highly relative. Consider flint-knapping in the 20th millennium or
planting in the 8th or irrigation in the 5th, just for three of the most
essential techniques, all high-tech in their day. One of them, planting,
requires a rather more than arithmetical knowledge of astronomy, and
irrigation is the principal reason for the early development of geometry. I
can recommend Levi-Strauss's _The Savage Mind_ which helped me to unmoor
myself from the assumption that technology is somehow an objective or trans-
historical category.
-Bill Everdell, Brooklyn