Hello Jack.
> The following four questions seem distinct to me. I do not propose any
> answer for any of them, nor do I mean to assert that any one of them is
> more or less telling or answerable than any other, or that they are the
> only legitimate questions, or even the most important ones. I do suggest
> that they are quite likely independent of each other, and thus that in the
> discussion it might be helpful to recognize each of them and to explicitly
> distinguish them from each other.
I'll briefly state my opinion on each of the questions.
>
> 1. Has the mathematics of Greek descent produced mathematically valuable
> or interesting results that other imaginable or existing "cultures of
> mathematics" could not produce?
This should be two questions.
Yes, Greek mathematics has produced mathematically valuable
results and principles that other existing cultures has not produced.
No, Greek mathematics has not produced results or principles that
could not be produced by other kinds of cultures.
>
> 2. Could other imaginable or existing "cultures of mathematics" produce
> mathematically valuable or interesting results that the mathematics of
> Greek descent can not produce or has not produced?
Again this should be two questions.
Yes, other cultures could produce results that Greek mathematics
has not produced.
No, other cultures could not produce results that Greek
mathematics could not produce.
>
> 3. Has the mathematics of Greek descent enabled valuable or interesting
> knowledge outside the field of mathematics that other imaginable or
> existing "cultures of mathematics" could not enable?
No. All cultures, sufficiently developed, lead to the same [
meaning equivalent ] body of mathematical knowledge.
>
> 4. Could other imaginable or existing "cultures of mathematics" enable
> valuable or interesting knowledge outside the field of mathematics that
> the mathematics of Greek descent can not enable or has not enabled?
This should also be two questions.
Yes, other mathematical cultures could enable non-mathematical
knowledge different than any that has flowed from the Greek
mathematics.
No, other mathematical cultures could not give us a non-
mathematical knowledge underivable from sufficiently developed
Greek style mathematics.
>
> Jack V. Wales, Jr.
> 5025 Thacher Road
> Ojai, CA 93023
>
> jwales@thacher.org
>
>