Progress in mathematics develops in response to its
internal needs, whether in application or internal explication.
Certainly Euclidean geometry couldn't address questions
of the measurement of curved space adequately. Attempts
were at best provisional. This contradiction wasn't resolved
until the rise of the insights of Lobachevsky, Bolya, and of
course, Gauss.
As for ethnomathematics, consider this. Until the 1970's,
there were many who either ignored or chose to downplay
progress from the Russian school. One loses count of the
number of omissions to individuals like Ostrogradsky or
Buniakovski in calculus books. Certainly the mathematical
establishment knew of their work, but stubbornly omitted
reference. Was this a legacy of the Cold War ? In short,
politics does play a role in the dissemination of knowledge.
With this in mind, I have much difficulty with the handful
of older texts which either deride or ignore the work of Muslim
mathematician. Certainly scholars like al-Haitham were
known to the community at large, but why did so many
historians of mathematics choose to downplay their contri-
butions ? Was it because they were unholy infidels ? Why
did the Spaniards burn every Mayan text (codex) they
collected. I recall reference to soldiers drinking and eating
for nights to the lights of the bonfires for several weeks.
Why was the library of Alexandria destroyed so many times?
>
No, the rise and spread of European business and commerce
ultimately retarded the further development of mathematics
in the countries which it came to dominate. I believe the term
is 'underdevelopment', certainly fashionable during the '70s.
After all, why should these colonized peoples be concerned
with abstract thought while their labor power could be used
to supply European countries with natural resources ?
In this regard, while ethnomathematics won't enable us to
determine how the curvature of space is dictated by the
distribution of matter or why the algebra of events is applicable
at the atomic level, it will help open our eyes to the progress
made by those societies which were dominated by European
capital. Certainly "lost" work by scholars in formerly colonized
nations must be recovered and translated. In this regard, we
can be grateful for the progress in that direction. Ultimately,
it's part of our legacy.
Al Barron