> In my view, the Greeks added something that no one else did, not just
> deduction, but the axiomatic approach in general. I don't see how we
> would ever have arrived at non-Euclidean geometry from any other point of
> view. This isn't Eurocentrism, in any case. Ibn al-Haitham worked right
> on the main line from Euclid to Lobachevsky, as did many other Muslim
> mathematicians.
>
> I have the highest admiration for those who achieved so much with
> intuition alone. But, fascinating as "ethnomathematics" is, you can't
> do quantum mechanics or relativity with it.
>
There is of course the claim that Aristotle mentions the possibility of non-
Euclidean geometry in the Eudemian Ethics. Toth makes that claim in
Scientific American. Did this come from axiomatic Greek mathematics, or was it
from earlier pre-Euclidean intuitions.
We don't know whether quantum mechanics would have developed from some other
scientific tradition because Chinese mathematics, i.e., got displaced by
Western mathematics after Ricci and the Jesuits. Needham suggests that the
Chinese tried to leap to the worldview of a quantum relativistic universe
without going through Newtonian mechanics first.
Also, what does the axiomatic method have to do with quantum mechanics? Sure,
von Neumann axiomatized it after the fact, but the work of Bohr, Schroedinger,
etc was all non-axiomatic. Newton in the early calculus was hardly using
axiomatic approaches. Nor was most classical physics axiomatic, but rather
bunches of problem solutions.
Your claim is pure chauvanism.
Val Dusek