(
Re-post
)

Let's get this straight: the Chinese (and Indians... and anybody except the Greeks of antiquity and modern Europeans) were extremely feeble thinkers. Their "thought" (as far as I can determine), before the 19th century and contact with Western science, mostly consisted of childish metaphors, false analogies (that they don't even follow through to the end), etc., instead of the actual shaping of exact conceptions. So the Chinese will be another excuse to talk about the Greeks. The former lacked:

* The notion of an exact mathematical proof, and more importantly, the necessity of proving things in general. The consequence of this is the lack of any complicated notions, or concepts that split into subconcepts in an involuted way (and so, no recursive concepts (like the notion of a "derivative" in calculus - and BTW, the notion of a derivative is necessary for any concept of "potential" in any part of physics, or pretty much just all of modern mathematics and physics), no genuine "models" of anything in reality). A Hungarian historian of science (I believe it was Szebo or some such) argued that the Greeks developed the notion of mathematical proof from the Eleatic philosophers, and their method of "indirect demonstration" (i.e., argument by contradiction). Now, contradiction arguments are in principle of limited technical interest - you only use fragments of the information given, and follow its deductive consequences. A proof only gets
interesting
, on the other hand, when you build
up
. That is, it leads to the making of
constructions
(such as in elementary geometry or number theory) that have no direct analogues with anything known, but which captures all of the information at once, from which something deductively follows. You are (in the attempt to prove something difficult) impelled to build up - by pure trial and error at first, with nothing more than the conviction that there must be something there; something more than merely one or other piece of the problem. An easy example of this would be the compactness theorem of predicate logic in the countable case (proved by Goedel) - you make a construction that captures all the information at once, rather than one at a time (by means of contradiction arguments).

This is actually the source of mathematical advance - first there must be the vast variety of different constructions (e.g., inductively defined objects) for specific purposes, and only then can you see the analogy between them - or the analogy between how one construction captures information in one case rather than another.

* But even without the above, what a formal proof impels one to do is to
break apart
or decompose conceptions, as Leibniz talked about - except one sees the analogy between
how
one problem is broken into subproblems, and the case in another. (It is all a matter of
*
how
*
it is split into subproblems, and the wrong way to decompose a problem will simply cause confusion.) And there is also the general notion of quantification, and the difference between the intensional and extensional view (Leibniz took the intensional view). The Chinese never systematically took concepts apart, never improved notation, etc., and so they never ... etc.

* More fundamentally, every single leap in our mode of knowledge is due to importing
methods
from one area of thought into another. The creation of pure mathematics is a case in point. Aristotle's categories, creation of formal logic, and general mode of "classification" (the simple and powerful notions that form the basis of metaphysics) were taken by applying methods of classification from medicine and biology, and one should not forget that Aristotle was an
*
Asclepiad
*
. Leibniz was the first to see the full
range
of symbolical analogy - consider, for example, the easy way in which he drew the striking correspondence between a n-th order differential operator and the exponentials of the binomial expansion (the
**
Rule of Leibniz
**
:

... or the way the Leibnizian notation developed into the calculus, and
*
these
*
were in fact (I am convinced) due to his application of methods from juridical reasoning and practice into mathematics (Euler then inherited the best tendencies of both Leibniz and Newton). Thomson's principle of seeking an analogy between different
regions
of physical theory was inspired by Boole's symbolical methods (at least this is very plausible - the one treatise came out when Thomson was a teenager). Maxwell took this
to its height
and it has only recently been
**
reconstructed
**
by moderns.

* The Chinese (and Indians) might be forgiven for not having the notion of proof, since the notion itself is so counterintuitive (in fact Newton first throught that Euclid was silly, since one should not "prove" what is obvious) that it is still an open question how the Greeks came upon it in the first place. But they cannot be forgiven for not thinking about the methods of thought. There is the kind of thinker that immediately classifies conceptions so as to maintain the broadest range of analogy and possible combinations between them - Leibniz was such a thinker, as was Boole and Thomson and Maxwell, and on a smaller scale, in modern mathematics we have the founders of functional analysis (like Riesz), Gel'fand, Margulis (the greatest possible variety of connections between heterogeneous methods of proof - from ergodic theory, semisimple groups, etc.). Now, the Chinese have a word for "analogy" in their language. But most damningly, they never saw that the entire point was not about the analogy, but the kind of
object
that might be distinguished (in a continuous way) that the analogy is between. (And without explicitly thinking about the methods of thought, one never arrives at the notion of a "resemblance between two relations of resemblance".)

* Where the Chinese (not Indians) excel is in a purely "technical" form of intelligence. This is purely technical genius, which does not have to think about the methods of thought (and doesn't even have to think about the "big picture" or strategic "center" of a certain subject, as Newton and others did), since it has some ability to adjust all mental operations to suit some activity. That activity involves having a very fine sense of discrimination, to navigate betwen the thickets where every notion strongly resembles everything else (like Norbert Wiener's technical genius, in fourier analysis), but
without
making a vast simplification. Rather, the complicated remains complicated. (In this category we have Lennart Carlson and Vinogradov, arguably the two greatest "technical geniuses" ever.) Now, the Chinese mathematicians are mostly purely technical except for Chern. India has produced two great thinkers - Ramanujan and Harish-Chandra, great at least in seeing the
deep
connections that are literally approximate resemblances (this can also be said for Archimedes, Newton, Heaviside, I. Schur), rather than the greatest
diversity
of analogy (like: Leibniz, C. S. Peirce, Riesz, Gel'fand).

The "philosophic" legacy of China is
**
exactly zero
**
. To put this in perspective, Poland alone (Twardowski, Lesniewski, Kotarbinski, Wolenski even) has a much stronger philosophic legacy than China.