I think it's very important that we acknowledge non-European sources of mathematics. For one thing, if we do not do this, we are actively teaching them the false notion that all mathematics is a European invention, and so we are not doing are duty as teachers. This is not just a matter of teaching incorrect historical knowledge, either - if students believe that math is exclusively European, then they are more likely to believe it is irrelevant to them. After all, if it is a product of a single cultural area, it can hardly be universal.
Regarding the issue of the names of mathematical concepts, it's certainly true that European mathematicians are given preferential treatment. Take, for example, the result from number theory that is commonly known as the Chinese Remainder Theorem. Unlike most other theorems, it is not named after the mathematician who introduced it (Sun Tzu) but its country of origin. The (perhaps unintended) implication is that not many useful results came out of China and that this one is an anomaly, which is certainly not true. It's hard to imagine the Bolzano-Weierstrass theorem being known as the German Convergence Theorem, but perhaps it should be - it's not as if there are no confusions as to what "Cauchy's Theorem" refers to.
Ha, great example with 'German convergence theorem', an attribution which would no doubt infuriate contemporary mathematicians. Well argued and well written!
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