I will add one thing; I want to answer directly the question appearing in your second paragraph. Indeed, reading the original work of an author (i.e. in the original language) is important in order to get the original feeling and to understand the original meaning. For example, I remember reading about a confusion over Michel Foucault's work: some American philosophers disagreed with the meaning of a certain word in the author's work, but actually the misunderstanding arose from the translation (I think the word was "folie", which can be translated as both "insanity" and "folly"). This issue can sometimes be resolved by returning to the original version, where nothing can be lost in translation.
However, you ask if the same is true of mathematics. As noted above, the answer depends on your intentions. When you are learning mathematics itself, you don't need to understand the author's cogitation. First of all, the results stand by themselves, regardless of whom discovered them. Moreover, what is really needed in general is motivation, which comes from within mathematics, and not from the author's cogitation. And again, the main issue has to do with notation and concepts, which evolves constantly and at an ever more rapid pace.