A recent New York Times article (http://www.nytimes.com/2010/08/29/magazine/29language-t.html?_r=2&pagewanted=1) discusses the existence of "geographical" languages, in which (to put it suggestively) local coordinates relative to one's body are foreign concepts, so that (e.g.) directions are always given as "turn west, then north" rather than "turn left, then right". The article suggests that native speakers of such languages tend to have highly acute and robust senses of direction compared to those persons with different linguistic backgrounds.

Now it seems to me that this is the sort of thing that could influence the initial formulation of an idea such as a manifold as we know it. Quite possibly there are other plausible or perhaps even demonstrable examples of this sort of thing. For instance the same article mentions a language that requires attribution of facts: it seems natural to think that this might be particularly conducive to mathematical thought. I could also imagine that (e.g.) Grothendieck's particular sense of language might have influenced his thought, rather than just the other way around. So: is there (anecdotal, concrete, or best of all scientific) evidence to support a connection between native language and aspects of mathematical reasoning?

Doing a search on "language" gives a question titled something like "What great mathematics are we missing out on because of language barriers?", which may be a near duplicate. I would scrutinize the MathOverflow database before posting the question. In particular, a better question might be to ask if people who are good at geometry in the abstract are good at directions and self-location in real life, and if there is a linguistic component attached. Or even: is there a correlation between number of languages one speaks and one's ability to do certain forms of algebra (manipulation of linguistic terms across more than one domain)? The current postulated question may be too broad.

Gerhard "Ask Me About System Design" Paseman, 2010.08.30 IST

Not a comment on suitability, but Steven Pinker discusses this at length in "The Stuff of Thought," and if I remember correctly, tears it to shreds. Of course, probably not all linguists (psycholinguists? linguistic psychologists? or whatever) agree with him, but he had some pretty compelling arguments.

@Steve- You may be interested by the first section of this talk by Steven Pinker, in which he seems to mention exactly what you are talking about (vis-a-vis motivation for definition of a manifold), as coming from a *universal* character of language. Worth watching, if only for the fact that his 'how we talk about space' section seems to basically be the theory of manifolds (with boundary) (which blew my mind just a tiny bit).

With regard to the question as a whole, I like it and think it's a good question, but what you are talking about is the territory of the Sapir-Whorf hypothesis (http://en.wikipedia.org/wiki/Sapir_Worf_Hypothesis), something which, at present at least, is only suspected in its weaker forms- indeed any such mathematical divergence based on language would be a *HUGE* deal in linguistics if it existed. While it is possible that such a huge deal exists unchecked, I would be skeptical that your question would give any decisive answer either way....