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That answer would be affected by what your perception of the role of Mathematics is. The public would be more concerned about the actual applications of Mathematics, but in Pure mathematics in subjects such as group theory, there are almost no applications whatsoever. In pure mathematics, TODAY i dont think there is any influence of culture, and I dont think that the mathematicians are missing out in any way. Pure mathematics is carried out for the mathematical knowledge that is gained from these subjects, and it is the desire for pursuit of knowledge that drives the Mathematicians, not any cultural influence. I also believe that in pure mathematics, we have exhausted our sources of revelation from culture, and the influence of culture is minimal - just as it should be .
In applied mathematics, the maths that is carried out is usually for some form of application to the general public. Take for example statistics and the bell curve, and its use in the SAts, IQ tests... A lot of what is done in Mathematics is also imported into other areas of knowledge.. for example Physics where the trig ratios and graphs are used in the analysis of AC currents. Culture here plays a pretty significant role, but as you said it's not part of the 'jelly.' it's what CAUSES the maths to be opened up, but does not affect the ACTUAL math. so culture does play some sort of role in Maths, or rather DID, the role of culture now even in applied maths is minimal, everything that is needed for our lives seems to have already been found.
So the answer to your question is... we may never know. We just dont know enough about our situation in this world to answer that question. We may think that we have unlocked most of the doors in Mathematics, but there may still be things out there that we cannot even imagine..something like the other dimensions. But to me, it seems that no one is missing out because of the mininmal influence of culture.
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