I guess I have a difficult time understanding what is actually being asked here. "Culture" is such an amorphous word that it needs to be better defined before we can really tell what you're talking about. Mathematics and the natural sciences are a part of our culture, and they only exist in service to it.
All math and science comes about to serve a cultural function, if it doesn't it becomes obsolete: anyone taking alchemy 101? Astronomy and telescopes came about in an effort to better understand messages from the gods in constellation form. Anatomy developed from painters' desire to portray the human body better. Computers were developed to break Nazi codes, and also to keep records of their final solution for the Jews.
Phukraut was right to point out that in the past these distinctions between "culture" and "science" as seperate worlds were non-existant. It's is really only in the past 150 years that we see specialization, mostly through the university system, of different fields of knowledge.
Rene Descartes (1596-1650) was the father of both Cartesian geometry and metaphysical philosophy. I'm sure he could have explained his philosophy in mathematical terms if he had to. Likewise if you delve into mathematics deeply, it's all just philosophical belief--the concept of numbers, zero, infinity, etc.
"Pure" knowledge is never pure, it's always framed by a cultural context and purpose. Even the most arcane mathematical theory is judged on the basis of it's applicability. If that application is to one-up your contemporaries or to impress coeds then it will likely be forgotten soon. Conversely if your theorem is useful in creating nuclear fission or predicting the weather, you will be remembered and celebrated.
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