I was thinking what kind of a culture I would want to surround mathematics and I thought of a few. I will briefly describe them here.
One is that idea of universality. As found from this site, an author claims that it is "unquestionably the only universal language" and I really have to agree. No matter where you are, calculus is calculus, number theory is number theory. How it is approached is different, but no matter what, the language of math is similar and the concepts are similar. I think in an increasingly globalized world, universality is important.
I think there is also the constant search for the explanation of the inexplainable, so I believe that it is almost a mystical kind of culture. We believe in this concept of infinity, which no one can touch, see or ever come in contact with. Different mathematicians have looked to mathematics to map hell, describe why it is safer to assume that God exists, or even attempt to reason the existence of God. We believe in the absolute logic of the mathematical language that the "proof" will come.
It is also the culture of precision and science. No other language could so eloquently describe the planets' movement around the sun or any such theory?
There are binary opposites in that it is the study of absolutes and unknowns; that sometimes there can be an exact answer and sometimes there are an infinite amount of answers and an infinite amount of ways to get there.
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