RSA- why does it work

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Recently studied some of the mathematics behind the RSA encryption scheme. From what I have seen, the proof that finding the prime factorization of a number is super-polynomial time is yet to be found. I'm trying to sharp my common sense about algorithms. How can the world of cryptography relay on this problem to be that "hard to calculate" so much and does not seek a solid method that has it's proof documented? I mean, it could be that it's not super polynomial time, and in one day everything will fall apart..