What does the Many-Body Problem say about mathematical physics? I was interested to read the answers to the other Many-Body Problem questions on this site and was left with one nagging question of my own. What does the Many-Body Problem reveal about reality and our attempt to understand it? To explain: if the solutions we find to this problem are in the form of lengthy iterative expansions may this not signify in some way that nature operates along discrete iterative paths? What does this say about our theories if these problems are so difficult/time-consuming for them but so quickly solved by the real world around us? Is this problematic? Will more complete theories-ie possibly string theory- address this or do they even need to? 
 A: The core of the question is about whether Infinite sums and similar expressions which appear in many attempts at an analytical solution to equations of motion can represent "how Nature does it". Well Feynman once noted something similar in an analysis which ended with the observation that "down at the electron there seemed to be a lot of computation going on in a very small region".
Part of the answer for classical physics is that we dont always represent the problem that Nature is solving locally: particles move in their local field according to local potentials. In analysing a larger system we find difficult analytics, but Nature never has to solve these.
In Quantum Mechanics (and its relatives) we reach the wavefunction ontology question. That is "is the wavefunction just our representation of the physical reality" or "is the wavefunction actually physical reality"?
Clearly if the wavefunction is just our representation then it is not telling us what Nature actually does; and the analytic issues we have with it (e.g. in the N body case) are just our problem, not Nature's. What Nature actually does would then be a theory which reduces to Quantum Mechanics. The compututational world might describe such a theory as "a theory which Implements Quantum Mechanics".
If the wavefunction corresponds directly to reality, then there probably is still some need to find a good "computational engine" for making it all work. The Quantum Computational school around David Deutsch seem to be in this area.
As far as N-body issues are concerned I am becoming impressed by the "emergent properties" found in that area by the Condensed Matter Physicists. Perhaps this is telling us that Nature has found "higher level descriptions" with which to work with complex systems.
I am still learning about String Theory, but I am getting the impression that it is quite "conventional" in terms of these types of fundamental issues with QM.
