A reasonable starting point for a discussion of the many-body problem might be the question of how many bodies are required before we have a problem. Prof. G.E. Brown has pointed out that, for those interested in exact solutions, this can be answered by a look at history. In eighteenth-century Newtonian mechanics, the three-body problem was insoluble. With the birth of general relativity around 1910, and quantum electrodynamics around 1930, the two- and one-body problems became insoluble. And with modern quantum field theory, the problem of zero bodies (vacuum) is insoluble. So, if we are out after exact solutions, no bodies at all is already too many.
– Richard Mattuck, A Guide to Feynman Diagrams and the Many-Body Problem