“How many bodies are required before we have a problem? G.E. Brown points out that this can be answered by a look at history.
In eighteen-century Newtonian mechanics, the three-body problem was insoluble. With the birth of relativity arround 1910 and quantum electrodynamics in 1930, the two- and one-body problems became insoluble. And within 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!”
R.D. Mattuck – A guide to Feynmann diagrams in the many-body problem (2 ed., McGraw-Hill, NY 1976)