TITLE: What are examples of (collections of) papers which "close" a field?
QUESTION [78 upvotes]: There is sometimes talk of fields of mathematics being "closed", "ended", or "completed" by a paper or collection of papers. It seems as though this could happen in two ways:

A total characterisation, where somehow "all of the information" about a field has been uncovered.
A negative result, rendering the field somehow irrelevant.

A possible example for 1 might be the classification of finite simple groups. Examples for 2 might be Goedel's theorem effectively halting Hilbert's programme, or results showing e.g. certain large cardinal axioms to be inconsistent undermining work which assumes it.
What are some other examples of results "closing" a field? 
Are there examples of a small number of papers "completing" a field in the sense of 1 above?
(Apologies for many scare quotes!)

REPLY [3 votes]: Hilbert's famous work seemed to have killed Invariant Theory. At least that's what Gordan felt at that time. In the historical book by Dieudonn'e' and Carrell  they say  invariant theory, presumed  dead, as coming back alive from the ashes like phoenix.