In mathematics, abstract nonsense, general abstract nonsense, and general nonsense are terms used facetiously by some mathematicians to describe certain kinds of arguments and methods related to category theory. (Very) roughly speaking, category theory is the study of the general form of mathematical theories, without regard to their content. As a result, a proof that relies on category theoretic ideas often seems slightly out of context to those who are not used to such abstraction, sometimes to the extent that it resembles a comical non sequitur. Such proofs are sometimes dubbed “abstract nonsense” as a light-hearted way of alerting people to their abstract nature.
More generally, “abstract nonsense” may refer to any proof (humorous or not) that uses primarily category theoretic methods, or even to the study of category theory itself. Note that referring to an argument as "abstract nonsense" is not supposed to be a derogatory expression, and is actually often a compliment regarding the sophistication of the argument.
Other articles related to "abstract nonsense, abstract, nonsense":
... abstract nonsense Also general abstract nonsense or generalized abstract nonsense, a tongue-in-cheek reference to category theory, using which one can ... introduced the very abstract idea of a 'category' — a subject then called 'general abstract nonsense'! —Saunders Mac Lane (1997) raised algebraic geometry to a new level of abstraction ...
... By a general nonsense argument, there is a map to the Eilenberg-MacLane space, corresponding to a non-trivial element in H2(M) ... difficult proof might be surprised—or even delighted—by this bit of general nonsense ...
Famous quotes containing the words nonsense and/or abstract:
“But its nonsense to think hed care enough.
You mean you couldnt understand his caring.
Oh, but you see he hadnt had enough....”
—Robert Frost (18741963)
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (18421910)