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.
Famous quotes containing the words abstract and/or nonsense:
“All abstract sciences are nothing but the study of relations between signs.”
—Denis Diderot (1713–1784)
“Men are born to write. The gardener saves every slip, and seed, and peach-stone: his vocation is to be a planter of plants. Not less does the writer attend his affair. Whatever he beholds or experiences, comes to him as a model, and sits for its picture. He counts it all nonsense that they say, that some things are undescribable. He believes that all that can be thought can be written, first or last; and he would report the Holy Ghost, or attempt it.”
—Ralph Waldo Emerson (1803–1882)