Book: Gödel Escher and Bach

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The book Gödel, Escher, Bach: An eternal golden braid, from 1979 by Douglas Hofstadter, contains many recursive and self-referential themes.

Examples of Russell's paradox are covered.

A detailed explanation of Gödel's incompleteness theorem is covered at a high level for intuitive understanding purposes.

That "out of the box" or "above" idea of "meta" as in "metaphysics" is used in computer science as a prefix to describe something about itself.

This idea became popularized by Douglas Hofstadter's book Gödel, Escher and Bach which discussed self-reference in general and Gödel's proof in detail.

An elegant statement of a recursive self-referential principle is Hofstadter's Law.

Hofstadter's Law: It always takes longer than you expect, even when you take into account Hofstadter's Law.

Gödel, Escher, Bach: An eternal golden braid

Mathematics is the study of mathematical systems.

Hofstadter: "Mathematics is what mathematicians do". Hofstadter, D. (1979). Gödel, Escher, Bach: An eternal golden braid. New York: Vintage Books., p. 559.

Hofstadter makes the claim that mathematics is what mathematicians do. Citing the example of Ramanujam, he goes on to assert that all mathematicians are isomorphic in the sense that they think in the same way. What exactly is that way? In part, mathematicians are able to abstract away details to such an extent that they become the butt of jokes indicating a loss of touch with reality. By the beginning of the 20th century, mathematics as a field had pretty much decided to divorce itself from reality (including philosophical questions) by making mathematics a formal system of symbols and symbol manipulation.