metamathematics n.

word-forming element of Greek origin meaning 1. "after, behind; among, between," 2. "changed, altered," 3. "higher, beyond;" from Greek meta (prep.) "in the midst of; in common with; by means of; between; in pursuit or quest of; after, next after, behind," in compounds most often meaning "change" of place, condition, etc. This is from PIE *me- "in the middle" (source also of German mit, Gothic miþ, Old English mið "with, together with, among").

The notion of "changing places with" probably led to the senses of "change of place, order, or nature," which was a principal meaning of the Greek word when used as a prefix (but it also denoted "community, participation; in common with; pursuing").

The third, modern, sense, "higher than, transcending, overarching, dealing with the most fundamental matters of," is due to misinterpretation of metaphysics (q.v.) as "science of that which transcends the physical." This has led to a prodigious erroneous extension in modern usage, with meta- affixed to the names of other sciences and disciplines, especially in the academic jargon of literary criticism: Metalanguage (1936) "a language which supplies terms for the analysis of an 'object' language;" metalinguistics (by 1949); metahistory (1957), metacommunication, etc.

"the science of quantity; the abstract science which investigates the concepts of numerical and spatial relations," 1580s; see mathematic (the older form of the word in English, attested from late 14c.) + -ics. Originally one of three branches of Aristotelian theoretical science, along with first philosophy (or metaphysics) and physics (or natural philosophy).

Mystical doctrines as to the relation of time to eternity are also reinforced by pure mathematics, for mathematical objects, such as numbers, if real at all, are eternal and not in time. Such eternal objects can be conceived as God's thoughts. [Bertrand Russell, "A History of Western Philosophy"]