"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"]
American English shortening of mathematics, 1890; the British preference, maths, is attested from 1911. "Math. is used as an abbreviation in written English in the U.K. but not in speech, the normal form being Maths" [OED].
It is the hypothetical source of/evidence for its existence is provided by: Greek menthere "to care," manthanein "to learn," mathēma "science, knowledge, mathematical knowledge;" Lithuanian mandras "wide-awake;" Old Church Slavonic madru "wise, sage;" Gothic mundonsis "to look at," German munter "awake, lively."
"mathematical science," late 14c. as singular noun, mathematik (replaced since early 17c. by mathematics, q.v.), from Old French mathematique and directly from Latin mathematica (plural), from Greek mathēmatike tekhnē "mathematical science," feminine singular of mathēmatikos (adj.) "relating to mathematics, scientific, astronomical; pertaining to learning, disposed to learn," from mathēma (genitive mathēmatos) "science, knowledge, mathematical knowledge; a lesson," literally "that which is learnt;" from manthanein "to learn," from PIE root *mendh- "to learn."
As an adjective, "pertaining to mathematics," from c. 1400, from French mathématique or directly from Latin mathematicus.
"one skilled or learned in mathematics," early 15c., mathematicion, from Old French mathematicien, from mathematique, from Latin mathematicus "of or belonging to mathematics," from Latin mathematica (see mathematic).
1832 in mathematics and physics, "a quantity which is assumed to be invariable throughout," from constant (adj.), which is attested from 1753 in mathematics. The general sense "that which is not subject to change" (1856) is a figurative extension from this.