Etymology
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mathematical (adj.)

"of, pertaining to, or of the nature of mathematics," early 15c., from Medieval Latin mathematicus "of or belonging to mathematics," from Latin mathematica (see mathematic) + -al (1). Also, by 1765, "pertaining to the quadrivium," comprising arithmetic, geometry, astronomy, and music. It also could include optics. Related: Mathematically.

The four mathematical arts are arithmetic, geometry, music, and astronomy; these anciently were termed the quadrivium, or fourfold way of knowledge. [Sir John Hawkins, "A General History of the Science and Practice of Music," Sir John Hawkins, 1776]
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geometrical (adj.)
late 14c., from Latin geometricus "of geometry" (from geometria; see geometry) + -al. Since 16c. it has been opposed to arithmetical in ratio, proportion, etc., reflecting the fact that problems of multiplication formerly were dealt with by geometry, not arithmetic. Related: Geometrically.
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quadrivium (n.)

"arithmetic, music, geometry, astronomy" (the four branches of mathematics, according to the Pythagoreans), by 1751, from Latin quadrivium, which meant "place where four roads meet, crossroads," from quadri- "four" (from PIE root *kwetwer- "four") + via "way, road, channel, course" (see via). Compare liberal arts, and also see trivium.

The adjective quadrivial is attested from mid-15c. in English with the sense of "belonging to the quadrivium," late 15c. with the sense of "having four roads, having four ways meeting in a point."

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trivium (n.)

by 1751, from Medieval Latin trivium (9c.) "grammar, rhetoric, and logic," the first three of the seven liberal arts, considered initiatory and foundational to the other four (arithmetic, geometry, astronomy, and music). From Latin trivium, in classical Latin "place where three roads meet; a frequented place; public street, highway," from tri- "three" (see three) + via "road" (see via). Compare trivia and also see quadrivium.

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-ics 
in the names of sciences or disciplines (acoustics, aerobics, economics, etc.), a 16c. revival of the classical custom of using the neuter plural of adjectives with Greek -ikos "pertaining to" (see -ic) to mean "matters relevant to" and also as the titles of treatises about them. Subject matters that acquired their English names before c. 1500, however, tend to be singular in form (arithmetic, logic, magic, music, rhetoric). The grammatical number of words in -ics (mathematics is/mathematics are) is a confused question.
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rational (adj.)

late 14c., racional, "pertaining to or springing from reason;" mid-15c., of persons, "endowed with reason, having the power of reasoning," from Old French racionel and directly from Latin rationalis "of or belonging to reason, reasonable," from ratio (genitive rationis) "reckoning, calculation, reason" (see ratio).

In arithmetic, "expressible in finite terms," 1560s. Meaning "conformable to the precepts of practical reason" is from 1630s. Related: Rationally. It is from the same source as ratio and ration; the sense in rational is aligned with that in related reason (n.), which got deformed in French.

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naught (n.)

mid-14c., "evil, an evil act," also " a trifle," c. 1400, "nothingness;" early 15c., in arithmetic, "the number zero;" from noht, naht (pron.) "nothing" (late 12c.), from Old English nawiht "nothing," literally "no whit," from na "no" (from PIE root *ne- "not") + wiht "thing, creature, being" (see wight). Also see nought.

Cognate with Old Saxon neowiht "nothing," Old High German niwiht, Gothic ni waihts, Dutch niet, German nicht. It also developed an adjectival sense in Old English, "good for nothing," which by mid-16c. had focused to "morally bad, wicked," though the modern adjective is naughty.

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multiple (adj.)

"involving many parts or relations; consisting of more than one complete individual," 1640s, from French multiple (14c.), from Late Latin multiplus "manifold," from Latin multi- "many, much" (see multi-) + -plus "-fold" (see -plus).

The noun is from 1680s in arithmetic, "a number produced by multiplying another by a whole number," from the adjective. Multiple choice in reference to a question in which the subject selects an answer from several options is attested by 1915. Multiple exposure "repeated exposure of the same frame of film" is recorded by 1891. In psychology, multiple personality is attested by 1886. The chronic, progressive disease multiple sclerosis is so called by 1877, because it occurs in patches (see sclerosis).

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liberal arts (n.)

late 14c., translating Latin artes liberales; the name for the seven attainments directed to intellectual enlargement, rather than immediate practical purpose, and thus deemed worthy of a free man (liberal in this sense is opposed to servile or mechanical). They were divided into the trivium — grammar, logic, rhetoric (see trivial) — and the quadrivium — arithmetic, geometry, music, astronomy. Explained by Fowler (1926) as "the education designed for a gentleman (Latin liber a free man) & ... opposed on the one hand to technical or professional or any special training, & on the other to education that stops short before manhood is reached."

The study of [the classics] is fitly called a liberal education, because it emancipates the mind from every narrow provincialism, whether of egoism or tradition, and is the apprenticeship that every one must serve before becoming a free brother of the guild which passes the torch of life from age to age. [James Russell Lowell, "Among my Books"]
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Gradgrind (n.)

"cold, factual person," from the name of the school-board superintendent and mill-owner in Dickens' "Hard Times" (1854):

THOMAS GRADGRIND, sir. A man of realities. A man of facts and calculations. A man who proceeds upon the principle that two and two are four, and nothing over, and who is not to be talked into allowing for anything over. Thomas Gradgrind, sir - peremptorily Thomas - Thomas Gradgrind. With a rule and a pair of scales, and the multiplication table always in his pocket, sir, ready to weigh and measure any parcel of human nature, and tell you exactly what it comes to. It is a mere question of figures, a case of simple arithmetic. ....
In such terms Mr. Gradgrind always mentally introduced himself, whether to his private circle of acquaintance, or to the public in general. In such terms, no doubt, substituting the words 'boys and girls,' for 'sir,' Thomas Gradgrind now presented Thomas Gradgrind to the little pitchers before him, who were to be filled so full of facts.
Indeed, as he eagerly sparkled at them from the cellarage before mentioned, he seemed a kind of cannon loaded to the muzzle with facts, and prepared to blow them clean out of the regions of childhood at one discharge. He seemed a galvanizing apparatus, too, charged with a grim mechanical substitute for the tender young imaginations that were to be stormed away. 
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