Etymology
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mutual (adj.)

late 15c., "reciprocally given and received," originally of feelings, from Old French mutuel (14c.), from Latin mutuus "reciprocal, done in exchange," from PIE root *mei- (1) "to change, go, move," "with derivatives referring to the exchange of goods and services within a society as regulated by custom or law" [Watkins].

The meaning "common" is from 1630s. "Used in this sense loosely and improperly (but not infrequently, and by many writers of high rank), especially in the phrase a mutual friend" [Century Dictionary].

That is common which pertains equally to two or more persons or things. That is mutual which is freely interchanged: mutual love, affection, hatred. The word is sometimes incorrectly used for common: our mutual friend, a phrase of very frequent occurrence, no doubt owing to the perfectly correct 'mutual friendship.' [J.H.A. Günther, "English Synonyms Explained & Illustrated," Groningen, 1904]

Mutual Admiration Society (1851) seems to have been coined by Thoreau. Mutual fund is recorded from 1950.

The Cold War's mutual assured destruction is attested from 1966. Assured destruction was a 1962 term in U.S. military policy circles in reference to nuclear weapons as a deterrent, popularized c. 1964 by Robert McNamara, U.S. Secretary of Defense under Lyndon Johnson, e.g. statement before House Armed Services Committee, Feb. 18, 1965. The notion was "the minimum threat necessary to assure deterrence: the capability to exterminate not less than one third of the Union of Soviet Socialist Republics' (USSR) population in a retaliatory nuclear attack." [Martin Folly, "Historical Dictionary of U.S. Diplomacy During the Cold War"].

By 1964, as the Soviet Union caught up to NATO in ICBMs, the mutual was added, perhaps first by Donald Brennan, conservative defense analyst and a public critic of the policy, who also noted the acronym MAD.)

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mutual (n.)
short for mutual fund, 1971; see mutual.
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mutuality (n.)

"reciprocity, interchange," 1580s, from mutual + -ity.

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mutually (adv.)

"reciprocally, in a manner of giving and receiving," 1530s, from mutual + -ly (2). The meaning "conjointly, in common" (1590s) is "Held to be an erroneous use" [Century Dictionary]. Mutually exclusive is recorded by 1650s. For mutually assured destruction, see mutual.

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mutualism (n.)

1845, in reference to the doctrine of French anarchist/socialist Pierre-Joseph Proudhon (1809-1865) that individual and collective well-being is attainable only by mutual dependence, from French mutuellisme. In biology, "a symbiosis in which two organisms living together mutually and permanently help and support one another," from 1876, from mutual + -ism.

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pari-mutuel 

1881 in reference to a form of betting, from French pari-mutuel "mutual wager," from pari "wager" (from parier "to bet," from Latin pariare "to settle a debt," literally "to make equal," from par, genitive paris, "equal;" see par (n.)) + mutuel "mutual," from Latin mutuus (see mutual (adj.)).

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*mei- (1)
Proto-Indo-European root meaning "to change, go, move," "with derivatives referring to the exchange of goods and services within a society as regulated by custom or law" [Watkins].

It forms all or part of: amiss; amoeba; azimuth; common; commune; communicate; communication; communism; commute; congee; demean; emigrate; emigration; excommunicate; excommunication; immune; immutable; incommunicado; mad; mean (adj.1) "low-quality;" mew (n.2) "cage;" mews; migrate; migration; mis- (1) "bad, wrong;" mistake; Mithras; molt; Mstislav; municipal; munificent; mutable; mutant; mutate; mutation; mutatis mutandis; mutual; permeable; permeate; permutation; permute; remunerate; remuneration; transmutation; transmute; zenith.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit methati "changes, alternates, joins, meets;" Avestan mitho "perverted, false;" Hittite mutai- "be changed into;" Latin mutare "to change," meare "to go, pass," migrare "to move from one place to another," mutuus "done in exchange;" Old Church Slavonic mite "alternately;" Czech mijim "to go by, pass by," Polish mijać "avoid;" Gothic maidjan "to change."
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agreement (n.)
c. 1400, "mutual understanding" (among persons), also (of things) "mutual conformity," from Old French agrement, agreement, noun of action from agreer "to please" (see agree). Early 15c. as "formal or documentary agreement, terms of settlement."
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coarticulation (n.)

"mutual or reciprocal articulation," 1610s, from co- + articulation.

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coadaptation (n.)

also co-adaptation, "mutual or reciprocal adaptation," 1803, from co- + adaptation.

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