Etymology
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proletarian 

1650s (n.) "member of the lowest or poorest class of a community;" 1660s (adj.) "of or belonging to the lowest class of people," hence "mean, vile, vulgar;" with -ian + Latin proletarius "citizen of the lowest class" (as an adjective, "relating to offspring"), from proles "offspring, progeny" (see prolific). In ancient Rome, according to the traditional division of the state, the proletarius was one of the propertyless people, exempted from taxes and military service, who served the state only by having children. The modern political sense of proletarian is by 1851.

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proletarianism (n.)

1844, "the condition, or political aims and influence, of the lower classes of a community," from proletarian + -ism.

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prole (n.)
short for proletarian (n.), 1887 (G.B. Shaw); popularized by George Orwell's 1949 novel "Nineteen Eighty-Four." As an adjective from 1938. Related: Proly (adj.); prolier-than-thou.
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proletariat (n.)

also proletariate, "the lowest and poorest class," 1853, from French prolétariat, from Latin proletarius (see proletarian). In political economics, "indigent wage-earners, , the class of wage-workers dependent on daily or casual employment" from 1856. The Englished form proletary was used 16c.-17c. in the older sense and revived in the modern sense by 1865. The Leninist phrase dictatorship of the proletariat is attested from 1918.

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*al- (2)
Proto-Indo-European root meaning "to grow, nourish."

It forms all or part of: abolish; adolescent; adult; alderman; aliment; alimony; Alma; alma mater; alt (2) "high tone;" alti-; altimeter; altitude; alto; alumnus; auld; coalesce; elder (adj., n.1); eldest; Eldred; enhance; exalt; haught; haughty; hautboy; hawser; oboe; old; proletarian; proliferation; prolific; world.

It is the hypothetical source of/evidence for its existence is provided by: Greek aldaino "make grow, strengthen," althein, althainein "to get well;" Latin alere "to feed, nourish, suckle; bring up, increase," altus "high," literally "grown tall," almus "nurturing, nourishing," alumnus "fosterling, step-child;" Gothic alþeis, Dutch oud, German alt "old;" Gothic alan "to grow up," Old Norse ala "to nourish;" Old Irish alim "I nourish."
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cultural (adj.)

1813, "of or pertaining to the raising of plants or animals," from Latin cultura "tillage, a cultivating, agriculture," figuratively "care, culture, an honoring," from past participle stem of colere "to tend, guard; to till, cultivate" (see colony). With -al (1). Figurative senses of "relating to civilizations," also "the cultivation of the mind," are attested by 1875; hence, "relating to the culture of a particular place at a particular time" (by 1909).

Cultural anthropology is attested by 1910, and cultural has been a fertile starter-word among anthropologists and sociologists, for example cultural diffusion, in use by 1912; cultural diversity, by 1935; cultural imperialism, by 1937; cultural pluralism, by 1932; cultural relativism, by 1948. China's Cultural Revolution (1966) began in 1965; the name is a shortened translation of Chinese Wuchan Jieji Wenhua Da Geming "Proletarian Cultural Great Revolution." 

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