fool-proof adj.

early 13c., "silly, stupid, or ignorant person," from Old French fol "madman, insane person; idiot; rogue; jester," also "blacksmith's bellows," also an adjective meaning "mad, insane" (12c., Modern French fou), from Medieval Latin follus (adj.) "foolish," from Latin follis "bellows, leather bag," from PIE root *bhel- (2) "to blow, swell."

The sense evolution probably is from Vulgar Latin use of follis in a sense of "windbag, empty-headed person." Compare also Sanskrit vatula- "insane," literally "windy, inflated with wind." But some sources suggest evolution from Latin folles "puffed cheeks" (of a buffoon), a secondary sense from plural of follis. One makes the "idiot" sense original, the other the "jester" sense.

The word has in mod.Eng. a much stronger sense than it had at an earlier period; it has now an implication of insulting contempt which does not in the same degree belong to any of its synonyms, or to the derivative foolish. [OED]

Also used in Middle English for "sinner, rascal, impious person" (late 13c.). Meaning "jester, court clown" in English is attested c. 1300, though it is not always possible to tell whether the reference is to a professional entertainer counterfeiting mental weakness or an amusing lunatic, and the notion of the fool sage whose sayings are ironically wise is also in English from c. 1300. The French word probably also got into English via its borrowing in the Scandinavian languages of the vikings (Old Norse fol, Old Danish fool, fol).

There is no foole to the olde foole ["Proverbs of John Heywood," 1546]

To make a fool of (someone) "cause to appear ridiculous" is from 1620s (make fool "to deceive, make (someone) appear a fool" is from early 15c.). Feast of Fools (early 14c., from Medieval Latin festum stultorum) was the burlesque festival celebrated in some churches on New Year's Day in medieval times. Fool's gold "iron pyrite" is from 1829. Fool's paradise "illusory state of happiness based on ignorance or erroneous judgment" is from mid-15c. (foles paradyce). Fool-trap is from 1690s. Foolosopher, a useful insult, is in a 1549 translation of Erasmus. Fool's ballocks is described in OED as "an old name" for the green-winged orchid. Fool-killer "imaginary personage invested with authority to put to death anybody notoriously guilty of great folly" is from 1851, American English.

Fool killer, a great American myth imagined by editors, who feign that his or its services are greatly needed, and frequently alluded to as being "around" or "in town" when some special act of folly calls for castigation. Whether the fool-killer be an individual or an instrument cannot always be gathered from the dark phraseology in which he or it is alluded to; but the weight of authority would sanction the impersonal interpretation. [Walsh, "Handy-Book of Literary Curiosities," 1892]

Fools rush in where angels fear to tread is a (shortened) line of Pope's "Essay on Criticism" (1711) popularized in Burke's "Reflections on the Revolution in France" (1793).

c. 1200, preove "evidence and argumentation to establish the fact of (something) beyond reasonable doubt," from Anglo-French prove, preove, Old French proeve, prueve "proof, test, experience" (13c., Modern French preuve), from Late Latin proba "a proof," a back-formation from Latin probare "to prove" (see prove). "The devocalization of v to f ensued upon the loss of final e; cf. the relation of v and f in believe, belief, relieve, relief, behove, behoof, etc." [OED].

The meaning "act of proving" is early 14c. The meaning "act of testing or making trial of anything" is from late 14c., from influence of prove. Meaning "standard of strength of distilled liquor" is from 1705, on the notion of "having been tested as to degree of strength." The use in photography is from 1855. The typographical sense of "trial impression to test type" is from c. 1600. The numismatic sense of "coin struck to test a die" is from 1762; now mostly in reference to coins struck from highly polished dies, mainly for collectors.

The adjectival sense "impenetrable, able to resist" (as in proof against) is recorded from 1590s, from the noun in expressions such as proof of (mid-15c.), hence extended senses involving "of tested power against" in compounds such as fireproof (1630s), rust-proof (1690s), waterproof (1725), fool-proof (1902), etc. Shakespeare has shame-proof. Expression the proof is in the pudding (1915) is a curious perversion of earlier proof of the pudding shall be in the eating (1708), with proof in the sense "quality of proving good or turning out well" (17c.).