late 13c., from Old English gemædde (plural) "out of one's mind" (usually implying also violent excitement), also "foolish, extremely stupid," earlier gemæded "rendered insane," past participle of a lost verb *gemædan "to make insane or foolish," from Proto-Germanic *ga-maid-jan, demonstrative form of *ga-maid-az "changed (for the worse), abnormal" (source also of Old Saxon gimed "foolish," Old High German gimeit "foolish, vain, boastful," Gothic gamaiþs "crippled, wounded," Old Norse meiða "to hurt, maim"), from intensive prefix *ga- + PIE *moito-, past participle of root *mei- (1) "to change, go, move" (source also of Latin mutare "to change," migrare "to change one's place of residence").
Emerged in Middle English to replace the more usual Old English word, wod (see wood (adj.)). Sense of "beside oneself with excitement or enthusiasm" is from early 14c. Meaning "beside oneself with anger" is attested from early 14c., but deplored by Rev. John Witherspoon (1781) as an Americanism. It now competes in American English with angry for this sense. Of animals, "affected with rabies," from late 13c.
Phrase mad as a March hare is attested from 1520s, via notion of breeding season; mad as a hatter is from 1829 as "demented," 1837 as "enraged," according to a modern theory supposedly from erratic behavior caused by prolonged exposure to poison mercuric nitrate, used in making felt hats. For mad as a wet hen see hen. Mad money is attested from 1922; mad scientist is from 1891. Mad Libs, the word game (based on the idea in consequences, etc.), was first published in 1958