mad

before 900; Middle English mad (adj.), madden (intransitive v., derivative of the adj.); Old English gemǣd( e) d, past participle of *gemǣdan to make mad, akin to gemād mad, foolish; cognate with Old Saxon gemēd, Old High German gimeit foolish

4. Mad, crazy, insane are used to characterize wildly impractical or foolish ideas, actions, etc. Mad suggests senselessness and excess: The scheme of buying the bridge was absolutely mad. In informal usage, crazy suggests recklessness and impracticality: a crazy young couple. Insane is used with some opprobrium to express unsoundness and possible harmfulness: The new traffic system is simply insane.

Mad meaning “enraged, angry” has been used since 1300, and this sense is a very common one. Because some teachers and usage critics insist that the only correct meaning of mad is “mentally disturbed, insane,” mad is often replaced by angry in formal contexts: The president is angry at Congress for overriding his veto.

The history of mad is complicated both in form and in meaning. In form mad goes back to Old English gemǣd “troubled in mind, demented,” the past participle of an unrecorded verb gemǣdan “to madden, make foolish,” a derivative of the adjective gemād (also mād ) “unreasoning, foolish, mad.”
The Old English forms are from the Germanic adjective gamaidaz “changed for the worse, abnormal.” The element maid- in gamaidaz is from Proto-Indo-European moi-, a variant of the root mei-, moi- “to change, exchange, go, move,” extended with a dental suffix ( -d in Germanic, -t elsewhere). The same suffixed variant moit- appears in Latin mūtāre “to change, exchange, give and receive in exchange.” Sicilian Greek (therefore likely to be influenced by Latin) has the noun moîtos “thanks, favor, reward,” which is possibly a borrowing from Old Latin moitus.
The progression of senses of mad starts with its original sense in Old English, “troubled in mind, demented.” The senses “rabid (dog),” “foolish or unwise,” and “overcome by desire or eagerness” are all recorded from around 1300. Mad in the sense “enraged, angry” arose after about 1400. This sense of mad is the usual colloquial term in the United States (the British are more likely to use angry ) and has been condemned by the arbiters of usage since the late-18th century. The sense “wildly lively, merry” is an Americanism, associated with jazz and African Americans, and dates to the early 1940s.
like mad (initially, for mad ) is quite old, from the 14th century. We take it today to mean “with great haste or energy,” but the original meaning was more literal: “in the manner of one who is mad.”