Etymology
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crazy (adj.)

1570s, "diseased, sickly" (a sense now obsolete); 1580s, "broken, impaired, full of cracks or flaws," from craze + -y (2). Meaning "deranged, demented, of unsound mind or behaving as so" is from 1610s. Jazz slang sense "cool, exciting" is attested by 1927. Related: Crazily; craziness.

To drive (someone) crazy is attested by 1873. To do something like crazy "with manic vigor or frequency" is by 1905. Phrase crazy like a fox has origins by 1935. Crazy Horse, name of the Teton Lakhota (Siouan) war leader (d. 1877), translates thašuka witko, literally "his horse is crazy." Crazy-quilt (1886) preserves the original "break to pieces" sense of craze (v.). Crazy bone as an alternative to funny bone is recorded by 1853.

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Definitions of crazy
1
crazy (adj.)
affected with madness or insanity;
Synonyms: brainsick / demented / disturbed / mad / sick / unbalanced / unhinged
crazy (adj.)
foolish; totally unsound;
a crazy scheme
Synonyms: half-baked / screwball / softheaded
crazy (adj.)
possessed by inordinate excitement;
was crazy to try his new bicycle
the crowd went crazy
crazy (adj.)
bizarre or fantastic;
had a crazy dream
wore a crazy hat
crazy (adj.)
intensely enthusiastic about or preoccupied with;
crazy about cars and racing
Synonyms: wild / dotty / gaga
2
crazy (n.)
someone deranged and possibly dangerous;
Synonyms: loony / looney / nutcase / weirdo
From wordnet.princeton.edu