"having the power of judging or discerning rightly," Old English wis "learned, sagacious, cunning; sane; prudent, discreet; experienced, practically knowing;" from Proto-Germanic *wissaz, reconstructed to be from past-participle adjective *wittos of PIE root *weid- "to see" (hence "to know;" compare wise (n.)).
The word is related to the source of Old English witan "to know, be aware of" (see wit (v.)). In Middle English also used in reference to a trade or craft, to warfare; an animal good at tracking by scent was wise of nese. Germanic cognates include Old Saxon, Old Frisian wis, Old Norse viss, Dutch wijs, German weise "wise."
The modern slang meaning "aware, cunning" is attested by 1896.
A wise man has no extensive knowledge; He who has extensive knowledge is not a wise man. [Lao-tzu, "Tao te Ching," c. 550 B.C.E.]
Wise man "man of good discernment" was in Old English; wise guy is attested from 1896, American English, ironic, "know-it-all; maker of wisecracks." Wise-ass (n.) is by 1966, American English (probably a literal sense is intended by the phrase in the 1607 comedy "Westward Hoe" by Dekker and Webster).
As a noun, "persons endowed with reason or prudence," by c. 1200. The use in phrases such as none or never the wiser la by late 14c. (lytel am I þe wyser).
Wisenheimer, with mock German or Yiddish surname suffix is by 1900 (it also is an actual surname).