The Collaborative International Dictionary of English v.0.48:

Madman \Mad"man\, n.; pl. Madmen.
   A man who is mad; lunatic; a crazy person.
   [1913 Webster]

         When a man mistakes his thoughts for person and things,
         he is mad. A madman is properly so defined.
                                                  --Coleridge.
   [1913 Webster]

WordNet (r) 3.0 (2006):

madman
    n 1: an insane person [syn: lunatic, madman, maniac]

Moby Thesaurus II by Grady Ward, 1.0:

35 Moby Thesaurus words for "madman":
   aliene, ass, bedlamite, borderline case, crackbrain, crackpot,
   dement, demoniac, donkey, energumen, fanatic, flake, fou, idiot,
   imbecile, jackass, jerk, kook, loon, loony, lunatic, maniac,
   meshuggenah, nincompoop, ninny, non compos, noncompos, nut,
   phrenetic, psycho, psychopath, psychotic, raving lunatic,
   screwball, weirdo