headpiece

baseball cap, beret, biretta, boater, bonnet, bowler, cloche, cocked hat, cowboy hat, cowl, derby, fedora, fez, hard hat, helmet, high hat, homburg, hood, miter (or mitre), nightcap, panama, pillbox, porkpie hat, service cap, shako, silk hat, skullcap, sombrero, sou'wester, Stetson, stocking cap, stovepipe, sunbonnet, tam, tam-o'-shanter, ten-gallon hat, top hat, topper, toque, tricorne (or tricorn), turban, zucchetto

eggheadedness, highbrowism, intellectualism

braininess, brilliance

acumen, alertness, apprehension, astuteness, discernment, discriminability, insight, judgment (or judgement), perception, percipience, perspicacity

common sense, horse sense, mother wit

aptitude, talent

sagacity, sapience, wisdom, wit

head, mind, skull