From Old English 'cene' (bold, brave) — the meaning shifted from 'fierce' to 'sharp' to 'eager.'
Having a sharp edge or point; intellectually acute; eager and enthusiastic.
From Old English 'cēne' (bold, brave, fierce, keen, wise), from Proto-Germanic *kōniz (brave, experienced, skillful, able), possibly from PIE *ǵneh₃- (to know, to recognize), the same root that produced Greek 'gignōskein' (γιγνώσκειν, to know), Latin 'gnōscere/cognōscere' (to know), and Sanskrit 'jñā-' (to know). The original Old English sense was 'brave' or 'fierce' — a keen warrior — which evolved through Middle English to 'sharp' (a fierce blade is a sharp one) and 'eager' (fierce desire becomes keen interest). The sense of 'intellectually sharp' connects back to the possible PIE
German 'kühn' (bold, audacious) is the exact cognate of English 'keen,' but has kept the original 'brave' meaning while English shifted to 'sharp' and 'eager.' The Scots/Northern English word 'ken' (to know) may be related — suggesting the original PIE root connected knowing, experience, and the boldness that comes from competence. 'Keen' as an Irish funeral wail (from Irish 'caoineadh') is a completely different word.