c. 1200, "in a mad manner, wildly, violently, irrationally," from mad (adj.) + -ly (2). Colloquial meaning "passionately" had emerged by 1767.
she fought back madly
the witch cackled madly
she was madly in love
Madeline
mademoiselle
Madge
madhouse
Madison
madly
madman
madness
madonna
Madras
madrasah