Madison began as an English surname — "son of Maud" or "son of Matthew," depending on the region. James Madison, the fourth President of the United States and chief author of the Constitution, gave the name its modern resonance.
Its use as a girl's name is a recent phenomenon, sparked by the 1984 film Splash, in which Daryl Hannah's mermaid character names herself Madison after seeing a street sign. By the 2000s it was in the U.S. top 5 girl names. It has slipped recently but remains in the top 100.
Madison reduces to one — the number of independence and natural leadership.