Hamilton continued his legal and business activities in New York City , and was active in ending the legality of the international slave trade . Vice President Burr ran for governor of New York State in 1804 , and Hamilton campaigned against him as unworthy . Taking offense , Burr challenged him to a duel on July 11 , 1804 , in which Burr shot and mortally wounded Hamilton , who died the following day
a duel
Burr–Hamilton duel
Alexander Hamilton