Reinforced the belief that the majority of power should remain in federal rather than state hands.
Created the first national standing army as major general during the Quasi War; before this point, the American military was composed of disorganized state militias that failed to maintain control of the American people.
Died a martyr at the hands of Vice President Aaron Burr during a duel, forever imprinting his name in the American conscience and challenging the stereotypical principles and idealism of the founding fathers. This was augmented by his affair with Maria Reynolds. .
Studied the stock exchanges in Great Britain and used them as a model for American finance. In this way, he strongly influenced the creation of the New York Stock Exchange, which is currently the world's largest and most influential market in both international and domestic trade and commerce.
Role as a Polemicist (Also delves into character): Alexander Hamilton was known for always speaking his mind and refusing to alter his viewpoints in order to cater to the popular will. This of course led to many conflicts between himself and other less audacious founding fathers (these conflicts became so severe that they eventually culminated in Hamilton's demise). With his colorful vocabulary and quick wit, Hamilton continually published written attacks and leaped into controversial debates. Naturally, his opponents responded just as harshly in their slanderous accounts of Hamilton, which is why his name is acknowledged less than other founding fathers. For all we owe to Hamilton as a founding father, he is lacking in recognition that compliment other founding fathers today, as many have forgotten the contributions he made to the union and remember instead his extramarital affairs and illegitimate birth on Nevis.
The opposite of the stereotypical American politician, who changes his beliefs in order to gain popular support and remains irresolute in times of conflict.