As we know from the wildly popular musical Hamilton, the views and contributions of Alexander Hamilton are being reexamined and revalued. Because he was never president, as Jefferson was, and because his personal life was somewhat scandalous, leading, of course, to the famous duel with Aaron Burr in which Hamilton was killed, he has been somewhat marginalized.
But Hamilton's Federalist views, which constituted a strong central government, have in fact been more dominant in shaping the way the United States has ended up being governed. Jefferson, on the other hand, was the original supporter of what we would now call "states' rights." Jefferson, a farmer from the South, did not believe in or foresee how the rise of industry in the North would demand a government that controlled interstate commerce, for example.
That these views could not be entirely reconciled is part of the reason for the US Civil War. Even today, the conflict between the federal government and states' rights remains a main source of political disagreement.
In the years after the creation of the Constitution of the United States, the country’s leaders split into two main political parties. These parties were the Federalist Party, which is most closely associated with Alexander Hamilton and the Democratic-Republicans, led by Thomas Jefferson. The ideas of these two men led to the creation of these political parties because those ideas were opposed to one another. Since there were coming to be two main streams of thought about what the country should be like, there naturally came to be two political parties.
The Federalist Party was the more conservative of the two parties. It wanted the country to become industrialized and economically powerful. This party held that America needed to get away from having just an agrarian economy and society. The Federalists realized that an industrial economy would make for a less equal society as some people got rich and others became poorer. The Federalists felt that this was an acceptable outcome. Relatedly, they were less attached to the idea of democracy. They felt that the common people lacked the knowledge needed for governing and that a natural elite should have more power. The Federalists came to back England in its war against Revolutionary France.
The Democratic-Republicans held views opposite to those of the Federalists. They believed that the US ought to be a democratic country in which all people (or at least all white men) were equal. They believed that economic inequality would lead to political inequality. Therefore, they believed that America’s economy should be made up almost solely of small independent farmers. They wanted more democracy so that there would be no rule by any group of elites. They came to back the French in their war against England.
Because Hamilton and Jefferson had different points of view (and because those points of view were shared by others) two political parties soon arose after the creation of the new governmental system under the Constitution.