Once it was confirmed that there would be a new President, passionate behind-the-scenes politicking occurred at the state level, which as a result of the Election of 1796, meant that the Federalist John Adams was President, and the Republican Thomas Jefferson was Vice-President. In so many ways, President John Adams was limited in what he could accomplish; among the reasons was his Cabinet. For obvious political reasons, Adams retained all of Washington's Cabinet, but that group was mediocre at best, and they were far more loyal to Hamilton than to the President. In Hamilton's mind, this was more-than-fine, in that he was able to "check" a fellow Federalist that had stated, years earlier, that certain aspects of monarchy may be desirable in America (Hamilton had campaigned hard in the Election of 1796 for Thomas Pinckney over John Adams, and it nearly cost Adams the Presidency).
In 1798, President John Adams signed into law the Alien and Sedition Acts; the Federalists felt more-than-justified in passing these restrictions due to the Whiskey Rebellion and the Genet Affair (basically, this was a brazen attempt by the Federalist Party to destroy Jefferson's and Madison's Republican Party). Due to recent tensions with France ("XYZ Affair") and the perceived internal threats, Washington was called to command an expanded U.S. Army (his commission took effect on 4 July, 1798). General Washington refused to leave Mount Vernon unless the U.S. was attacked, so the Second-in-Command would be the actual commanding officer, and there was quite the "Depth Chart" for that rank. Vying for that title/rank, among others, were Henry Knox, Charles Pinckney, and Alexander Hamilton. President Adams wanted to remove Hamilton from any consideration for that rank (revenge for 1796?), but for political reasons, had to keep him in play. Hamilton held some kind of rank in the Army for almost two years, and since there was no fighting, he became obsessed with the "little stuff" (e.g. marching formations, buttons on uniforms, etc.). After Washington's death in 1799, and the de-escalation of tensions with France, Congress downsized the Army in June, 1800; Hamilton was the officer that took care of the necessary details to carry out that Act of Congress.
(Below: A segment from the "John Adams" miniseries - President Adams and "2nd-in-Command" Hamilton")
After all the Electoral Votes were counted, Jefferson and Burr were deadlocked at 73 votes each (the voter that had the honor of sending his Vice-Presidential Electoral Vote to someone other than Burr apparently forgot to do so). For the first time, the House of Representatives had to elect the President (each state's delegation votes, and each state counts as one total vote), and after the first ballot, Jefferson and Burr each had eight states.
Aaron Burr's main problem was that he was a Narcissist (exceptional interest in or admiration of oneself); he was able to talk a good game, but following through was problematic . . . he was all interaction, with nothing at his core, and it would cost him dearly, starting at this point. General Washington was among the first to figure out that Burr was a Narcissist (Burr only lasted ten days as an aide to Washington), and Hamilton viewed Burr in much the same way. Hamilton took it further than Washington, however, in that he didn't want Burr to hold any major elected office at all. Hamilton not only viewed Burr as a Narcissist, but also as someone that could be a serious threat to the future of the U.S., and he wrote numerous letters to Delaware's only Representative, James Bayard, imploring him to change his vote from Burr to Jefferson. On the 36th ballot, James Bayard abstained, and Thomas Jefferson became the 3rd President (8 states to 7 for Burr); little did Burr realize that he had already reached the pinnacle of his political career.
According to Brookhiser (pictured), there are three modes of leadership: The highest is "Inspiration", which is also the most rare. Next is "Demonstration", which is sharing your reasons with everyone, and model appropriately. Last is "Flattery", which is all talk with little-or-no action; this type can lead to situations where the leader fools the followers, or worse yet, the leader and the followers are both fooled. "Flattery" usually occurs when the leader(s) and followers can't think of anything else to do (e.g. lack of vision). Hamilton rarely reached "Inspiration", and he refused to resort to "Flattery" - Hamilton was a "Demonstrator." Jefferson inhabited all three, but mostly he exhibited "Inspiration" (Declaration of Independence) and "Flattery", which further fueled the rift between Hamilton and Jefferson. Aaron Burr spent virtually his entire political life in "Flattery", which also explains much as to why Hamilton viewed Burr as a "dangerous man."
Specific applications for Hamilton's beliefs concentrated on contracts. Contracts were related to debt, which helped explain his plan as SecTreas to repay the massive Revolutionary War debts incurred by the government. According to Hamilton, special privileges were the hallmark of despots and slave-owners, while contracts were the handiwork of free men. In yet another reason for the chasm between Hamilton and others was that in a way, Jefferson, Madison, and Burr were "Born on 3rd Base", with a very short trip to "Home Plate". Hamilton, on the other hand, had to work his way around all the bases, and the key to his success was the contract.
Hamilton did not have a violent temper; his pride and stubbornness far exceeded any rage in his machine. What Hamilton had plenty of was ARDOR (enthusiasm, passion); he loved his ideas, his work, and family and friends. Like most of the other Founders, Hamilton also had the passion of lust, but he was the only Founding Father to freely admit his lust (to this day, Hamilton's admission of adultery remains the most frank among politicians). It must have galled Hamilton to no end that Jefferson denied any involvement with Sally Hemings, or Burr's continuous attendance at whorehouses, yet the media focused on Hamilton and Maria Reynolds, due to his candor.
Aaron Burr was struggling as well in late-1801; his (calculated?) indecision in the House phase of the Election of 1800 had cost him his political future; President Jefferson made sure that in the Republican Party, Vice-President Burr was persona non grata. Yet Burr was still seething with ambition, and he started to focus his political energies in New York state-level politics in an effort to re-start his career.
Hamilton's ambition had been ebbing away since he lost his high rank with the dissolution of most of the U.S. Army in the Summer of 1800, and the death of his son Philip in 1801, but he still distrusted Burr, and he basically made it his business to block Burr's efforts in their home state of New York. In 1804, Burr was a FEDERALIST candidate in the New York gubernatorial election; he used his many connections among prominent Federalist families to gain his spot on the ballot. However, Burr was soundly defeated, in part due to being associated with New England Federalists that wanted to secede from the Union, but also due to the tireless efforts of Hamilton's anti-Burr letter-writing campaign. Burr (remember, he was a Narcissist) in no way saw his situation as his fault, and President Jefferson was untouchable, so Burr started to focus on Hamilton as the reason for his political failure. The only one that was open about opposing Burr in the election was Hamilton, and dueling was considered an acceptable political weapon by many to restore one's reputation. Actually, in the "Honor Culture", it was very common for a losing candidate to challenge the winner to a duel; it was the only way to publicly save face and be "electable" in the future. However, almost all of those challenges were resolved long before they reached the stage of firing pistols on the "Field of Honor"; such was not the case with Burr and Hamilton . . .
On 11 July, 1804, at Weehawken, New Jersey (the same site where Philip was killed), Vice-President Aaron Burr faced former Secretary of the Treasury Alexander Hamilton in the most famous duel in American History. We'll never know the true circumstances and sequence of the duel, but it's almost certain that both men fired at the same time. Hamilton's shot went high, clipping a cedar branch, while Burr's shot was mortal, hitting Hamilton in his abdomen.
Assuming that this duel was with light sabres instead of pistols, it could have been possible that Hamilton saw Philip off to the side, and decided to let Burr shoot him; maybe by his death he could thwart Vader's, I mean Burr's, efforts at political ascendancy. In the "Reynolds Affair", Hamilton chose to save his public life at the expense of his personal life, not once, but twice. In his duel with Burr, it's possible that Hamilton chose to risk his life in order to protect the nation from Burr. I would argue that if he had not been so depressed and consumed with guilt over the advice that he gave Philip almost three years before, he almost certainly would have figured out that one of his enemies, President Jefferson, had his Arch-Enemy, the Narcissist Burr, well-contained, and he was no real threat to anyone at all but himself.
it's one of the best documentaries I've ever seen about the Burr-Hamilton Duel)