On July, 11, 1804, fierce political rivals Alexander Hamilton and Aaron Burr settled their differences with a duel in Weehawken, NJ, that left Hamilton mortally wounded and turned Burr into one of American history’s most notorious villains.

Today, less than 15 miles from the site of that famous shootout, the descendants of the men peacefully kayak together.

Alexandra Hamilton Woods — the four-time great granddaughter of Alexander Hamilton — and Antonio Burr — a descendant of Aaron Burr’s cousin — met at a party for those working in psychology several years ago. It didn’t take them long to realize they had a fraught family connection, but it was a love of the river that they quickly bonded over.

Burr was on the board of the Inwood Canoe Club, which offers kayaking and canoeing on the Hudson, and Hamilton Woods was keen to start paddling herself.

“Somebody introduced us,” recalls Hamilton Woods, 64, a psychoanalyst living in Manhattan. “I was very interested in this kayaking club, and he was the commodore.”

She soon joined the boating organization, and the two became good friends.

“I used to tease him about our respective history,” Hamilton Woods says. “We’ve had a number of interesting conversations. But I have great fondness and respect for Antonio.”

Their ancestors’ connection became quite the opposite.

Aaron Burr and Alexander Hamilton were once close, even practicing law together in New York. But in 1790, Burr drew Hamilton’s ire when he beat Hamilton’s father-in-law, Philip Schuyler, in a race for the US Senate. In 1800, Burr ran for president, and Hamilton humiliated him by voicing his support for Thomas Jefferson for president over Burr. Burr lost the race. In 1804 — when Burr ran for New York governor — Hamilton again worked to prevent his election. Burr lost once more, and tensions broiled.

The final straw came in February 1804, when it was reported in a New York newspaper that Hamilton shared a “despicable opinion” about Burr at a dinner party. Heated letters were exchanged between the two, Hamilton refused to apologize and Burr challenged him to a duel, set for 7 a.m., July 11, 1804, in Weehawken.

The classic retelling of what happened next — and the story told in Lin-Manuel Miranda’s hit Broadway musical “Hamilton” — is that, at the dueling grounds, Hamilton fired his shot into the air, missing Burr on purpose, while Burr fired to kill, mortally wounding the Founding Father.

But Antonio, 62, who happens to be a forensic psychologist, says that fateful day was more complicated than it’s typically presented.

Hamilton, he says, wanted to die.

“There was something either suicidal or death-wishy on [his] part,” says Burr, who played his notorious ancestor in a 2004 reenactment of the duel. “Hamilton did not avoid the duel and he sort of instigated it. Burr had asked for an explanation and Hamilton did not make any effort to explain anything.”

Antonio cites Hamilton’s state of mind when entering into the duel: his oldest child, Philip, had died just three years earlier in a duel, defending his father at the exact same spot in Weehawken. His eldest daughter, Angelica, went insane shortly after. And his political ambitions were extinguished back in 1797, when he publicly revealed his extramarital affair.

The night before the fateful showdown, Hamilton wrote a note, entitled “Statement of Impending Duel with Aaron Burr,” denouncing dueling and stating he would “throw away my first fire.”

But why, then, did he pursue a potentially deadly face-off?

‘We’ve had a number of interesting conversations. But I have great fondness and respect for Antonio [Burr]’ - Alexandra Hamilton Woods

“I think [Hamilton] knew what would happen when those letters were made public,” Burr says. “Hamilton told the story that ensured he would pass on in history as a hero, and Burr would pass through as a despicable guy. I think he wanted that.”

Burr met with Miranda when the director was developing the play, sharing his thoughts on the Hamilton-Burr relationship with him over several bottles of wine.

While Burr calls the biography “Alexander Hamilton” by Ron Chernow, which inspired the musical, “poisonous” in its vilifying of his ancestor, he approves of Miranda’s representation on the stage.

“I thought he treated Burr with a lot of respect and not the usual condemnation,” he says. “And this is a theater production, so I give him all the artistic license that he needs, or wants.”

Hamilton Woods, who will gather with 11 other Hamilton descendants on Monday evening at a New-York Historical Society gala, has her own allegiances, but agrees with Burr that their ancestors’ rivalry was complex.

“Obviously I know where I lie and sit,” she says. “But I don’t think that it’s black and white.”

The two friends now find themselves in their own political situation. Hamilton Woods sits on the Inwood Canoe Club board as treasurer, and Burr is the president emeritus. They might have the occasional disagreement, but they settle things peacefully.

“We do a lot of negotiating,” says Hamilton Woods. “But he and I find ourselves usually on the same side.”