The death of Osama bin Laden is, without question, a defining moment in American history, a defining moment for America’s president and a revealing moment for the country itself. At the same time, however, it alters little in the way of closing the global chasms between the United States and others who would seek to cripple or destroy us.

It is certainly a crucial moment for Barack Obama’s presidency. It burnishes his credentials as a master in the fight against terrorism and provides him with a legitimacy that has eluded him in this time of militaristic passions exceeding even those that defined the Bush-Cheney era.

The success of the siege in that fortified compound in Abbottabad now offers many Americans a fresh perspective on the Barack Obama presidency. The president has presided over a complex, highly sensitive military operation that was clearly well planned and expertly executed. (It also provides a stark contrast with the unsuccessful embarrassment of the Bay of Pigs Invasion exactly 50 years ago, when the Kennedy administration failed in its attempt to use a CIA-trained force of Cuban exiles to overthrow Fidel Castro.)

But even in this extraordinary accomplishment, Obama’s approval ratings have climbed by just about 10 percent. That’s decent, but not outstanding. That may be a sign that the drama and euphoria of the moment have not erased from the public’s mind the concerns over the stubborn recession and jobless recovery.

It’s also a sign that the approval that he is receiving is given grudgingly at best, and that there is a significant swath of Americans who simply refuse to favorably accept this commander in chief’s accomplishments, no matter how Herculean.

There are other lessons here as well. In the midst of this notable moment in history, there is a disturbing underside. In the minutes after the news emerged about the death of the al Qaeda leader, there were impromptu celebrations that exploded near the White House and here in New York at Ground Zero. There is something unsettling about seeing the cheers and celebration of anyone’s death, no matter how monstrous the deceased might have been.

The Rev. Calvin O. Butts III, the pastor of the Abyssinian Baptist Church in Harlem, put it aptly: “Many of us in the Christian community in America were very critical of Muslims who danced in the streets right after 9/11. We talked about how horrible it was. And it seems to me that we, especially in the Christian community, ought not to be doing the exact same thing now and rejoicing like that.

“We acknowledge that the government did what it felt had to be done, but we need to start thinking about how we develop the reconciliation that we really need between the two sides.”

That’s similar to the Catholic Church’s take on the matter: “Faced with the death of a man,” the church said in a statement following Bin Laden’s killing, “a Christian never rejoices, but reflects on the serious responsibility of everyone before God and man, and hopes and pledges that every event is not an opportunity for a further growth of hatred, but of peace.”

Despite the political overtones, the death of Bin Laden doesn’t affect the order of things in the life into which the world was plunged after the carnage at the World Trade Center a decade ago. Terrorism remains an imminent threat that will continue to cause concern and restlessness, particularly here in New York. In the days after the killing of Bin Laden, the subways and bus stations were policed with greater vigilance, with officers brandishing MP5 submachine guns.

The fact of the matter is, as Gov. Andrew M. Cuomo said in the aftermath of Bin Laden’s death, “We’ll be fighting this war every day.”