NEW ORLEANS — It is a wonder that any of it is here at all: The scattered faithful gathering into Beulah Land Baptist Church on a Sunday morning in the Lower Ninth Ward. The men on stoops in Mid-City swapping gossip in the August dusk. The brass band in Tremé, the lawyers in Lakeview, the new homeowners in Pontchartrain Park.

On Aug. 29, 2005, it all seemed lost. Four-fifths of the city lay submerged as residents frantically signaled for help from their rooftops and thousands were stranded at the Superdome, a congregation of the desperate and poor. From the moment the storm surge of Hurricane Katrina dismantled a fatally defective levee system, New Orleans became a global symbol of American dysfunction and government negligence. At every level and in every duty, from engineering to social policy to basic logistics, there were revelations of malfunction and failure before, during, and after Katrina.

Ten years later, it is not exactly right to say that New Orleans is back. The city did not return, not as it was.

It is, first of all, without the more than 1,400 people who died here, and the thousands who are now making their lives someplace else. As of 2013, there were nearly 100,000 fewer black residents than in 2000, their absences falling equally across income levels. The white population decreased by about 11,000, but it is wealthier.

The city that exists in 2015 has been altered, by both a decade of institutional re-engineering and the artless rearrangement that occurs when people are left to fend for themselves.

Empowered by billions of federal dollars and the big ideas of eager policy planners, the school system underwent an extensive overhaul; the old Art Deco Charity Hospital was supplanted by a state-of-the-art medical complex; and big public housing projects, at once beloved and notorious, were razed and replaced by mixed-income communities with housing vouchers.

In a city long marinated in fatalism, optimists are now in ascendance. They promise that an influx of bright newcomers, a burst of entrepreneurial verve and a new spirit of civic engagement have primed the city for an era of greatness, or, at least, reversed a long-running civic-disaster narrative.

“Nobody can refute the fact that we have completely turned this story around,” said Mayor Mitch Landrieu, talking of streamlined government and year-over-year economic growth. “For the first time in 50 years, the city is on a trajectory that it has not been on, organizationally, functionally, economically, almost in every way.”

The word “trajectory” is no accident. It is the mayor’s case that the city is in a position to address the many problems that years of government failures had allowed to fester. He did not argue that those problems had been solved.

Areas with significant

flooding from Katrina

Numbers mark flood

depth in feet.

CENTRAL

BUSINESS DISTRICT

Areas with significant

flooding from Katrina

Numbers mark flood

depth in feet.

CENTRAL

BUSINESS DISTRICT

Areas with

significant flooding

from Katrina

CENTRAL

BUSINESS

DISTRICT

As before, there are two cities here. One is booming, more vibrant than ever, still beautiful in its best-known neighborhoods and expanding into places once written off; the other is returning to pre-Katrina realities of poverty and routine violence, but with a new sense of dislocation for many as well.

Old inequities have proved to be resilient. The child poverty rate (about 40 percent) and the overall poverty rate (close to 30 percent) are almost unchanged from 2000. Violent crime remains a chronic condition, and efforts, both federal and local, to fix the city’s criminal justice system have had mixed results: While the city’s jail population has been substantially reduced, the incarceration rate is more than twice the national average.

The ability of many residents to afford housing — in a city of escalating rents and low wages — is morecompromised than before. In a recent ranking of 300 American cities by income inequality based on census data, New Orleans came insecond, a gap that falls starkly along racial lines. According to the Data Center, a New Orleans-based think tank focusing on Southern Louisiana, the median income of black households here is 54 percent lower than that of white households.

Many here are more impatient than ever to fix these old problems, yet are ambivalent about all the outside expertise and weary of so much change after a decade of upheaval. Others, particularly black residents, see something more nefarious at work.

“They want to push us to the side like we don’t matter,” said Janie Blackmon, a champion of still-struggling New Orleans East, home of much of the black middle class.

New Orleans, of course, has long wrestled with disparities of race and class. For most of its history it has experienced the demographic churn of a port town and a simultaneous anxiety that it was always on the cusp of losing its character.

And as far back as 1722, when a four-year-old New Orleans was flattened by a hurricane, it has entertained a notion that after disaster it would finally get things right.

The difference now is that this proudly distinctive American city has become a giant workshop to test solutions to problems — in housing, education and social mobility — that are confounding the entire country.

Success or failure will nonetheless be gauged ward by ward, neighborhood by neighborhood and block by block.