Of all the numbers that tell the story of Philadelphia today, one stands out as an unambiguous expression of confidence in the city's future.

Last year, developers received building permits for 2,815 units of new residential housing, the most approved in a decade. Those units are worth an estimated $465 million, the highest annual amount on record.

Investors appear to be betting that Philadelphia's population, which rose for the seventh straight year in 2013 to 1,553,165, will keep growing and that many of the new residents, young and old, will be looking for new homes and apartments.

There is some demographic evidence to support this expectation. In recent years, the city has experienced rapid growth in its population of young adults, many of them well-educated and upwardly mobile. In addition, an increasing number of aging baby boomers are leaving the suburbs and moving into the city. And the middle-class population appears to have stabilized after decades of decline.

Even with the new construction and the rising population, though, there are plenty of reasons to question whether good times are in store for Philadelphia. As detailed in Pew's new report, "Philadelphia: The State of the City, A 2014 Update," the chronic problems have not gone away, and progress, when it happens, has proved difficult to sustain.

Consider the homicide numbers. They were one of last year's bright spots: In 2013, Philadelphia recorded 247 killings, down 25 percent from the year before and the lowest total since 1968; major crime as a whole continued what has been a gradual and relatively steady decline. In the early months of 2014, however, homicides in Philadelphia were up again, generating renewed concern about public safety in a number of neighborhoods.

Poverty is marginally less prevalent than it has been in recent years, down to 26.9 percent of the city's population in the most recent estimate from the Census Bureau. But that remains the highest rate among the nation's 10 most-populous cities, which means it is still a major concern for local policymakers and a drag on the city's economic prospects.

The job market in Philadelphia is sluggish, although it has shown some signs of life. Last year, there were an estimated 3,800 more jobs in the city than the year before, and for the first time, the total was higher than in 2008, the last year before the Great Recession hit with full force. Many other cities had moved beyond their prerecession job totals in previous years.

The city's annual average unemployment rate dropped slightly in 2013, but stayed in double digits at 10.3 percent, far above the national figure of 7.4 percent. The city's rate fell markedly in the final months of the year. But because the number of jobs rose only slightly during that period, the decline in unemployment could have two other explanations: that an increasing number of city residents found work in the suburbs or that they stopped looking for employment.

The condition of the schools remains a serious issue as the district's financial struggles continue. In the 2013-14 school year, enrollment in district-run schools fell nearly 6 percent, the largest drop in percentage since at least 2000. At the same time, the number of students in publicly funded charter schools continued to rise, and the number of students attending schools run by the Archdiocese of Philadelphia stabilized after a prolonged period of decline.

And although building permits increased a lot, annual home sales rose only a little, keeping them at less than half the prerecession peak. So the indicators on the residential housing front did not all point in the same direction.

Put it all together and the state of the city once again is decidedly mixed, with some of the positives and negatives perhaps a bit more pronounced than in years past. There are ample reasons for optimism, but the underlying challenges are as daunting as ever.