First off, we have to recognize that the chant of "the greatest city in the world" in the play is coming from characters in New York City in a play based in New York City so obviously this claim should be taken with a grain of salt.

Once we get past that, there are a million ways of looking at what "the greatest city in the world" is. Is it the city with the highest population? The most money? The smartest people? The most creative endeavors?

Let's answer the first one. In 1790, New York City WAS the biggest city in the United States, but not by much. Philadelphia was just a few thousand behind, according to the 1790 US Census. By 1800, NYC had gained a sizable lead over Philadelphia.

As far as money goes, NYC and Philadelphia were the centers of the Industrial Revolution in America. Both cities experienced huge growth towards the end of the 18th century as they were the centers of urbanization for many Americans looking to make money off of these new machines Samuel Slater had brought over from England. So if you wanted to get rich quick at the time, these two cities were the place to be.

Intelligence is obviously very hard to quantify, however, we can look at the concentration of knowledge in New York City and make a strong case for it being one of, if not the smartest. The fifth oldest institution of higher learning in the United States is King's College -- founded in 1754 in New York City. After the Revolutionary War, it was renamed Columbia University. If colleges aren't your style, we could look at the concentration of brain power from 1789-1790 when New York City served as the first capital of the United States after the ratification of the Constitution. Although if you wanted to use that argument, you could give the nod to Philadelphia as it served as the nation's capital for most of the 1780s.

For creative endeavors, we first need to define what "creative" means. If we are purely talking about art, you could point to the foundation of the Hudson River School of Art in the mid-19th century, but I think that is a little too late to fit our time frame. Unfortunately, I don't have the depth of knowledge of early American art to truly name New York City as the hub. Maybe someone else can help out here.

Ok. So that gives us an idea of where New York City fell as the greatest city in America, but it tells us nothing about whether or not it is "the greatest city in the world." If we expand our scope to include the entire world, New York City pales in comparison to hundreds of cities. Remember, the United States has only truly existed as its own entity for 20 or so years, so no city inside of it could possibly compare to the great cities of the world. For example, in 1800, New York City had roughly 60,000 people. At the same time, Bejiing, China had over one million people. New York certainly did not compare to the wealth of London, Paris, Naples, etc. at the end of the 1700s. Again, intelligence is hard to quantify, but there are hundreds, if not thousands, of institutions of higher learning that could easily make an argument at being "more intelligent" than New York City at the time. Finally, in the "creative" category, I think it is safe to say that New York City was not "the greatest." Again, I do not claim to be an arts expert, but I believe I can assert with some confidence that New York City was not the creative capital of the world.

So, does this mean New York City was not, in fact, "the greatest city in the world"? I think that is subjective. By any one data point, I don't think you could unequivocally argue that New York City was the greatest. However, if you are Alexander Hamilton, an orphan immigrant with absolutely no money to his name, who's only hope of survival is by using his brain that is wired for political science and economic theory, you could certainly make the case that it was indeed "the greatest city in the world."

Sources:

Chernow, R. (n.d.). Alexander Hamilton.

Lio, A. (n.d.). Top 10 Cities of the Year 1800. Retrieved February 17, 2016, from http://geography.about.com/library/weekly/aa011201e.htm

Appleby, J. O., Brinkley, A., Broussard, A. S., McPherson, J. M., & Ritchie, D. A. (n.d.). United States history to 1877.

(n.d.). Retrieved February 17, 2016, from http://www.census.gov/population/www/documentation/twps0027/tab01.txt

I am going to have to disagree with /u/tstaff777 here. Few people in America or anywhere else would have called New York the greatest city in the world during the time of the play.

Let's look at when this song is set, and who's singing it. In one of the play's historical lapses, this section of the play is set in 1776 - squarely in the midst of the Revolution, rather than on its brink. The main characters in this piece are the three Schuyler sisters, Angelica, Elizabeth, and Peggy. All three were well educated by private tutors as far as we can tell, and were noted for their looks (except Peggy, who would, in the words of one writer "be as pretty as Angelica, if she had any teeth"). They grew up in an Georgian mansion in Albany, a house their father filled with English luxuries (purchased on a lengthy trip to London during the 1760s) and surrounded with gardens on the English style. Like all proper British ladies, they were educated with an aim towards the social graces, witty enough to make polite conversation and trained to sing and play instruments to entertain guests.

Sensing a pattern here? A distinctly English pattern, even for an entirely Dutch family like the Schuyler-Van Rensselaers? The colonists were well aware that they lived on the periphery of the British empire, and looked to England for their cultural norms and sense of style. Like other wealthy Americans, they proclaimed their sophistication by conspicuously displaying and consuming the latest English clothing, food, and material goods.

With in this mind, it is inconceivable that any member of the Schuyler family would have considered New York, a small, dirty port on the edge of the world's greatest empire that was frequently wracked by mob violence as the greatest city in the world. London and Paris were the shining lights of 18th century culture, and no one would ever think of putting 1770s New York in the same category as those two cities.

Sources: T.H. Breen, The Marketplace of Revolution

Schuyler Mansion State Historic Site