Manhattan was over 60,000 people per square mile in 2000
What was Manhattan's total population density in 1910? It is my belief that it was much higher then, as even though NYC's population was in the 7M range all along, the records that we are seeing now (city went over 8M for the first time ever in 2000) is due to the fact that even though Manhattan is less dense now than it was back then, Queens, especially, which was a rural farming county 100 years ago (even though it, including all of its little farming communities, was fully a part of NYC back then) filled in with city-style urban development during the mid-20th century. Staten Island has done a lot of filling in since then, too.
You are right. Manhattan's population peaked about a hundred years ago. Around 1910, the population density of the lower east side peaked at about 500,000 people per square mile. This was probably the highest human population density ever.
And there were nohigh rises. It was just walk ups.
Manhattan's population peaked at an incredible 2.8 million in 2010. By 1930 slum removal had pushed that figure back down to 1.8 million and it grew to 1.9 million by 1950. It fell to a low of 1.4 million in 1980. It is now back up 1.86 million or so.. the highest point since 1950. I have no idea what they did to 900,000 people in 20 years between 1910 and 1930.
Manhattan's an interesting case because it is one of the few places where, over a very sustained area, there is bid-rent curve competition for residential and basic industries from commercial office and other programs. This probably explains why fluctuations in Manhattan population can be so extreme, so quickly. Depending on relative yields, either a lot of residential gets displaced quickly by commercial or, as is happening now Downtown, vice versa.