I read a novel recently set in the 1840s and the narrator mentions the rapid rate at which New York is expanding over the island. When was this complete?
Louis Tremante's doctoral thesis on agriculture and food systems in New York (Iowa State, 2000--PDF) indicates (p.4) that the last farm known on Manhattan operated until the 1940s. Christopher Sellers (Crabgrass Crucible) states that the last closed in 1940, but I don't for some reason have the footnotes to see what he cites.
The Franklin PA News-Herald (thanks, selective PDF newspaper access!) however has a story from 5 April 1940 that gives more details and even a location (from the OCR text):
'The last farm in Manhattan has finally given up the ghost and turned iself into a parking-place. Vincenzo Benedetto, 10th Avenue and 214th Street, held out as long as he could. Practically every year he was good for a story in the papers about "the last farm in Manhattan." In fact, Benedetto himself wearied of this. "Go 'way," he would say. "I am sick and tired of talking about the farm." Well, he needn't talk any more.'
Benedetto, according to census records, was born in Italy in 1886, but I don't know when he arrived in the US. This story seems to have been carried widely, but I don't have access to corroborating data (census, tax information, etc) to say for certain that it was the last operating farm, its size, what it was like in terms of output, and so forth. For that, we'd need cadastral maps (or Sanborns, if they go that far north) that would show the lot, and possibly tax documents or other city information.
That has never happpened. There are several operating farms in Manhattan to date. One citation: