In the old photograph, a lonely farmhouse sits on a rocky hill, shaded by tall trees. The scene looks like rural Maine. On the modern street, apartment buildings tower above trucks and cars passing a busy corner where an AMC Loews multiplex faces an overpriced hamburger joint and a Coach store.

They are both the same spot. Not so long ago, all things considered, the intersection of Broadway and 84th Street didn’t exist; the area was farmland. “The Greatest Grid: The Master Plan of Manhattan, 1811-2011,” now at the Museum of the City of New York, unearths that 1879 picture of the Brennan Farm among other historic gems. The show celebrates the anniversary of what remains not just a landmark in urban history but in many ways the defining feature of the city.

After all, before it could rise into the sky, Manhattan had to create the streets, avenues and blocks that support the skyscrapers. The grid was big government in action, a commercially minded boon to private development and, almost despite itself, a creative template. With 21st-century problems — environmental, technological, economic and social — now demanding aggressive and socially responsible leadership, the exhibition is a kind of object lesson.

Simeon De Witt, Gouverneur Morris and John Rutherfurd were entrusted with planning the city back in 1811. New York huddled mostly south of Canal Street, but it was booming, its population having tripled to 96,373 since 1790 thanks to the growing port. Civic boosters predicted that 400,000 people would live in the city by 1860. They turned out to be half-right. New York topped 800,000 before the Civil War.