Astor Place has the makings of a great urban space. The dominant presence has long been Cooper Union, the original brownstone building of which, from the 1850s, is among the rare Manhattan buildings that is completely freestanding. Frederick Peterson’s design was strong enough that the building has anchored its site with admirable authority for a century and a half.

All around it, however, is a hodgepodge of structures that has done nothing to make of this the special place it cries out to be. Now, several fancy new buildings have risen, are rising, or will rise soon around Cooper Union.

At 4th Street, the Bowery splits off into Third Avenue, which heads straight north, and Fourth Avenue, which runs northwesterly to 14th Street before straightening out. This fork in the grid is called Cooper Square. A small triangular park between 6th and 7th streets holds the fine Peter Cooper Monument by Augustus Saint-Gaudens. On the other side of 7th Street stands the main Cooper Union building. Between 4th and 8th streets the buildings have Cooper Square addresses.

One of them, 41 Cooper Square, is where Cooper Union’s new academic building is now going up. Designed by the 2005 Pritzker Architecture Prize recipient Thom Mayne of the California-based firm Morphosis, with the New York firm Gruzen Samton, this building has received a great deal of positive attention. It’s an object building, meant to stand out from its surroundings. Frank Lloyd Wright’s Guggenheim Museum and Frank Gehry’s Guggenheim Bilbao are famous object buildings. One may find such buildings in pre-Modernist architecture. St. Peter’s Basilica is an object building — but with the dissimilarity being that it doesn’t speak a language different from the lesser buildings around it.

There’s nothing inherently wrong with object buildings, so long as they observe principles of sound urbanism (which are independent of aesthetics). Many Victorian buildings expressed something about the raw power and violence of American cities during a time of explosive growth. The Morphosis building has, to my incredulity, been described as “playful,” though it’s one of the most violent building designs I’ve ever seen. The giant gash out of its glassy front evokes a bomb blast. It’s Victorianism redux, though without the Victorians’ leavening ornamentation.

Across 8th Street from Cooper Union is the college’s banal 1960s School of Engineering building (with a 1990s add-on Starbucks in a widely admired design by Smith-Miller + Hawkinson). The school has sold this site to developer Edward J. Minskoff Equities, which is going to build a 13-story mixed-use building designed by the Tokyo-based 1993 Pritzker winner Fumihiko Maki, with Adamson Associates Architects. The drawings indicate sharply angular forms, with a polished black Canadian granite slab along Fourth Avenue and a glassy base and stepped-back mass along Third Avenue. This, too, is an object building, though one very different in feeling from the Morphosis design. Mr. Maki’s is a sleek, Modernist building bearing a striking resemblance to the tower he’s designed for the World Trade Center site (150 Greenwich St., also known as Tower 4).

Mr. Maki, who turns 80 later this year, trained at Harvard’s Graduate School of Design and worked in America before establishing his Tokyo firm in 1965. He’s an orthodox Modernist whose most admired works include the Fujisawa Municipal Gym in Fujisawa, Japan, and the Spiral Building in Tokyo. His works exhibit the precision-tooled geometrical compositions of steel, glass, and concrete associated with the 1950s Harvard generation. Mr. Mayne is nearly 16 years Mr. Maki’s junior and attended Harvard’s graduate program in the early 1970s. His work is Deconstructivist rather than orthodox Modernist. Many of his works are meant to be disturbing and exhilarating by turns.

Gwathmey Siegel & Associates Architects designed the curvy apartment high-rise that extends along the south side of Astor Place from Lafayette Street to Cooper Square. Charles Gwathmey was one of the “New York Five” (with Michael Graves, Peter Eisenman, Richard Meier, and John Hejduk): Young Turk architects featured in a 1969 Museum of Modern Art exhibition.

In the early 1970s, a group — the “Grays” — emerged, led by Robert Venturi, Robert A.M. Stern, Jaquelin Robertson, and others, who challenged the formalist, anti-contextual presumptions of the “Whites” (so-called for their commitment to formal purity, as opposed to shades of gray), including the New York Five. The divide has defined New York architecture ever since. The Young Turks came of age during New York’s fiscal meltdown and debated more than they built. Should we endure such fiscal misfortune again, a new architecture will emerge, and you can be sure that Messrs. Mayne’s and Maki’s buildings — and I don’t mean this as criticism — could look very old-fashioned sooner than their adulators suspect.