The world's largest terrestrial mammal produces its excrement in unbelievably large packages. Elephant dung is one material that the British-born artist Chris Ofili used to create his canvas Prince Among Thieves (1999), which now hangs in the contemporary section of New York's newly reopened Museum of Modern Art. As supersized as the elephant dung, the galleries and open spaces at the new MoMA left me gasping. The Japanese architect Yoshio Taniguchi has doubled the size of the museum, creating a walk-through lobby between West 53rd and 54th Streets, an atrium 110ft high, good rooms for the museum's unrivalled collections and a huge open space on the gallery's sixth floor for exhibitions.
It is recommended that you start at the top, where two enormous pieces hang in almost solitary splendour with what seems like acres of polished wood floor in between. James Rosenquist's F-111 (1965), an 80ft-wide oil depicting a warplane mingled with scenes from the all-American life, faces Ellsworth Kelly's Sculpture for a Large Wall (1957), a series of coloured anodised aluminium panels suspended between parallel aluminium rods, casting exotic shadows on to the gallery's white walls. Our visit begins with shock and awe. A newly acquired Francis Bacon triptych of 1991 and a glorious Chuck Close self-portrait share this vast top floor. The Close is a huge face brilliantly composed of colourful patterns that blend at a distance to reveal flesh, spectacles and beard.
Roof skylights beckon the natural light and offer glimpses of the midtown Manhattan skyline surrounding MoMA, reminding us that the city is itself a museum of modernism. One black-glassed tower block slices incongruously through MoMA. Designed by Cesar Pelli to bring in extra revenue, it was completed in 1984 and has survived Taniguchi's cull of past extensions.
The main art collection is not generous-ly accommodated, though it has space enough, and is hung quite conventionally in a maze of rooms on floors five and four. The visitor is not forced to follow a strict chronology, and the museum does not commit itself to a prescriptive view of how modern art evolved from one movement to another. However, the hanging gives special places to Henri Rousseau's The Dream of 1910, Matisse's Seated Nude of 1925-29 and Paul Signac's portrait of Felix Feneon, a fantasy in pointillist dots that must have stunned on its appearance in 1890.
The depth and quality of the collection are extraordinary. Some of Cezanne's finest pieces, including The Bathers , share a room with Seurat, Van Gogh and Gauguin. The Picassos on display range from his placid Boy Leading a Horse of 1905-6 to his horrifying Charnel House of 1944-45. Matisse's Dance I is presented on a staircase: the Russian merchant who commissioned it intended to hang it thus. Kandinsky's exuberant abstract Four Panels for Edwin R Campbell are at home in New York, having been painted for the entrance foyer of the motor tycoon's Park Avenue apartment.
As we move through the second half of the 20th century, the growing influence of Americans is strongly reflected in the collection. Warhol and Pollock are joined by Johns, Judd, Liechtenstein, Wesselman, Oldenburg, Chamberlain, Diebenkorn and others. Examples of foreign artists, such as the Briton Bridget Riley with her 1964 Currents, become rarer.
In Taniguchi's new design for the museum, each floor has been cut away to provide balconies over the galleries beneath, offering vertiginous vistas through the building's core. From almost anywhere in the museum, you can lean over the glass barriers to gaze upon two more of the collection's giant pieces: Monet's Water Lilies of 1920, painted over three large canvases; and Barnett Newman's Broken Obelisk, built from steel between 1963 and 1969.
Oddly, those eye-catching pieces welcome visitors to the second floor, which is devoted to contemporary art, defined here as anything after 1970. This level of the museum offers the most beautiful areas but the least compelling part of the collection. Recent works are not especially well represented. An honourable exception is an acquisition dated 2003, Modernity, Mirrored and Reflected Infinitely by Josiah McElheny, a pleasing cabinet of blown glass and aluminium receptacles that stretch out endlessly in mirrors that, miraculously, do not reflect the viewer.
In its new home, MoMA's collection effortlessly reasserts that it has no equal. In the 75 years since its foundation, it has acquired brilliant pieces, an extraordinary amount of money from its patrons and now a stunning building. Nowhere could you learn more of the history of modern art. During much of the museum's existence, New York has defined what it is to be modern and been at the forefront of artistic development.
Is that true of the city today? I sense a nervousness that the scene has moved elsewhere. The very term "modern art" now has a dated ring to it. Perhaps in an effort to put the Big Apple back in its rightful place, the museum has sent its historic collection upstairs and set aside its most spectacular space for works that have yet to be created. MoMA stretches the hand of welcome to artists of the future, but is New York where they will want to be?