The Geometry of Hope” which just opened at NYU’s Grey Art Gallery, quietly promises to be one of the most compelling shows of the young season. Originally organized by the Blanton Museum at the University of Texas at Austin, it displays several dozen choice works of midcentury South American abstraction from the Patricia Phelps de Cisneros Collection.

While it is true that some of these artists — Lygia Clark and Helio Oiticica, for example — have appeared on the New York scene in recent years, most of them, like the continent of their origin, remain an unimagined world for the Chelsea-centric crowd.

As such, the show will appear as something of a surprise. For the abstract paintings and sculptures on view are hardly the second hand, thrice warmed-over derivatives you might expect from a region of the world that looked so longingly toward Europe and from so far away. The one fact that sears itself most emphatically and instantaneously upon the eyeball is how very accomplished and self-assured they are. This is an art that needs no apologies and no special pleading. It stands forth on its own two feet.

The title of the show is an inversion of a famous phrase of the British critic Herbert Read, “the geometry of fear.” Read applied the phrase to postwar British artists such as Barbara Hepworth and to the nervous, dangerous times in which she worked. By contrast, this show argues, Hepworth’s South American contemporaries were animated by the same geometric, as opposed to organic, impulses in their abstractions, but they felt a utopian hopefulness that World War II had dashed forever among the artists of Europe.

“The Geometry of Hope” is a tale of five cities: Montevideo, Buenos Aires, Sao Paolo, Rio de Janeiro, and Caracas. Paris is also included among them because it was, up until WWII, the lodestar of artistic culture, the Mecca to which many South Americans trekked to receive their longed-for initiation into the rites of high culture.

Chronologically, the story begins in 1934 in Montevideo, the once bustling, now sleepy capital of Uruguay. That was the year in which Joaquin Torres-Garcia returned to the country of his birth after more than 40 years in Paris. Though the fortuities of space in the Grey Gallery relegate him to the back of the basement area, he is one of the most admirable artists on view. His charm, and the eminence he enjoys in his homeland, make him unique among modern artists. His gridlike applications of synthetic cubism owe a great deal, in texture and tone, to artists such as Ferdinand Léger, while his palette at times recalls Georges Rouault.

Yet in his understated and infinitely earnest manner, Torres-Garcia wins his way into your heart with the jazzy, early modernity of his compositions. Spare lines among interlocking color fields are enriched by the odd word and by scattershot allusions to the bustling world of pre-war billboards. Not only is Montevideo’s best museum devoted to his art, but he is the formal inspiration for much of his country’s stamps and banknotes. Is there any other abstract artist who can make that claim?

Meanwhile, just across the Plate estuary in Buenos Aires, Alfredo Hlito and Tomas Maldonado were creating fine-spun abstractions that represent an original variation on the Bauhaus, with wobbly, pencil-thin lines and narrow stripes of color that take the place of the bold blocks of blue and red that Piet Mondrian pioneered.

Perhaps the most fertile South American soil for geometric abstraction was Brazil, where Lygia Clark, one of the founders of the Neo-Concretist movement, worked before she went on to participate in the dada-inspired Tropicalia movement with Oiticica. In “The Geometry of Hope,” both artists are represented by severe exercises in radically reduced forms that succeed in drawing a great deal of visual power out of a narrow field of aesthetic terms.

One of the revelations of the show is the work of Willys de Castro, displayed in two magnificently, wittily minimalist sculptures. His translation of Barnett Newman’shard-edgedcolorfieldpaintings into these diminutive exercises in canary yellow on hardboard and various tropical woods is little short of genius. A solo exhibition devoted to this artist would be much appreciated.

A show like “The Geometry of Hope,” devoted to the mid-century abstract art of South America, invariably provokes the question of where South America stands today on the international art scene. The picture is far less balanced now than it was then. When everyone looked to Paris, there was something like equality between New York, Buenos Aires, and Berlin. But today, with New York as the new center of the international art world, and Europe’s various capitals as branches of Chelsea, South America seems more marginalized thanitdid50yearsago. Meanwhile, within South America, the importance of Montevideo and Uruguay has diminished, as the centripetal force of Sao Paolo has increased.

It may be that “The Geometry of Hope” provides a skewed image of mid-century South American abstraction, due to the seemingly infallible eye of the collector, Patricia Phelps de Cisneros. But it is hard to imagine that much new work from that continent can match the distinction of the objects now on view at the Grey Gallery.

Until December 8 (100 Washington Square East, between West Fourth Street and Waverly Place, 212-998-6780).