NEW YORK, NY.- Air, light, height, with a tingle of vertigo, are what the Guggenheim Museum’s spiraling rotunda is about. Which makes it a near-ideal setting for the buoyant, lucent, constellational work of the German-born Venezuelan artist Gertrud Goldschmidt, who called herself Gego, and who made some of the most radically beautiful sculpture of the second half of the 20th century.

As seen in the Guggenheim’s five-star, five-story survey, “Gego: Measuring Infinity,” opening Friday, hers is an art that may have started out in a conventional Modernist groove, but quickly went rogue, rejecting the most basic orthodoxies. “Sculpture: three-dimensional forms in solid material,” she wrote in a notebook. “NEVER what I do!”

I remember the first time I saw her work, in a 1997 New York group show three years after her death at 82. There were two pieces by her, both abstract. One was of a spare, spidery web done in ink on paper. The other was of a similar web, but made from twisted wire and dangling in midair. It was part of a series of free-hanging or wall-dependent sculptures she called “Dibujos sin papel” (“Drawings without paper”) that appeared, no two alike, in steady stream from the 1970s well into the 1980s.

There are almost 40 examples from the series — sometimes also referred to as “drawings in space” — among the 200-plus pieces in the Guggenheim’s show. And I can assure you that you will not see any contemporary works, by anyone, in any New York museum, more stimulatingly inventive than these.

Gego was born in 1912 to a secular Jewish banking family in Hamburg, Germany. She started making art when young but studied architecture and engineering in school, fields she perceived as having useful social applications. In 1938, one of her university teachers urged her to leave Germany as the Nazis rose to power. Her parents fled to England, but the only visa she could secure was for Venezuela. Leaving Hamburg, she wrote, “I gave my sofa and my bedroom stool to charity, closed the house, and threw (in a pathetic gesture witnessed only by myself) the key into the Alster River.”

Settling in Caracas, she worked for an architectural firm, married, had two children, became a Venezuelan citizen, divorced, and met her life partner, the graphic designer Gerd Leufert. After World War II, under a military dictatorship, Venezuela was pumping out oil and frantically building up its cities. Paradoxically, the government both brutally suppressed dissent and, with an eye to international stature, avidly supported aspects of progressive culture, welcoming young artists like Alejandro Otero and Jesús Rafael Soto as they returned home from Paris, bringing the latest developments in abstract geometric and kinetic art with them.

At this time, in the early 1950s, Gego dropped architecture as a profession and began to focus on painting, drawing, printmaking and, soon, on sculpture. One of the earliest items in the Guggenheim’s chronologically mapped survey show is an impressionistic 1953 watercolor sketch of Caracas. But by the end of the decade, she’s producing abstract metal pieces that reflect her attention to avant-garde work around her, in this case kinetic art — by then a Venezuelan national style — meaning art incorporating an element of physical or optical motion.

Paying attention did not, for her, necessarily lead to emulation. By overlaying patterns of parallel lines she gives some of these early sculptures a visual buzz. But her 1957 painted aluminum “12 Concentric Circles,” with its openwork curves spinning off into space, is a departure from the foursquare Constructivist model set by much geometric work of the period. Already she’s into throwing forms off-kilter, emphasizing instability and fragility, making art unpredictable and a little crazy, like the world.

People noticed the difference, and liked it. Pretty quickly she got offers to exhibit, despite the fact that she was neither a revered veteran nor a hot “emerging” talent. When her first Caracas solo opened in 1955, she was 43. Two years later, she was exhibiting with young stars like Otero and Soto, both her juniors by nearly a decade.

And the work kept coming, and changing. Walk up the Guggenheim’s ramp and you encounter ever more complex series of drawings, dramatically unconventional print-work, and sculptures that leave available models behind. The metal pieces get wild and unruly, becoming bristling bunches of pin-sharp metal rods that shoot straight upward or lie horizontally as if flattened by a sideways wind.

Then, beginning in 1969, more strangeness: The sculptures gain in size and become porous, and delicate. Most are still made of metal, but of thin tubes tied together by wires, creating the netlike effect of openwork weaving, and the graphic eccentricity of star charts. The resulting shapes are mostly three-dimensional — globes and columns — but they’ve shed bulk and weight, so much weight, in fact, that pieces displayed in suspension can be seen to faintly sway when a movement of air — created by groups of viewers passing or the museum’s air-conditioning — stirs them.

And you would surely have seen such stirrings in Gego’s fabled series of environments she called “Reticuláreas.” When she switched to creating netlike work — made incrementally, with her own hands, and without the assistance of welders or other technicians — she opened the potential for limitless extension of her forms. And she tested this potential in several wraparound, walk-in installations that she assembled, on site, in various public spaces.

Few, if any, of these were intended to be permanent. The components of the last “Reticulárea” she designed and oversaw — in Germany in 1982 — are lost. So, in lieu of an actual Gego-made example, the exhibition’s two curators — Pablo León de la Barra and Geaninne Gutiérrez-Guimarães, both of the Guggenheim — have filled a high-ceilinged gallery at the bottom of the rotunda ramp with more than a dozen individual openwork pieces from the 1970s and ’80s.

It’s a dense, circulatory ensemble. It puts you right in the middle of the art, a breath away from it, encourages you to consider both its hard-won, hands-on formal variety, and its refusal of easy readings: Are these seemingly ethereal works liberatory or entrapping? Existential flotation devices or cages?

Questions intensify in the show’s concluding section, high up on the fifth ramp, which holds late work, in this case the most head-spinning of all. By the end of the 1980s, the artist no longer had the strength for large-scale projects and began to reduce her “drawings without paper” to tabletop size, using household materials close at hand: thread, cardboard, frayed window screening, plumbing fixtures, product packaging, screws, buttons, worktable scraps.

Conceptually, the effect is dizzying, disorienting. The grid, that staple of modernist balance, which Gego had ceaselessly pulled and stretched, is here a thing of stray wires and loose ends, or is missing altogether, an absence in a crooked frame. The smooth, cool, official Modernism of decades past — which Gego never subscribed to — is long gone, though right to the end she has something interesting to replace it.

By 1989, the date of the final pieces — which Gego collectively called “Bichitos,” “Little Bugs” — the work has become hold-in-the-palm-of-the-hand-size tiny, but materially dense and rich: nuggets of all-but-unidentifiable, piled-up colored matter that have the charisma of jewels.

Looking at them I flashed on an image that certain Buddhists have of the universe as a high place, a mountain, canopied by a sheer, limitless light-spilling mesh — Indra’s net, it’s called — and sewn with faceted gems, each of which reflects the other jewels. It’s an image of interconnectedness that seems to suit Gego’s art.

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Gego: Measuring Infinity: Opens Friday through Sept. 10, Guggenheim Museum, 1071 5th Ave, Manhattan, (212) 423-3500; guggenheim.org.

This article originally appeared in The New York Times.