“Myth and Modernism” marks a reconciliation of sorts. Before a museum in Bilbao was even a gleam in the eye of Guggenheim Director Thomas Krens, the city’s mayor had asked Jorge Oteiza (1908-2003), one of Spain’s leading sculptors and a tireless champion of Basque culture, to create a gleaming new center for avant-garde art. The project fell through, and the charismatic (some would say difficult) Oteiza later turned down the offer of a show at the new Frank Gehry-designed museum.

The artist, however, might have been secretly pleased by this traveling exhibition, which in fact did originate at the Guggenheim Bilbao. For many New Yorkers, this will be the first look at an artist little known outside his own country.

Filling two upper ramps at the New York museum, his 125 small, abstract sculptures and drawings reflect the lively influence of Malevich’s spare, geometric designs. As a young man, Oteiza’s fascination with anthropology and mythology took him to South America, where he experienced Neolithic art firsthand. He began writing and lecturing on what became a lifelong pursuit: a new art that linked the mysteries of prehistoric art and new concepts of space.

Wandering along the Guggenheim’s ramps, viewers may well be struck by the amount of method in Oteiza’s mysticism. The single artwork that best illustrates his methodology is probably his “Experimental Laboratory,” a huge collection of tiny maquettes produced in quickly worked, impermanent materials – wood, chalk, wire, tin, plaster, and paper – that explores various mathematical and visual concepts.

Oteiza was absorbed in the portent of the void; art became for him “an integrating, re-linking process, between man and his reality, which always departs from a nothingness that is nothing and concludes in another Nothingness that is Everything, an Absolute.” This sounds more like existentialist poetry than a working program, and, indeed, in 1959 Oteiza announced that he had achieved the “Experimental Laboratory’s” goals and would cease sculpting. Except for brief periods of updating old sculptures, he devoted the remaining four and a half decades of his life to the promotion of Basque culture. This exhibition concentrates on his last and most productive decade of active sculpting.

Wall texts helpfully illuminate the evolution of his thinking, which placed paramount importance on the details of process. A bronze statuette from 1950 consists of a slab like torso gouged by deep fissures, and shows the early influences of Jacob Epstein and Henry Moore. But Oteiza shortly turned to totally abstract forms, embarking on a series of projects he variously called “transstatue,” “light condensers,” “macles” (after a mineralogical term for twinned crystals), and “empty constructions.”

Each project explored the way a sculpture addresses the void around (or inside) it, using deep articulations of surfaces, bored holes, translucent materials like alabaster, or assemblages of what he called “Malevich units”: irregular four-sided planes. Some of these processes can be seen in “The Earth and the Moon” (1955), in which the hollowed contours of two limestone towers playfully sculpt the space in between. Holes dot their surfaces, sometimes continuing all the way through the block, creating sudden specks of light. For another series Oteiza cut deep slices into small marble blocks with a grinder.

The abrupt overhangs and troughs in the stony surfaces of “Opening the Polyhedron by Disk-Cuts” (1955) lend it a remarkably tense compactness. Here, too, slight shifts of viewpoint turn dark channels into shafts of light that penetrate from the other side. Other notable sculptures include the marble “Empty Construction” (1957), whose Cubistic forms seem to alternately hunch and stretch with a kind of buoyant gravity, and the stainless steel “Weightless Spatial Pair” (1956) with its dramatic scissoring of semicircular planes.

With his “Open Boxes,” Oteiza turned to cube-like steel constructions perforated by irregular cutouts. They seem perpetually on the brink of grasping air, with light and shadows playing pleasingly on their interior surfaces. His final phase, “Metaphysical Boxes,” features more regular angles and a greater sense of enclosure, some of which have an eerie austerity. In “Homage to Velazquez” (1958) a long, eighth-inch-wide slit between two broad panels feels like a momentous, defiant escape.

These works have a certain affinity with the Minimalist sculptures that would soon be produced by Tony Smith and Donald Judd. But the Minimalist space – one of empirical, physical connections – was entirely different in tone from Oteiza’s intimate, soulful one.

Likewise, in “Empty Boxes” and “Emptying the Sphere,” pieces created after 1957, the rather even development of forms tends to hamper their spatial momentum. This may explain why these smallish pieces often feel truly small: Unlike similarly sized sculptures by Arp, Henri Laurens, and Giacometti, they never transcend the role of maquettes. Only a few sculptures here actually achieve the plastic power of Mondrian’s paintings. Oteiza’s concepts, rigorous as they are, don’t necessarily lead to forceful rhythms of masses and spaces.

Still, Oteiza’s tumble of eloquent ideas shows a great artist’s spirit of inquiry. He could talk passionately of the poignant emptiness surrounding the core of a half-eaten apple, draw a sketch of it, and produce a sculpture exemplifying the idea. In this instance the sculpture (the “Triple and Lightweight Unit” from 1950) powerfully manipulates the air around it. With a little hunting, you’ll find other gems like it in the show.

Until August 24 (1071 Fifth Avenue, between 88th and 89th Streets, 212-423-3500).