And what’s spiritual these days, if not museums? They’re our cathedrals, as cultural pundits like to say. Which makes the opening this week of Ando’s Ft. Worth museum a transcendently big deal. Ando has long been famous among design buffs; MoMA in New York singled him out for an exhibition as long ago as 1991. In ‘95 he was awarded the Pritzker, architecture’s biggest prize. But until the last year or so, he’d built almost no projects outside Japan. Now, besides Ft. Worth, he has the Pulitzer museum in St. Louis (and down the road are plans for a Calder museum in Philadelphia and an addition to the Clark in Williamstown, Mass.). The Ft. Worth commission was daunting. The site is next door to the 1972 Kimbell Art Museum–arguably the most beautiful museum in America and designed by one of Ando’s heroes, Louis Kahn. And Ando’s a devout modernist–who still sketches, for heaven’s sake–in an age of edgy theorists and techno whiz kids who’ve tossed out the grid in favor of the blob.

The most stunning recent museums–yes, I’m thinking of Frank Gehry’s gorgeous Guggenheim in Bilbao, Spain–are art objects themselves. Ando’s Ft. Worth project is not. Its front exterior seems so unprepossessing it could be a corporate headquarters, all sleek glass and aluminum panels. But Ando is up to something else, something that can be suggested but not truly conveyed by the often dazzling photographs of his work. He’s an alchemist of space, with a nearly flawless eye for scale and proportion and a magical gift for using natural light. In Ft. Worth he’s created a rich architectural experience of materials and movement–you feel drawn through galleries that are both logical and mysterious, simple and surprising. These are elegant and generous spaces, but they never overwhelm what’s on the walls. The museum is a close marriage between architecture and art–in this case, a highly selective collection of first-rate postwar work, from Mark Rothko to Ron Mueck. Curator Michael Auping assembled most of it in the past eight years–and he could think about just where to put pieces as the building was going up. There are fantastic moments as you amble through: start up the grand staircase, with its gently vaulted ceiling (a homage to the Kimbell) and see Andy Warhol’s big green self-portrait pop into view. Don’t miss that balcony overlooking a double-height gallery, with Martin Puryear’s “Ladder for Booker T. Washington” soaring away, or the spot where Richard Long’s circle of stones sits, just on axis with a Henry Moore sculpture out on the grass.

Ando, 61, seems a modest man, given to smiles and slight bows, who admits that building next to Kahn’s masterpiece brought him “a good deal of anxiety.” But Ando’s ambitions are hugely assured. “For him, the ideal is if this museum could be the heart of the community,” says his associate Kulapat Yantrasast, who also acts as his translator. “He wants to create places that people feel are inspiring.” His scheme for the $65 million museum is a series of pavilions, made of velvet-smooth concrete, each one wrapped in glass, set in a reflecting pool. As you move through the museum there are ever-changing plays of light and views of the silvery water and surrounding “nature”–albeit a nature shaped by the architect on the 11-acre site, and interrupted occasionally by a carwash or fast-food sign poking up just beyond Arcadia.

The man-made pool and landscape are very Japanese. So are the serene spaces between the glass and concrete walls of the pavilions, inspired by the traditional engawa (veranda to you). Ando, who grew up in a wood-and-paper house in Osaka, never trained as an architect. As a kid, he loved to hang out at a carpenter’s shop, and learned to build with his hands. Later he became a professional boxer. In his travels outside Japan, he discovered the great modern architects who would most shape his work, especially Le Corbusier, the master of classic proportions in concrete. Ando even named his late beloved dog Corbu, but unlike his idol, who painted in the mornings and liked to go out at night, Ando mostly works. He has, he says, “no hobbies, except architecture.”

His drive for perfection is legendary. The Pulitzer Foundation for the Arts in St. Louis, a jewel of a private museum that opened last year, is only 30,000 square feet (compared with Ft. Worth’s 153,000) but took four years to build. The trickiest aspect: those poured-concrete walls, whose ridiculously smooth finish–think of 400-count Frette sheets–comes from formwork made of imported Finnish veneer. “If I’d had any idea of what was involved, I wouldn’t have done it,” laughs founder Emily Rauh Pulitzer, who chose Ando on the recommendation of artists Ellsworth Kelly and Richard Serra. “But I’m glad I did.” Inside, the place is alive with shifting daylight and reflections from a long pool set between two pavilions. The best detail: a narrow slot in the ceiling, above the main gallery, admits a wash of light that seems to come straight from heaven.

While the Pulitzer is a small fortress of enchantments, the Ft. Worth museum signals a shift to a grander and more transparent space, starting with the almost too-vast glassed-in lobby. The classic Ando details are here–the knife-edge concrete corners, the precision with which a glass wall meets its steel frame–but the essence of Ando is in the human-scale galleries and glass pavilions. “A space is never about one thing,” Ando has said. “It is a place for many senses: sight, sound, touch and the unaccountable things that happen in between.”

Ando’s few detractors say he’s so 20th century. But Ando proves modernism is neither dead nor boring. His serene spaces are charged with emotion. They blanket your mood the way a great abstract painting does–say, Rothko’s “White Band No. 27” at Ft. Worth. And for all its subtlety and silence, his architecture is dynamic in unaccountable ways–hard as granite and fluid as water, tough as concrete and airy as sunlight. Ando is the pugilist in the paper house, shadowboxing with your spirit. “You employ stone, wood and concrete, and with these materials you build houses and palaces; that is construction,” wrote his main man, Le Corbusier, 80 years ago. “But suddenly you touch my heart… and I say: ‘This is beautiful.’ That is Architecture.” Though a writer hates to admit it, we couldn’t say it better ourselves.