Earlier this month, as the Guggenheim Museum’s exhibition of the formerly little-known Swedish painter Hilma af Klint drew to an end, art world power broker Thelma Golden posted an unusually emotional Instagram caption. “For these past months the Guggenheim has felt like church,” she wrote. “All about spirit and soul. I have loved every visit.” Many of her peers, who had also posted about their last pilgrimage to the show, shared similarly jubilant impressions.

This message by the director of the Studio Museum made explicit what the museum world already understands: The Hilma af Klint show marks an important moment for a cultural industry struggling with hypercommercial forces, ethical crises, and an urgent pressure to diversify at every level.* Audiences are clearly hungry for provocative, unusual, eye-opening aesthetic experiences that draw them away from their screens and into communal aesthetic experiences. How will museums respond to an environment that rewards the right kind of curatorial risk? Which institutions will take the lead in this new era?

Hilma af Klint imagined a new visual and mystical universe as early as 1906, before many of the recognized pioneers of the avant-garde (“the male trinity of Kandinsky, Malevitch and Mondrian,” as the New York Times’ Roberta Smith put it). She devised a manifesto for living with a group of women called the Five, transforming visions from medium séances into “paintings for the future.” She produced more than 200 paintings, along with notes, drawings, and diagrams, mostly in secret, demanding that her work not be shown until 20 years after her death. The images were to be displayed, ideally, in a divine temple; they found their home in the Guggenheim, Frank Lloyd Wright’s spiral-shaped altar.

The exhibition’s unexpected critical and commercial success has rarely been seen in the art world. It brought 600,000 visitors to the museum, becoming the Guggenheim’s most popular show since the museum opened 60 years ago; 30,000 catalogs were sold (more than Kandinsky’s 2009 record-breaking book sales at the museum); the Guggenheim recorded a 34 percent increase in memberships. “When I saw the show I was just surprised at how strongly I reacted to the work, especially when you walk up the ramp and see these large, fragile paintings,” explained Eugenie Tsai, senior curator at the Brooklyn Museum. “Part of the draw is the fact that they’re not representational. The abstract language is poetic and it’s very soothing but also points out to the existence of a larger reality. It doesn’t speak the same language of the contemporary visual overload.”

Nevertheless, the exhibition was adopted by the platform of contemporary visual overload, Instagram, with almost 39,000 hashtagged posts from the af Klint show showing the singularly organic forms and cool pastel tones. On the gram, af Klint provoked reactions that ranged from queer pride (“Artsygaylove,” with two women kissing in front of a painting) to the New Age–y (“Feeling all sorts of spiritual,” posted a young woman posing scantily dressed in front of her pink-and-yellow poster). In an era obsessed with feminine liberation and spirituality, it transformed the artist into a cult of her own.

As the once male, Western-centric history of art is expanded and rewritten to include those it traditionally pushed out, female artists are experiencing revivals and being praised for their pioneering visions. Institutions that have recently chosen to showcase radical women have been rewarded with massive recognition—and dollars. The success of af Klint can be viewed as a successor to Marina Abramovic, who drew crowds to MoMA in 2010, and Yayoi Kusama, who at 90 is breaking museum attendance records around the world with her polka dots and infinity mirror rooms. Many other underrecognized artists outside the white, male-centric narrative, such as the black sculptor Betye Saar and the Lebanese painter and poet Etel Adnan, have received late and sudden fame after decades of struggle.

“There may now be a greater openness to women and to the belief they can tell the truth,” said said Tsai, whose Brooklyn Museum has seen recent hits like Frida Kahlo: Appearances Can Be Deceiving and the female-heavy Soul of a Nation.* She compared af Klint to Kahlo and to the rising sculptor Simone Leigh, whose show now follows af Klint’s at the Guggenheim, as “incredibly powerful artists who have so much to say, but whose voices had been ignored or stifled.”

“I wonder if Hilma was an unexpected blockbuster,” continued Tsai. “To me this show was an affirmation of the importance of the museum; it took on a life of its own. Everything was in alignment: the art, the architecture, the moment. Exhibitions don’t happen in a vacuum; they reflect a collective state of mind, a hunger for something transcendent.”

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Now several museums are getting ready to exhibit more work by lesser-known artists from previously marginalized groups, such as MoMA, which is totally revamping its collection and curatorial purpose for the first time in its history. As women such as Joan Mitchell, Suzanne Lacy, and others get their own exhibitions, the lessons of Hilma af Klint are clear. Transforming museums and galleries into malls hasn’t proved to be a successful strategy and has failed to inspire the public, sparking activist backlashes instead. In our era of awakening, audiences want to see themselves represented in culture. They want to connect with great stories, which institutions should continue to tell.

“I think this shows us that we have narrowed the field of ‘blockbuster’ artists to a very small number of men,” said the critic and curator Helen Molesworth, citing Warhol, Basquiat, and Picasso. “But there are other great artists that capture the imagination of the public.” Some risk-averse museums will continue leaning on those “blockbuster” artists, to their detriment. (Please, not another Old Masters or Bill Viola show!) But when institutions expand their own perspectives, take bold risks, and bring in a wider range of voices, they connect with deeper social movements and with visitors—sometimes more of them than an institution ever expected.