Gertrude Stein in full form at Portrait Gallery

She was a trust fund kid who moved to Paris in 1903 and made some very successful bets early in her career as an art collector and wannabe writer. Gertrude Stein, whose family prospered in the San Francisco real estate market and streetcar business late in the 19th century, used her money to buy paintings by Matisse and Picasso long before they became world-famous. She latched onto artists, celebrated their work, associated her name with them and, especially in the case of Picasso, used them to establish her own reputation as an astute connoisseur and observer of modern art.

And then she began perpetrating one of the longest and most successful literary frauds in cultural history. As an author, she wrote reams of gibberish, either in a singsong style that one critic aptly described as “literary baby talk” or in a hermetically sealed private language that she absurdly considered an analog of cubism. As an art collector, she often showed remarkably bad taste, especially after the early years of her alliance with Picasso. Her theater work, either unintelligible or profoundly cliched, survives because other people set it to music or choreographed it. Even her moral reputation — courageously living with her female partner, Alice B. Toklas, championing a woman’s right to be eccentric — has been sullied by recent scholarship showing that she while she rode out World War II in a French country house, she was protected by a particularly unsavory and anti-Semitic official of the collaborationist Vichy government.

But Stein was convinced she was a genius, and she was a savvy manipulator of the fame machine. The National Portrait Gallery’s fascinating exhibition “Seeing Gertrude Stein: Five Stories” uses photographs, art, film and memorabilia to demonstrate how she did it: strategic friending, careful self-invention and always collaborating with people who were not only more talented, but happy to do all the work. (“Five Stories” refers to the five divisions in the show: Stein in photos and paintings; as literary celebrity; as domestic partner; as arts networker, and as muse to artists of several generations.)

aspects of the It boils down to a simple formula that served her well for a half century: It’s all about me.

Stein arrived in Paris after failing Latin at Radcliffe and flunking out of Johns Hopkins medical school. She and her brother Leo Stein, who had a similarly distinguished academic career, lived together and pooled their money to shop for art. They weren’t out-of-sight rich, like the Philadelphia collector Albert Barnes, who, Stein said contemptuously, “looks like a Jew.” But the Jewish Stein family, which included another brother, Michael, and his wife, Sarah (Matisse considered her the brains of the outfit), had enough money to hoover up paintings by the younger generation of modern artists. The results of their collecting, gathered in an exhibition, The Steins Collect (seen in San Francisco last summer, and arriving at New York’s Metropolitan Museum of Art in February), is astonishing, a wall-to-wall greatest hits of the years between the turn of the century and World War I.

Among the treasures was Picasso’s 1905-06 portrait of Gertrude, looking like a cross between Madame Defarge and a statue from Easter Island. Stein loved the heavy, peasant-like intellectual ferocity of the image, and frequently appeared in photographs under or near the famous painting. (The Picasso is not in the Portrait Gallery show but is in the traveling “Steins Collect” show that will go to New York.) She also claimed (preposterously) that it took more than 80 sittings for the great artist to get her just right. The painting became her brand, or logo, and associated her name forever and always with that of Picasso, whose accomplishment and fame soon eclipsed her own. In the tedious little book Stein wrote about Picasso, filled with absurd generalizations and essentializing claims that explained Picasso by virtue of his Spanish heritage, she put her finger on one of the great delusions of the art world, a sin she furthered with all her prodigious energies: “A picture lives by its legend, not by anything else.”

Stein certainly lived by her own legend, and you can see her buffing it to a shine in almost every photograph in the National Portrait Gallery show. In domestic scenes with her lover Toklas, Stein gravitates to the center of attention. A 1922 photograph by Man Ray, who was her unofficial house photographer until he asked for payment and was given the boot, shows Gertrude large and impressive at her desk, with poor Alice framed by the doorway like a servant, seemingly mousy in her dreary weeds (she was, in fact, every bit as monstrous as Stein). Readers of Stein’s 1933 “The Autobiography of Alice B. Toklas,” receive a quick surfeit of Gertrude’s imperious egotism. The seemingly clever ruse of writing her own story as if told through the voice of her lover is transparently an excuse to amp up a narcissism and self-congratulation that would be utterly insufferable parsed if in the first person.

The National Portrait Gallery show, first seen in a larger version at San Francisco’s Contemporary Jewish Museum last summer, doesn’t flinch from examining Stein’s ugly side. It gets a lot of it just right: “Stein was an arts networker,” one panel says, which is the best way to describe her. But it gives too scant attention to her association with Bernard Fay, a French bigot whose star rose under the Vichy regime, and it takes too much for granted Stein’s self-assessment as a great writer.

The Fay controversy is increasingly dogging the Stein legacy. Fay was among the young homosexual artists and aesthetes who gravitated to the Stein-Toklas household. His specialty was a perfervid anti-Masonic loathing, which he was able to practice with deadly results after Hitler blew into France and the Vichy regime was set up to do his bidding in the unoccupied territories. After World War II, when Stein and Toklas were discovered perfectly safe despite being Jewish, lesbian and avatars of the avant-garde in territory controlled by Hitler, who had no love of any of these things, there was a mystery: How did these remarkable ladies ride out the tempest?

Fay helped them. “Their friend Bernard Fay, who had the ear of the occupation government in Paris as well as of the Vichy regime, used his influence to ensure their well-being,” says the exhibition wall text, far too blandly. One other brief mention, and that’s about it. The Fay alliance should surprise no one. Janet Malcolm discussed it in her 2007 book “Two Lives: Gertrude and Alice,” and Dartmouth professor Barbara Will explores it in depth in the recently published “Unlikely Collaboration.” Politically, Stein had long been a reactionary. Perhaps she was being ironic when she said Hitler should be given the Nobel Peace Prize, but she was all too in earnest in her support of the fascist government in Spain. Picasso may have said of her (the source, James Lord, is as unreliable as Gertrude herself): “A real fascist, what’s more. She’s always had a weakness for Franco.”

It will take time and some painful readjustment for the Stein legend to absorb all of this, for the general public to realize that the great gibbering earth mother of ungrammatical gobbledygook is essentially in the same category as Ezra Pound (fascist-sympathizing poet), Louis-Ferdinand Celine (collaborationist writer) and Paul de Man (anti-Semitic literary critic).

But it’s not easy to agree with this, from Wanda Corn’s introduction to the catalogue for “Seeing Gertrude Stein”: “Along with James Joyce and Virginia Woolf, she was one of the most radical experimenters with language that the modern world of European and American letters has known.” Corn has done thorough work in curating a fascinating show that gets almost everything right except the basic premise of Stein’s talent. Stein didn’t have Joyce’s erudition and wit, nor Woolf’s haunting penetration of character. Nothing Stein wrote rose to the level of Woolf’s “To the Lighthouse” or Joyce’s “Ulysses” or “Dubliners.” Stein’s literary innovation was simplistic and mechanical. She had one linguistic trick and like Yoda it was.

After selling herself as the Picasso of the literary world, Stein spent her later years dominating an increasingly dreary circle of B-list talent. She enjoyed a few genuine successes, including a lecture tour of the United States in 1934-35. The Associated Press began one of many stories about Stein’s American promenade by announcing: “Gertrude Stein is among Gertrude Stein’s favorite authors.” There were also collaborations with artists who were as assiduous in using Stein to the climb the greasy pole of fame as Stein was in her manipulation of the Picasso association. She quarreled with her young proteges over everything, including the size of the name Gertrude Stein in the proposed publication of her translation of poems by Georges Hugnet. And she collected lots of bad art.

“If you want to see how much she really understands about painting, all you have to do is look at the crap she now likes,” said Picasso. That included works like the paintings of Francis Rose, whose work is on inglorious display at the National Portrait Gallery show. Stein continued ungenerous and manipulative in her treatment of younger artists, which came back to haunt her from time to time. The Russian painter Pavel Tchelitchew, better than Rose, produced a wonderful drawing around 1931 depicting Stein with an artist’s canvas where the head should be, a not-so-subtle comment on her use of other people to bolster her reputation.

Hating Stein puts one in loathsome company. Throughout her life, she attracted the worst sort of critics — anti-Semites, misogynists, homophobes and philistines. Stein Haters will have to deal with the last room of this exhibition, devoted to the ongoing legacy of Stein in the arts. If she is still an icon among artists, then perhaps she wasn’t a fraud. But that misses a central paradox of how influence works in the arts. A mediocre patron saint is often a better, less-threatening spiritual friend than an artist of real substance. Stein thrives in part because she simply gives artists license. And given the blankness of her writing, it’s impossible to misinterpret her.

But that’s also her darkest legacy to the art world. Stein modeled a familiar figure still swanning the galleries of cultural capitals around the world: Intellectually infantile, cheerfully amoral, profoundly insecure and nakedly ambitious. She is the patron saint of every mediocrity who woke up one day and realized, I want to be an artist.

at the Smithsonian National Portrait Gallery until Jan. 22. For more information visit www.npg.si.edu.