What exactly does it mean to be a “self-taught genius”?

A new exhibition by that name at the New Orleans Museum of Art doesn’t provide an easy answer. But there are still plenty of great things to look at while you’re trying to figure it out.

Organized by the American Folk Art Museum in New York City and consisting of more than 100 objects spanning three centuries of American art, “Self-Taught Genius: Treasures from the American Folk Art Museum” arrives in New Orleans this month after previous stops in Davenport, Iowa; San Diego; and Fort Worth, Texas. It will move on to St. Louis and Tampa, Florida, after it closes at NOMA in May.

Broadly speaking, “self-taught art” is a term that has come to supplant “folk art” and “outsider art” in recent years (though the American Folk Art Museum doesn’t seem to have decided to change its name just yet).

But it’s a label that also can be a little confusing.

“‘Self-taught’ refers to artists who created work outside of a traditional artistic academy or environment,” explained NOMA curatorial assistant Anne C.J. Roberts. “It’s more of an umbrella term.”

Semantics aside, though, the art in the show is what really deserves attention. And despite its curators’ attempts to organize the show via themes, which occasionally amount to little more than an assortment of overlapping buzzwords (there doesn’t seem to be much difference between what the show defines as a “Messenger” and a “Guide,” for example), much of the best and most memorable work in the show defies any sort of easy categorization anyway.

Those works include the enormous architectural model at the entrance to the exhibition. Marino Auriti’s soaring “Encyclopedic Palace” was intended to be a monumental building housing the entirety of mankind’s technological and intellectual achievements, from the wheel to the satellite. It’s not difficult to understand why it was never built, but in its unbridled optimism it perfectly encapsulates the visionary spirit that animates much of the subsequent work in the show.

Nearby, an elaborately detailed drawing of a cathedral by Achilles G. Rizzoli was intended to serve as a birthday tribute for the artist’s mother. The level of technical expertise involved belies the notion that “self-taught art” is by definition crude or naive — Rizzoli, after all, had considerable training as an architectural draftsman, and there are many other instances in the show of artists bringing other types of vocational or technical experience into their art-making process.

Between these and other examples, the exhibition tends toward making the “self-taught” label more problematic than illuminating. But you only have to look at works like Thornton Dial’s intricately textured assemblages, George Widener’s staggeringly complex numerological tribute to the victims of the sinking of the Titanic, and Sam Doyle’s double-sided paintings on pieces of tin roof to realize that the “genius” part is beyond dispute.

“Self-Taught Genius” is further augmented by a small but smartly chosen show elsewhere in the museum of similar works from NOMA’s own collection. Despite its size, “Unfiltered Visions” manages to fill in a few of the gaps in the larger exhibition while demonstrating the ample depth and breadth of self-taught art here in New Orleans. A richly detailed (if somewhat discomfiting) drawing by Henry Darger actually outshines a similarly sized piece by the same artist in the AFAM show, and an exuberantly colored quilt by Clementine Hunter is one of the highlights of both shows combined.

Viewed together, the two shows provide ample evidence of the considerable talent that has always existed in American art outside of the artistic mainstream — no matter where that genius comes from.

John D’Addario writes about art. He can be reached at jd70117@gmail.com.