For more than 30 years, the Outsider Art Fair has been one of the world's preeminent showcases of self-taught artists from around the globe. The fair has returned to Chelsea this weekend for its 31st iteration, spread out within the sprawling space of the Metropolitan Pavilion. It’s a dizzying assemblage of some of the finest amateur artwork you’ll ever encounter, featuring more than 300 artists from eight countries.

One of those artists is Gregory Horndeski, a trained mathematician who retired from teaching in the 1980s to focus on his artwork.

"I used to be a tenured associate professor of mathematics at the University of Waterloo in Canada," Horndeski told Gothamist. "Quit that job, moved on to Dallas, taught myself how to paint. So I feel like I identify with the people that are the outsider class."

One of his paintings on display is “Our Future Retirement Home.” It depicts a surreal, lush natural landscape. It also incorporates a delightful makeshift pinball machine — the ball literally travels through the painting and lands in a little cup at the bottom.

“It's symbolic of life," Horndeski said. "You're born, you come outta darkness, you take a random path through the world careening all around. But no matter what path you take, you end up in the cup in the ground or a cup on the mantle. The world continues without you. The whole point is try to enjoy the ride through life.”

Gregory Horndeski with “Our Future Retirement Home"

Horndeski exemplifies the Outsider Art spirit that fair owner Andrew Edlin tries to foster every year. Edlin manages his namesake gallery in Lower Manhattan, and has been running the fair since 2012. Along with Birdsong Project co-founder Randall Poster, Edlin co-curated this year's showcase exhibit, "We Are Birds," which features dozens of works inspired by birdlife, by Greg Burak, William Edmondson, Minnie Evans, Tony Fitzpatrick, William Hawkins, Chris Johanson, Pam Lins, Eleanor Ray, Fred Tomaselli and Bill Traylor.

Edlin says the artists chosen for the fair generally have had no formal training.

"When you see contemporary artists, they've all been schooled," he said. "They're all in some ways riffing or commenting or showing their influences, and even in an overt dialogue with it. These artists have had no formal training, and they're not trying to be part of any academic conversation."

Edlin says the goal of the fair is to promote artists who don't have the infrastructure of the art world already behind them.

"Nobody told these artists what the rules were,” he said, “and there's a certain soul that this fair and these artists, really their work, exudes. These aren't just commodities, you know? These are people who are visionaries, who for the most part are really underdogs."

Edlin says much of the artistic talent is discovered by the dealers, which includes local galleries and nonprofits who specialize in finding people who don’t self-identify as artists or promote their work commercially.

Roger Jones's Metrocard pieces

There are 64 exhibitors in the fair this year, including Rachel Weisman, director of the Fountain House Gallery, a non-profit space in Hell’s Kitchen that works with artists living with serious mental illnesses. One of their “star students,” Roger Jones, is showing several pieces at the fair that incorporate found objects from around the city, including coins and Metrocards.

“He is someone who has experienced significant hardships in his life, housing insecurity, etcetera," Weisman said. "He's obviously heavily influenced by being a person in New York City. So the Metrocards have been a really incredible kind of homage to this ubiquitous thing that every New Yorker is familiar with, that is soon to be retired – a way to really immortalize this incredible part of being a person in New York."

Situated next to Jones' work are dark psychedelic paintings by Marina Marchand, another Fountain House artist, who is taking part in the fair for the first time this year. She says her works are heavily influenced by Pop Art and 1960s animation. She has no formal training, but has practiced her craft for decades.

"It feels absolutely great [to be here]," Marchand said. "Like a big evolution for me, from humble beginnings going all the way up and up and up."

Bill Arning, another exhibitor, has galleries in Houston and Hudson, New York. He believes that contemporary art has become too professionalized, and loves the space for more experimental work the fair provides.

“This is a fair that doesn't just privilege people who are trained differently; it privileges people who have different goals and make choices that are deliberately non-commercial," he said. "This is where people like us, who are a little bit contrary in our natures, end up.”

Thedra Cullar-Ledford

One of his clients is Thedra Cullar-Ledford, a first-time participant. "It's exciting and a little nerve-wracking,” she said. “But really, I'm just taking pictures of people's shoes and the $3,000 purses.”

Cullar-Ledford, who sports bright pink hair and a hat inscribed with her first name, spent Thursday's V.I.P. preview hours chatting with people in front of a wall of breasts and vulvas she’d painted on platters and sterling trays. She was inspired to create them after she underwent a double mastectomy, to serve as a commentary on the reasons women feel compelled to reconstruct their breasts. The process of finding the trays in old thrift stores in Texas, as well as the actual painting, was a form of therapy for her.

According to Horndeski, the mathematician-turned-painter, what unites all the disparate artists at the fair is not that they were self-taught, but rather that they have an "obsession" to create art.

"I think they're more original, more tied to what art should be about: a humanistic adventure in which we try to approach people and their problems and existence," he said. "That's what I try to do through my art — to convince people that the world is just this amazing place, you only have a finite amount of time to enjoy it, so do all you can to appreciate existence while you can."