The exotically shaped creatures that began to sprout silently all over the cozy lecture hall were soon spilling onto empty chairs and into women’s laps and shopping bags. When fully grown, these curiously animate forms will find a home as part of a mammoth version of the Great Barrier Reef. But at the moment they were emerging at a remarkable pace from the rapidly flicking crochet hooks wielded by members of the audience.
As she explained to the 40 people, nearly all women, who had gathered at New York University on Saturday, “This has grown from something that was a little object on our coffee table” to an exhibition that, so far, spreads over 3,000 square feet. And that was before the addition of that day’s catch.
Ms. Wertheim, a science writer, and her twin sister, Christine, who teaches at the California Institute for the Arts, came up with the idea of creating a woolly homage to the reef about two and a half years ago. The Wertheims, 49, grew up in Queensland in Australia, where the approximately 135,000-square-mile reef — and the billions of tiny organisms that it comprises — is located. But the Hyperbolic Crochet Coral Reef (more on that in a moment), is much more than a warning about global warming. It marks the intersection of the Wertheims’ various passions: science, mathematics, art, feminism, handicrafts and social activism.
For that reason the project has attracted a wide range of participants, including the Harlem Knitting Circle (which arrived with 10 members), a student from a Westchester high school’s environmental science club who had never crocheted before, a geoscientist and a former mathematics teacher and sheep farmer in Australia who creates algorithms to calculate the length of yarn she’ll need before spinning and dying the wool from her own sheep. In Chicago, where the exhibition appeared a few months ago, about 100 women contributed to the reef.
News of the project has been all over the online knitting and crochet world, which is how Njoya Angrum, the founder of the Harlem Knitting Circle, and Barbara H. Van Elsen of the New York City Crochet Guild discovered it.
“It pushes the boundaries of crochet, using different materials,” said Ms. Van Elsen, who wore to the gathering a bright orange yellow and green necklace that she had crocheted. “Exploring texture and color, it frees you up.”
It’s also “the greatest way to get people really aware of what’s going on in the world,” she added.
For Ms. Wertheim, a lithe woman with a no-nonsense attitude and closely cropped black and gray hair, the project embodies the “beauty and creativity that comes out of scientific thinking,” what she refers to as “conceptual enchantment.” As it turns out, the gorgeously crenellated, warped and undulating corals, anemones, kelps, sponges, nudibranchs, flatworms and slugs that live in the reef have what are known as hyperbolic geometric structures: shapes that mathematicians, until recently, thought did not exist outside of the human imagination.
“For God’s sake, please give it up,” Wolfgang Bolyai told his son, Jonas, a 19th century mathematician who was working on this sort of non-Euclidean geometry. “Fear it no less than the sensual passion, because it too may take up all your time and deprive you of your health, peace of mind and happiness in life.”
Actually these hyperbolic forms can be glimpsed all around, in the ruffled edges of kale leaves, the ruching that “Project Runway” designers favor, rippling ballerina tutus and drugstore scrunchies that girls use to gather a ponytail.
Yet mathematicians hadn’t focused attention in their direction. It wasn’t until 1997 that Daina Taimina, a mathematics researcher at Cornell who had learned to crochet as a child in Latvia, realized that by continually adding stitches in a precise repeating pattern she could create three-dimensional models of hyperbolic geometry.
For the first time mathematicians could, as Ms. Wertheim said, “hold the theorems in their hands.”
The Wertheims read about Ms. Taimina’s work a few years ago and invited her and her husband, also a mathematician, to speak at their Institute for Figuring, a nonprofit educational organization that they founded and run from a Los Angeles post office box. From these oddly frilled forms the Wertheims got the idea for the Hyperbolic Crochet Coral Reef. The Institute for the Humanities at New York University is co-sponsoring the exhibit, which will appear in the university’s Broadway Windows at East 10th Street and at the World Financial Center April 5 through May 18.
In the university’s auditorium Ms. Wertheim opened a large bag and began throwing out long snaking tubes, tightly scrunched blooms, fat textured spirals, and hairy coiled cactuses created out of yarn, thread, plastic bags, ties, can flip tops, videotape, ribbon, tinsel and more in a riotous splash of reds, blues, pinks, oranges, greens, tans, purples and yellows.
Later the group members traipsed upstairs to a large jewelry studio where they settled at one of six thick wooden worktables and began crocheting. The woven organisms developed so quickly it seemed as though time-lapse photography was at work.
“I was curious at first about how to do the forms, but then I was more intrigued by the message,” said Tina Bliss, a graphic designer who lives on Staten Island. Now, with two knitting groups, she has become “an evangelist” and wants “to bring a coral reef back to Staten Island.”
Mr. Wertheim emphasizes that the art and the science — the “conceptual enchantment” — are open to everyone. Aniqua Wilkerson, a member of the Harlem Knitting Circle, explained she first learned to knit seven years ago from books and through trial and error. She had tried to crochet hats, but they kept buckling. “That was a mistake,” she said as she finished up a tightly woven urchin in lime green, melon and turquoise. “I realized it was from increasing the stitches too much.” Which is precisely the method used to create hyperbolic forms.
“Wow,” Ms. Wilkerson said, “I’d been doing that all along.”
