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It's feminine handicrafts, it's mathematics, it's ecology ... the Hyperbolic Coral Crochet Reef

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In a whitewashed room in the basement of the Royal Festival Hall in London, a scientist called Margaret Wertheim is gamely attempting to explain complex geometry - to a group of women wielding crochet hooks.

Straight lines and spheres, everyone can manage. But when she starts to describe "hyperbolic space", in which it is possible to draw an infinite number of lines through a single point, each one parallel to a straight line below, faces glaze over. To her left, an artist called Inga Hamilton is knotting her fingers through a ball of fuzzy wool. As Wertheim's talk ends, Hamilton reveals what she has been concocting: a fluffy model of hyperbolic space. It is a surprisingly beautiful object, its edges rippling like an Elizabethan ruff. Suddenly excited, the women crowd round.

In 2003, Wertheim, a spry, engaging physicist and mathematician, set up the Institute for Figuring with her twin sister, Christine. Its aim is to explore everything that is "aesthetic and poetic" about science. Previously, the IFF has staged talks and exhibitions on subjects such as how the world looks to a spider, and the physics of snowflakes. But the IFF's biggest project is the sisters' own creation: a crocheted homage to the Great Barrier Reef, which has already been exhibited in Los Angeles, New York and Chicago. For the next two months, it will inhabit the Hayward Gallery in London.

The Hyperbolic Crochet Coral Reef came about by accident. Wertheim read about a discovery by a mathematician called Daina Taimina: that you could model hyperbolic space using crochet, simply by increasing the number of stitches in each row until the fabric warps. Mathematicians had previously struggled to demonstrate hyperbolic surfaces, despite the fact that they appear throughout the natural world - in lettuce leaves, for example.

Wertheim was so inspired that she picked up a crochet hook for the first time in 20 years, and encouraged her sister to do the same. It was Christine, a lecturer in feminism and popular culture at the California Institute of the Arts, who noticed how all the pieces of crochet accumulating on the sisters' coffee table looked like coral. Wertheim recalls her sister saying: "We could crochet a coral reef."

Since then, Wertheim says proudly, the reef has developed along evolutionary and art-historical lines. The sisters are now in their "postmodern phase", working on a "toxic reef", crocheted using plastic carrier bags sliced into ribbons and reels of videotape - a comment on the environmental damage being wreaked on the real Barrier Reef by pollution and waste. "People ask: is it art or science?" says Wertheim. "But I don't believe in those classifications. This project is feminine handicrafts, it's mathematics, it's ecology - it crosses those boundaries."

Back at the Festival Hall, a table has been spread with bits of reef made by the Wertheims and various collaborators. Some are huge, in garish pink, flaming orange and fluorescent green; others are tiny and delicate, their curved edges curiously sensual. And although no one in the room seems entirely to have grasped the bit about hyperbolic space, the 20 women (and two men) are enthused by the crochet.

One woman bounds up to Wertheim to tell her how liberating it feels to invent a coral shape, having always adhered to patterns. "There's no question," says Wertheim, "that in the hierarchy of our society, science is up here and girls crocheting is down there. For many of the women who come, it's immensely uplifting to hear women's work 'legitimated', as it were, by the contextualisation with science and mathematics."

It's time for us to start making our own pieces of coral, to be displayed as a "sister reef" in the foyer upstairs. I'm keen, but there's a snag: I don't know how to crochet. Wertheim promises to teach me, assuring me that, since I can knit, I'll pick it up in no time. I keep twisting the stitches in a manner she finds peculiar. After four attempts to correct me, she wisely gives up.

Over the past year, the Wertheims have become what they call "full-time reef wranglers". When their reef is not being exhibited, it lives in their shared home in LA. "Instead of filling it with furniture," says Wertheim, "we filled it with reef."

The sisters may sound eccentric, but it's not hard to see how their obsession began. Despite the twisted stitches, my tiny piece of crochet quickly begins to form a satisfying ruffle; with every row, I enjoy the peculiar impression that it is developing a life of its own.

We're all invited back to the Festival Hall two months later to drop off our contributions for the sister reef. When I arrive, the table is covered with gloriously weird shapes, including a huge, bulbous entity covered in tampons, and a malevolent-looking piece somehow crocheted using copper wire. My two confections - one pearly white as though bleached by pollution, one in iridescent blues and greens - look conservative by comparison.

Although Wertheim is thrilled that galleries are queuing up to display the work, she hopes one day to find a permanent home for it, preferably not in her own sitting room. As she explains to the group in the Festival Hall how the Great Barrier Reef is slowly dying, you start to wonder whether the crochet homage might one day be all we have left, physically, to remind us of the real thing.

· The Hyperbolic Crochet Coral Reef is on display at the Southbank Centre, London SE1, from June 11. Details: 0871 663 2500