Mathematics Meets Fashion: Thurston's Concepts Inspire Designer

An ABC News report, "Fashion and Advanced Mathematics Meet at Miyake: Fashion and advanced mathematics collide at Japanese label Issey Miyake," (2010) generated a lot of interest in the mathematics and fashion communities. Drawings by William Thurston (a pioneer in the field of low-dimensional topology, 1982 Fields Medal winner, and professor of mathematics and computer science at Cornell University) inspired designer Dai Fujiwara (Issey Miyake, Inc.).

Thurston and Fujiwara

William Thurston and Dai Fujiwara with a turkshead knot (of hyperbolic type). Photograph by Takeshi Miyamoto.


Mikaye models on the runway, wearing clothing inspired by topology. Photograph by Frédérique Dumoulin.


One of Thurston's Geometry Link Models that inspired Fujiwara.


Some linked scarves modeled after Thurston's drawings, on display at the reception in Paris. Photograph by Olivier Baco.

Photographs used with permission of Issey Miyake, Inc.

Thurston's brief essay below on mathematics and creativity and his connection with designer Fujiwara was available at the fashion show:

"Beauty is truth, truth beauty,--that is all Ye know on earth, and all ye need to know."

This famous and provocative quotation of John Keats is echoed on the emblem of the Institute for Advanced Study, where I took my first job after graduate school.

Last summer, after reading an account of my mathematical discoveries concerning eight geometries that shape all 3-dimensional topology, Dai Fujiwara made the leap to write to me, saying he felt in his bones that my insights could give inspiration to his design team at Issey Miyake. He observed that we are both trying to understand the best 3-dimensional forms of 2-dimensional surfaces, and he noted that we each, independently, had come around to asking our students to peel oranges to explore these relationships. This resonated strongly with me, for I have long been fascinated (from a distance) by the art of clothing design and its connections to mathematics.

Many people think of mathematics as austere and self-contained. To the contrary, mathematics is a very rich and very human subject, an art that enables us to see and understand deep interconnections in the world. The best mathematics uses the whole mind, embraces human sensibility, and is not at all limited to the small portion of our brains that calculates and manipulates with symbols. Through pursuing beauty we find truth, and where we find truth, we discover incredible beauty.

The roots of creativity tap deep within to a place we all share, and I was thrilled that Dai Fujiwara recognized the deep commonality underlying his efforts and mine. Despite literally and figuratively training and working on opposite ends of the earth, we had a wonderful exchange of ideas when he visited me at Cornell. I feel both humbled and honored that he has taken up the challenge to create beautiful clothing inspired by the beautiful theory which is dear to my heart.

See the video "Interview with Dai Fujiwara and Professor William Thurston at the Issey Miyake Fashion Show in Paris" and "Issey Miyake Fashion Show: Women's Ready to Wear Autumn/Winter 2010/11" on YouTube, and read "Designers Outline a New Geometry" (Suzy Menkes, New York Times, March 5, 2010).