Unraveling Topological Crochet

“Models in this book look magical. And as you cannot learn magic just from watching it being performed, so it is with topological crochet. In this book the magic of topological crochet is carefully revealed to the reader step by step. Follow it by making your own models and you will be rewarded with a deep understanding of topology and your own collection of beautiful crochet sculptures.”

—Daina Taimina, mathematician and author of Crocheting Adventures with Hyperbolic Planes: Tactile Mathematics, Art and Craft for all to Explore

“This wonderful book introduces crochet crafters to fun and intriguing mathematics, and mathematicians with a crafty bend to making beautiful and fun objects illustrating symmetry and topology, to their own delight and maybe that of their friends and students! Shiying and Eve are crochet magicians—and their boundless energy and sense of fun is now yours to enjoy as well in this great book.”

—Ingrid Daubechies, winner of numerous mathematics awards, including the National Medal of Science, and first female president of the International Mathematical Union

“A wonderfully practical introduction to the art and craft and math of Shiying's virtuoso sculptures, laying out exactly the math you need, with detailed project instructions to follow as you learn. There are ingredients from knot and graph theory, geometry and topology, and so many forms to explore, from elegant loops to wild fanciful polyhedra. I've always needed a model in my hands to understand geometry, and crocheting is such a friendly way to visit with these beautiful shapes.”

—Bathsheba Grossman, pioneering mathematical sculptor known for her 3D printed work in steel

“Topology has long been a curiosity of mine, even as a non-mathematician. Now, with nothing more than familiar tools—yarn, hook, and stitch markers—Shiying guides us through topological structures that make sense in our hands, even when the math seems out of reach. This isn't a quick skim-and-stitch pattern book, but a new way of making fiber art. Your hands will understand more than you expect!”

—Edie Eckman, fiber artist, knitting and crochet teacher, and author of several best-selling knitting and crochet books, including The Crochet Answer Book: Solutions to Every Problem You'll Ever Face; Answers to Every Question You'll Ever Ask

Shiying Dong grew up in rural China, where bamboo weaving was an inseparable part of life, which kindled her passion for mathematical craft. Before she started creating original shapes with her hands, she devoted most of her energy to the traditional paper-and-pencil way of studying spacetime. Shiying has a PhD in theoretical physics from the University of Illinois Urbana-Champaign and a Master’s in mathematics from the University of Pennsylvania. She won a Silver Medal and the Best Female Participant Award in the first Asian Physics Olympiad in 2000. In November 2023, Shiying was one of the two grand prize winners of the Einstein Mad Hat Awards, organized by MoMath and the UK Maths Trust. She was also the recipient of the Best Textile, Sculpture or Other Medium Award in the JMM Mathematical Art Exhibition, 2025, featured in the NY Times. Since 2023, she has been exhibiting her work at MoMath, Gathering 4 Gardner, JMM, Bridges, Vogue Knitting Live, and various museums. She has given dozens of talks on topological crochet and held more than a hundred workshops on crochet and mathematical art and craft. She was the Innovator-in-Residence of the Innovation Lab in Greenwich Library, Greenwich, CT, from September 2025 to November 2025.

Eve Torrence has loved art, crafting, and mathematics since she was a child. She has been very lucky to build a career that merged these passions. She has a PhD in mathematics from the University of Virginia and is professor emeritus at Randolph-Macon College, where she was a member of the faculty from 1994 to 2021. Eve designed and taught many mathematical arts courses at R-MC, in which she used knitting, crochet, bead crochet, and origami to introduce, explain, and illustrate mathematical topics. She has exhibited her mathematical artwork at numerous juried shows at the JMM and Bridges conferences. Eve's sculpture Day was awarded the People’s Choice Award at the 2015 Bridges Mathematical Art Exhibition. She is currently a member of the Board of the Bridges Organization and serves as the managing editor of the Bridges Conference Proceedings. Eve is the author of Cut and Assemble Icosahedra: Twelve Models in White and Color and co-author of The Student’s Introduction to Mathematica and the Wolfram Language. In 2013, Eve received a State Council of Higher Education for Virginia Outstanding Faculty Award. She has served as the chair of the Maryland-DC-Virginia Section of the MAA and President of Pi Mu Epsilon National Mathematics Honor Society.