Susan Goldstine

Susan Goldstine
First and foremost, I am a professor of mathematics. Over the past decade, I have slowly realized that I am also an artist and a designer of jewelry and knitwear, but at the core of my practice is the desire to share the beauty of mathematics with others through my visual and tactile works.

Hand-knitted garments hold a particular fascination for me. There is something profoundly satisfying in knowing that every inch of yarn in an intricate shawl or sweater has flowed directly through my fingers.

I am currently Professor of Mathematics at St. Mary’s College of Maryland and an Associate Editor of the Journal of Mathematics and the Arts. Ellie Baker and I wrote the 2014 book Crafting Conundrums: Puzzles and Patterns for the Bead Crochet Artist, which contains many of our jewelry patterns. My knit and crochet designs are listed on Ravelry, where my username is sgoldstine.
Photographer: Justin Foreman. Model: Natasha Pillai.
Hand-knit merino/alpaca yarn
Collection: The Symmetry Completist

Each of the pieces in this collection catalogs all the symmetries of a particular mathematical type that are possible in a particular form of knitting color work. The three unifying design principles are as follows: the designs in each garment fall into one or several visually compatible families of patterns with shared motifs; each possible symmetry type appears exactly once in the garment; the resulting garment has a pattern that an experienced knitter can easily reproduce.


Double knitting is a form of two-color knitting that yields color-reversed versions of the same pattern on the front and the back. Its thick, reversible fabric is particularly suited to scarves.

Of the seventeen wallpaper groups (the possible symmetry types for designs in the plane that repeat in multiple directions), exactly nine are compatible with the regular grid of a double-knitting design. Crystalline contains each of these nine symmetry types. The nine designs fall into three families of three; a family with heart motifs with reflection symmetry, a family with scroll motifs with rotational symmetry, and a family with vine motifs with glide-reflection symmetry.

The pattern for Crystalline appears in the Deep Fall 2016 issue of the popular online magazine Knitty. Sneaking an account of symmetry groups into a general knitting magazine is one of my proudest feats of stealth mathematics.
Photographer: Justin Foreman. Model: Natasha Pillai.
Photographer: Justin Foreman. Models: Jasmine Long, Natasha Pillai, Sasha Jarvis.