2026 Joint Mathematics Meetings
Katherine Vance
Artists
Katherine Vance
Associate Professor of Mathematics
Department of Mathematics and Computer Science, Simpson College
Indianola, Iowa, USA
Statement
I began knitting as a child, long before I became a knot theorist. The rigorous habits of mind and careful attention to both small details and the big picture that I have developed as a mathematician also serve my fiber arts, and I have won several blue ribbons in knitting and spinning at the Iowa State Fair. I love thinking about the connections between knot theory and knitting or spinning, whether that be the braids formed by knitted cables, linking numbers and intarsia, or framing and writhe in handspun yarn.
Artworks
A knitted, braided table of knots
61.0 x 46.0 cm
knitted wool-nylon yarn
2025
This knitted table of the fourteen non-trivial knots of seven or fewer crossings was inspired by the connection between mathematical knots and knitted yarn. Using minimum braid representatives retrieved from Scott Morrison and Dror Bar Natan's online Knot Atlas (http://katlas.org), I knitted a braid representation of each knot. The braids are formed by twisted knit stitches traveling across a reverse stockinette field. Below each braid is a label with a row of purl bumps indicating the knot's crossing number and a "subscript" giving its number in the table.
I chose the purple yarn in memory of Tim Cochran, who was a wonderful mentor to me and many other knot theory graduate students at Rice University, and who often wore lavender shirts.