When someone mentions knitting, it’s unlikely that the first word to spring to mind is “mathematics”, but it turns out that fibre arts such as knitting and crochet have strands of mathematics woven into their very fabric. This talk is a journey through the history, geometry and topology of knitting. Learn how crochet allowed us to visualise complex mathematical surfaces long before they could be studied with 3D computer models. Discover the careful computations behind beautiful knitted creations. Find out how the same punchcard technology that programmed early computers and took humans to the moon had its origins in weaving and is still used today in modern domestic knitting machines. Warning: this talk may provoke a desire to own more knitting machines than you currently do. No prior experience of knitting or maths is necessary to enjoy this talk, and yet there will be new ideas for even the most mathematically inclined fibre artists present!