We had no intention of making afghans until we received an email, in 1995, from Brown Sheep Co. Inc. asking if we would design an afghan for them. We agreed, not knowing what an afghan was. This name for a blanket or throw was not used in UK at that time. We did some research and eventually sent them four designs. They chose the one that we considered to be the least interesting. It was a design based on an idea we had used many times before and would use many more times afterwards.

That email completely changed our thinking and we never really went back to designing for sweaters and other conventional items. We realised that the large flat surface of an afghan could be a canvas to express mathematical ideas that would not fit on smaller items.

We were soon full of ideas and started to create large knitted ‘visual aids’ to be used in our own Mathematics classrooms. They were entirely for our own use. Before long, they were attracting interest from many quarters, and many people were asking to buy them. We didn’t want to sell them, partly we used them ourselves, partly because we didn’t want to make the same thing again for someone else when we had so many new ideas waiting to be made, and partly because the length of time taken to make them would make the costs prohibitive. We have only ever sold four and they were to the Science Museum (London). One doesn’t refuse when a National Collection wants to buy! We started to write booklets of instructions in response to the demand.

Afghans fall into a number of categories. They might be:

• A visual aid to help in explaining a mathematical idea or concept;  to help in the visualization process; to give a concrete basis for work with geometry, algebra or number.
• An article to promote mathematical interest and questioning; to help in building mathematical vocabulary and thinking about mathematical problems in a more relaxed way.
• A ‘pretty picture’ with a mathematical basis used to brighten up a wall.

The first afghans were all knitted, using the Woolly Thoughts methods we had already been using for several years. They were either straight knitting or had shapes with angles that were always a multiple of 45 degrees; they only used one yarn at a time. We continued with these self-imposed rules for a long time, until we were asked, by the Curator of Mathematics at the Science Museum, if we could create a Peano curve. It was impossible in knitting but we eventually realised it could be done in crochet. (The result was Spacecraft.)

Once we had broken away from our rules we were able to explore many ideas that had not been possible before - and the collection gradually grew to 70 afghans. The mathematical ideas expanded but construction remained simple. Our designs are within the capabilities of most knitters or crocheters, however inexperienced.