©Pat Ashforth & Steve Plummer 2019

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Pat Ashforth & Steve Plummer

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We are Pat Ashforth and Steve Plummer - a husband and wife team of creative mathematicians.

We taught Mathematics in UK High Schools for over thirty years and retired some years ago. Steve was also trained to teach Art. Pat is a self-taught Textile Artist.

Over the years we have worked with many different media, for crafts, and many techniques, for teaching Maths. In the 1990s our passion for teaching an understanding of Maths, rather than rote learning, unexpectedly collided with our craft work.

Knitting and Crochet

Our first book, Woolly Thoughts, was published in 1994. It was intended to inspire knitters to create their own designs using tessellating shapes and some simple calculations, without alienating those with a fear of Maths.   

Soon after, we were asked to design an afghan for Brown Sheep Co. Inc. and came to realise that an afghan could become a canvas for representing mathematical ideas. It did not have to be merely for keeping warm. It could become a work of art and hang on a wall. We went on to design and make over eighty afghans, most with a mathematical message. These have been exhibited in UK, and elsewhere, and four were bought for the Mathematics Collection of the Science Museum (London).

These are works of art in their own right. To some, the mathematical message is irrelevant and, in more recent years some of our designs were based on fitting shapes together to create optical illusions, rather than conveying a precise mathematical idea. Others such as Ring-road were anamorphic designs.

The afghans were originally for our own teaching in school but they were soon in demand elsewhere. It wasn't possible to make them for other people so we wrote booklets of instructions for anyone to make their own. We were in demand for talks and workshops in a huge variety of different areas.

As the result of an exhibition during MathsYear2000, we worked in collaboration, for eight years, with the British Hand Knitting Confederation for schools to create their own afghans as a combined Maths and Technology project. (This is still continuing in some areas and our mathematical input has also been used in similar projects in other countries.)

The afghan designs led to many other items which you can find on our Woolly Thoughts web site. Amongst the most popular have been cushion designs and instructions for making mathematical curiosities. Amongst knitters our most popular curiosities are Hexaflexagon Cushion and Octopush.

Illusion Knitting

In 2008 we stumbled across illusion knitting. At first we created simple geometric designs then thought ‘We can do better than that!’ Steve’s designs based on famous art works have become more and more spectacular and he is now considered the world expert on this form of art. He also teaches people, online, to create their own designs.


The original Woolly Thoughts book contained Steve's cartoon drawings of sheep and most of our other books have included cartoons. These led to books of cat and dog cartoons and to Steve being commissioned for the illustrations in books such as Alan Titchmarsh's Avant-Gardening in the 90s. He does very little such drawing these days - there are not enough hours in the day!


We had always said we could not reproduce our large wall-hangings for other people because they took so long to make the costs would be prohibitive. After years of being unable to provide what we were being asked for we realised we could re-interpret some of our original designs in other media and, in particular, returned to the use of fabrics, which had been our first love before the yarn took over … and so a mental block was lifted and MENTAL BLOCKS arrived.

Since then we have experimented with a range of mathematical and optical designs using screen-printing, block-printing, appliqué and other textile techniques. Some of the results are shown on this site. A few of the pieces are still available for sale. Contact us if you are interested.

Printing has taken a back seat in recent years but we still have our large printing table.

What we do now

Since retirement we have continued with the two main aspects of our work which are creating art works, and trying to dispel the belief that Maths is difficult and boring. We are at our best when we can combine these two.

Our time has become more flexible so we have been able to spend more time passing on our ideas, in person, through workshops and on the internet. Amazingly, the Woolly Thoughts group is one of the biggest groups on the mega knit and crochet site Ravelry.

3D Printing

At the start of 2019 we have bought a 3D printer and immediately started to reinterpret some of our previous ideas into 3D designs. There is no knowing where this will lead. We plan to add designs and information to this site and to our new blog.

Why Mental Blocks?

It doesn’t take long to notice that many of our titles can be interpreted in more than one way. In addition to creating mind-boggling designs we delight in finding names that leave you wondering.

Mental? Are these things of the mind?

Blocks? Do we mean printed with blocks? Are we referring to blocks of colour printed with silk-screens? Blocks of work for Maths lessons? Or maybe the building blocks of Mathematics and the barriers some people see.

Our dictionary says, amongst other things, that a block is a stupid person.

Perhaps we mean all of these!