Various Gemma Anderson publications about or touching on drawing in mathematics

There are a whole bunch of good papers up on Gemma Anderson’s website about drawing as a research process in art and mathematics. I’m very interested in the idea of drawing “honing the human being as a scientific instrument” and drawing representing the embodied experience of the seeing process. That could be very interesting – what if we say the drawings are ‘of’ nothing but the seeing process anyway? Is that a bit Kantian?

I’d like to think about the Thinker/Drawer dialogue a bit more, and what informs the drawing process. How do we decide how to think about problems? That’s a big question, but that tells us how to lay one out on a board.

  • comparison
  • groupings, similarity
  • symmetry
  • what’s background, what’s detail
  • what’s smooth and what’s sharp


Anderson, G. 2016 ‘Drawing as a way of knowing’, Interalia Magazine, Drawing Thoughts, 20/21, January 2016.

In Writing on Drawing – essays on drawing practice and research (2012) Steve Garner argues for the value of drawing research to communities beyond the art world, namely  the scientific and cultural: ‘drawing research presents a powerful opportunity to demonstrate the ability to generate new knowledge about the visual and to communicate this through the visual’ (Garner, 2012:15). Garner’s view, like John Berger in Ways of Seeing (Berger, 2009), challenges the assumption of the supremacy of the written word in visual research.
When probing into the unknown, drawing is an ideal tool because drawing is thinking, pointing; it makes things present and puts them at a distance, it is a mode of inquiry. Drawing can represent the seen and present the unseen, the known and the unknown (Klaas Hoek, A Call for Drawings, 2015)
Drawing Research Theory and Practice (DRTP) (Intellect Ltd) which published its first volume in 2015 might be a good thing to check out.
I value drawing as both process and object. Through the act of drawing, time and space are contained and mediated by the drawn line. Drawing allows for an expansion of the subject through a time-based practice. One way of looking at drawing is to see it as a honing of the human being as a scientific instrument, an idea which is  important to the process of Goethean observation: ‘For Goethe, the human being is the most powerful and exact instrument if we take the trouble to sufficiently refine our sensibilities’ (Naydler, 1996: 23). In the dynamic process of drawing, then, both
the artist and scientist become the mediating instrument as the eye constantly moves over areas of contrast in the dynamic process of seeing. The eye navigates the object searching for lines, structures and patterns, for dark and light and for colour. Drawings not only represent the subject they describe but also the embodied human experience of the seeing process itself. (Emphasis added)

Hernly, K. 2015, Drawing the real and the unknown: A look at a project by Gemma Anderson’, Drawing Research Theory and Practice Journal, Intellect Press.

On a workshop on finding the fourth dimension by Anderson and Corti

This paper outlines a couple of picture-proofs and their project:

Published in TRACEY| journal Thinking December 2014
Special Edition: Drawing in STEAM
Gemma Anderson a, Dr Dorothy Buck b, Dr Tom Coates b, Prof. Alessio Corti b

The literature on art and mathematics has focused largely on how
geometric forms have influenced artists and on the use of computer
visualization in mathematics. The authors consider a fundamental but
undiscussed connection between mathematics and art: the role of
drawing in mathematical research, both as a channel for creativity
and intuition and as a language for communicating with other scientists.
The authors argue that drawing, as a shared way of knowing, allows
communication between mathematicians, artists and the wider public.
They describe a collaboration based on drawing and “inverse vision”
in which the differing logics of the artist and the mathematician are
treated on equal terms.
The Thinker exists in the world of linear logical thinking. The Drawer operates
in the world of the imagination and of inverse vision.
Having said a little about what we mean by thinking and what we mean by drawing, we are ready to examine the use of drawing in mathematical research as a channel for intuition and creativity. This use of drawing is hidden—rarely spoken about among mathematicians and undiscussed in the literature on drawing. This absence of discussion is surprising, given how widespread the practice is in research mathematics, even in those sub-fields that frown on drawing-based proofs.
Oh yeah? Sub-fields? Drawing-based proofs are pretty widely frowned upon according to Giaquinto.
On the one hand, drawing gives the Thinker a way to organize thoughts. By listening to the Drawer, the Thinker is led to choose a sequence of logical steps that reflects the Drawer’s inner vision. Thus the Drawer helps the Thinker to overcome otherwise unmanageable complexities. On the other hand, the Thinker’s geometric rigor [7] helps the Drawer to focus and sharpen the inner vision, and the dialogue continues.
In this paper, we focus on the drawing of imaginary objects— that is, objects that we see with our mind’s eye. Whether the drawn object be physical or imaginary, all drawing is a sort of inverse vision [4]. By drawing with pencil on paper we give physical form to our mental images, and in the process we learn to see them better. Thus, in this context, drawing is a tool to train ourselves to see imaginary things better.

OK, this is cool. But I’d like to formalise this idea a lot more.

I had started to see similarities in shapes repeated across the natural world. I noticed that certain sets of patterns recur in the animal, vegetable and mineral kingdoms, but I couldn’t find anything that documented these relationships. I realised that, as an artist, I could visualise relationships in a way that would be more difficult for scientists, because their work is so specialised.

Take drawing seriously as a mode of enquiry. Encourage your students to look closely at different examples of plants in the classroom, and they may start to genuinely see the five-fold symmetry or spiralling leaves of a particular flower. Don’t underestimate drawing as a way of learning and making comparisons.


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