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This essay investigates the practical ways that artists and craftspeople cultivate mathematical sensibilities through their practical immersion in making and problem-solving. Mathematical sensibilities refer to skilled kinds of perception and heightened levels of attention and discernment regarding the qualitative properties of an object or composition, such as its shape, proportion, balance, symmetry, centredness, alignment or levelness. It also includes an ‘intuitive’ quantitative sense of volume, mass, weight, thickness and dimension. The objective of the investigation is not to describe the ways that a maker’s existing knowledge and training in formal mathematics is put into practice, but rather to elucidate the ways that their practices of making produce kinds of ‘non-formalised’, context-dependent mathematical understanding and knowledge. The starting point for exploring embodied mathematizing is therefore not from the cognitive or neurosciences, psychology or formal mathematics, it is argued, but rather from a phenomenological approach – ‘an opening on the world’ – that attends to person, materials, tools and other physical and qualitative features that make up the total environment in which activity unfolds.
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