Making with Rigour

There are 3 ways to incorporate a mathematical element into art(/craft) making:

• As a tool, similarly to a brush, or printing press. Often, then, the mathematics is obscured by the medium (e.g. computer art)
• As a subject where the use of mathematics is literal
• As an inspiration, where the mathematics is a starting point, but its use is less literal

We investigate the use of mathematics as a tool for specific teachinques or media, then use our findings as inspiration to produce artefacts that make more explicit the mathematical thinking inherent in them.

Making with rigour is a research methodology that combines the making of exemplars of specific media with a reflective attitude that seeks to capture emergent thinking, here specifically of a mathematical nature. This approach requires accountability for what is made, the how and the why, in an effort to show the richness of the mathematical structures underlying the practice. It combines methods from a variety of practices, including:

• mathematics research methods, such as generating and classifying cases, induction, deduction, conjecturing, proving, etc.
• artistic practices
• reflective crafting with a focus on intrinsic mathematical elements, by means of strategies derived from
  • experimental archaeology
  • reverse engineering
  • critical making
  • primary creative practices

These approaches also incorporate problem posing (math) or problem finding (art):

• Blending: throwing together two or more ideas, techniques, subjects or concepts, then observing and analysing the mathematics of the result (dial up the math)
• Transposition: re-interpreting the representation of a mathematical object in ways that make it less explicit (dial down the math)
• Technology: exploring how a technology or medium works (mathematically) and making it explicit (dial up the math)
• Open play: playing with a pattern, discovering and exposing the underlying structure (dial up the math)