Appears in collection : 2026 - T1 - WS1 - Rigorous Illustrations - Their creation and evaluation for mathematical research
What can mathematical illustration learn from studio art research methodologies, and how canvisual principles and poetics be developed together to illustrate abstract concepts? Thispresentation bridges two worlds that share more than is immediately visible: both mathematicalresearch and studio art practice pursue forms that do not yet exist, working iteratively throughobservation, experimentation, and responsive adjustment to reveal patterns that resist verbaldescription.Drawing from fifteen years teaching Art Foundations alongside studio research tracing invisiblephenomena, I propose that rigorous illustration shares core methodological ground with what TimIngold calls "thinking-through-making." Both practices involve following rather than imposing,allowing form to emerge through correspondence with the subject rather than throughpredetermined design.In studio practice, we do not begin knowing what the work will look like. We enter throughobservation, material exploration, or formal questioning, then develop understanding throughiterative mark-making, allowing materials and subjects to guide us toward unimagined forms.Mathematicians visualizing abstract concepts engage in parallel process: testing configurations,following emergent patterns, discovering which formal elements—color, scale, spatialorganization, rhythm—reveal structure most effectively.Through my collaboration with mathematician/artist Edmund Harriss and artist/technologistVincent Edwards visualizing chaos theory—translating the logistic map's bifurcation into physicalvessels from equations to bitmaps to clay—we demonstrate how foundations' emphasis on formal,poetic exploration of color, pattern, and form develops the reasoning required for rigorousmathematical illustration. The collaboration brings strength through interplay of mathematicalprecision, material correspondence, and poetic formal inquiry. The presentation reframesillustration not as communicating pre-existing knowledge but as inquiry itself—one both artists andmathematicians employ when pushing into territories "not yet understood well by anyone."
