Illustration as a Mathematical Research Technique

Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool to research for as long as research has taken place. We use the term illustration to encompass any of the many ways one might bring a mathematical idea into physical form or experience, including computer visualization, 3D printing, and virtual reality, among others. With modern tools, illustration can even make mathematics an experimental science, so that computational results can drive the cycle of problem, conjecture, and proof. Today, modern technology for the first time places the production of far more complicated 3D models within the reach of many individual mathematicians. Moreover, the very process of illustration itself challenges our understanding of a mathematical topic and forces us to answer questions we may not have posed otherwise. This trimester program will bring together mathematicians using illustration as a research tool with mathematicians newly learning these tools. The group will be comprised of members from various areas of mathematics. The mains goals of the trimester are: - advancing research through the use of mathematical illustration; - disseminating the skills for the creation of mathematical illustration and its use in research; - furthering the theory of illustration as a tool.