It is impossible to “find” a mathematical idea without explaining it; exploration and exposition are two sides of the same coin. One striking example of this is the epochal work of William Thurston; often his theorems were accompanied by pictures and computer programs, illustrating the underlying ideas.

The Illustrating Mathematics Summer 2021 program took place July 19-23, virtually “at” the Park City Mathematics Institute (PCMI). It brought together mathematicians from a range of fields, and practitioners from the digital arts (animation, 3D printing, laser cutting, CNC routing, virtual reality, computer games, etc) to share their expertise in mathematics and with the procedural tools used to illustrate mathematics. Although officially a PCMI Graduate Summer School, the program was targeted both to graduate students and to mathematics community members from all backgrounds. In addition to online lectures from a variety of mathematicians and practitioners, the week consisted of several workshops to train participants in a variety of digital media (see below for a detailed schedule).