The art of illustrating mathematics

Edmund viscerally remembers, during his PhD, Simon Donaldson describing the hopf fibration, sketching it on the board and discussing it. Those words and images triggered something, and a fundamental intuition of the hopf fibration was created in his mind. The experience was so intense that he could still picture the room, down to the people sitting in it. Edmund created Figure 1 shortly after. An act of resonance, as in Gromov’s words above, had occurred, and it did so without the transcription of logical symbols. This story highlights the intriguing mixture of the personal and objective that good illustration enables. The articles in this special issue,many inspired by the 2019 semester on Illustrating Mathematics that took place at the ICERM,1 show this idea in many different ways. We begin, however, by considering the role of illustration in mathematics and its relationship to art.