Focus on the Visual (The 2022 Presidential Address)

There are visual components of mathematics that are vital to the learning of the subject and should be a focus for its teaching. One aspect is the impressive capacity of the brain to visualise, an important element in the discovery process of some prominent mathematicians and scientists. The pedagogical importance of diagrams in mathematics is considered, with examples showing their role in problem-solving, elucidation, persuasion and decision making, concluding with some particularly stimulating and revealing diagrams for use in the classroom.