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Explore browser-based interactive mathematical visualizations through this 57-minute conference talk that demonstrates CindyJS, a powerful tool for creating dynamic mathematical illustrations. Learn how illustration serves as a vital component in mathematical outreach, pedagogy, exposition, and experimentation, while also playing a crucial role in informal communication between mathematicians. Discover through concrete examples how visual elements, including approximately 100 doodles, can be essential to mathematical proofs and why certain visual representations become integral to mathematical understanding, particularly in low-dimensional topology where specific surface cartoons are considered part of the Ph.D. curriculum. Understand the challenges mathematicians face when attempting to formalize visual proofs and why visual elements sometimes remain indispensable despite efforts to remove them from formal presentations. Gain insights into the intersection of technology and mathematical communication through this presentation recorded during the thematic meeting "Illustration as a Mathematical Research Technique" at the Centre International de Rencontres Mathématiques in Marseille, France.
