Data visualization has become ubiquitous in web and print media, and fashionable in academic circles. About twenty years ago, Edward Tufte created the foundations for this visualization renaissance with his “Visual Display of Quantitative Information” and subsequent books. I attempted to build on these foundations in writing an illustrated number theory text. In this talk, I will discuss some design principles for visualizing mathematics — not just data sets, but also theorems, definitions, and proofs. Examples will be taken from number theory, but I hope these principles can apply more broadly across mathematics.