Reciprocity is a project to make educational resources available regarding the grand research programs of contemporary mathematics to new and existing communities. Its goal is to broaden appreciation of, and access to, the beauty of mathematical ideas by producing content that, being conceptual, theoretical, philosophical, and historical, offers fresh and accessible presentations on the significance of the objects, theories, and questions that engross mathematicians today.

Given the sprawling scope and technical depth of many research programs in mathematics, extension of intelligibility to new communities requires novel labors to distill the crucial themes, conceptual overtones, findings, objectives, and stakes of contemporary mathematical research. Such labor can produce resources useful to math-adjacent communities, such as those of computer scientists, philosophers, physicists, and artists.