This metamathematical project applies mathematical techniques to investigate mathematics itself. The central aim is to evaluate the “optimality” of various mathematical definitions, beginning with the challenge of formally defining “optimal.” Descriptive set theory, a branch of logic focused on the definability and classification of mathematical objects, offers a rigorous framework for this endeavor. One question the project explores concerns coordinate systems, which are foundational to analysis. The research seeks criteria for efficiently determining which spaces admit such structures. Beyond its academic contributions, the project addresses educational concerns. Mathematics is often seen as intimidating or overly complex. By eliminating unnecessary complications, such as redundant quantification over abstract entities, the project aims to clarify mathematical concepts and make them more accessible.