This dissertation examines the changing editions of Bernardo Montón’s Secretos de artes liberales y mecánicas (Madrid, 1734 through 1814) to argue that an important yet unexplored contribution of Spain to the Enlightenment project was the institutionalization of its craft tradition wrought by the new developments in science (mathematics and chemistry). A hybrid collection of arts and crafts (even including scientific recipes for architectural materials), this book of “secrets,” now made public, aided the Enlightenment’s campaign against the sequestering of empirical knowledge. It is unprecedented in its application of the new mathematical probability theory to generate infinite designs of Islamic tiles (azulejos). Yet the book’s subsequent editions were gradually purged of occult elements such as alchemy and magic. The disappearance of these patterns from the book was concurrent with the eclipse of azulejos from architectural practice. My study will show that Spain’s participation in the Enlightenment demanded a constant reevaluation of its Islamic heritage of science and crafts. The Fine Arts Academy in Madrid, established in 1752, inevitably renewed interest in crafts when it undertook to document Arab monuments, while the later Economic Societies, viewing crafts as assets for economic progress, challenged their classifications as “low,” instead tying their production to science and abstract drawing. The changed valuations growing out of this debate were part of Spain’s gift to European artistic and architectural thought, and deeply informed Owen Jones’s celebrated work on the Alhambra.