Visions of That Which Is Sought

Mathematics has been expressed in the language of visual metaphors since the earliest times. Examples are given from Old Babylonian, ancient Greek, and Renaissance traditions to suggest that solving the kinds of problems at the origins of contemporary number theory and algebra has historically been conceived as the process of divesting the solution of its invisibility. Visual metaphors have accompanied mathematics' evolution toward more abstraction over the past two centuries, but their nature has changed. What contemporary number theorists seek to bring to light is less the solution to an equation than the answer to the question: what question should we have been asking all along?