Several promising approaches have been developed to represent conscious experience in terms of mathematical spaces and structures. What is missing, however, is an explicit definition of what a ‘mathematical structure of conscious experience’ is. Here, we propose such a definition. This definition provides a link between the abstract formal entities of mathematics and the concreta of conscious experience; it complements recent approaches that study quality spaces, qualia spaces, or phenomenal spaces; and it provides a general method to identify and investigate structures of conscious experience. We hope that ultimately this work provides a basis for developing a common formal language to study consciousness