A Mathematical Interpretation of the International Classification of Headache Disorders 3rd Edition
International Classification of Headache Disorders (ICHD3) provides definition of headache disorders that can be used to construct a mathematical basis for headache classification. We seek to construct a theoretical framework for such a construction.Headache and facial pain conditions are interpreted as bundles of phenotypes. ICHD3 diagnoses are then defined as sets. We proceed to show that observations, in the form of theorems, can be proved with our set theoretic construction for the ICHD3.The all-present “not accounted for by another ICHD3 diagnosis” criterion must be removed in order for our system to be set theoretic consistent. Furthermore, our system can be used to construct a categorical approach to headache medicine in the tradition of category theory.Mathematical interpretation of ICHD3 is possible and may provide significant implication for understanding the structure and organization of headache diagnostic classification.