Data Science: Mathematical Modeling (Definitions)

"[mathematical] modeling is an activity, a cognitive activity in which we think about and make models to describe how devices or objects of interest behave." (Clive L Dym & Elizabeth S Ivey, "Principles of Mathematical Modeling", 2004)

"A representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form and expressed using a Mathematical language. Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models." (Ignacio Blanquer & Vicente Hernandez, "Grid Technologies in Epidemiology", 2009)

[conventional *]: "The applied science of creating computerized models. That is a theoretical construct that represents a system composed by set of region of interest, with a set of parameters, both variables together with logical and quantitative relationships between them, by means of mathematical language to describe the behavior of the system." (Gloria Bueno García et al, "Energy Minimizing Active Models in Artificial Vision", Encyclopedia of Artificial Intelligence, 2009) 

"Description of a system using mathematical concepts and language." (Oscar Tamburis et al, "A Mathematical Model to Plan the Adoption of EHR Systems", 2014)

"Mathematical modeling is the application of mathematics to describe real-world problems and investigating important questions that arise from it." (Sandip Banerjee, "Mathematical Modeling: Models, Analysis and Applications", 2014)

"A process that gives a result to a representation of a physical phenomenon using mathematics." (Luis R S González & Avenilde Romo Vázquez, "Didactic Sequences Teaching Mathematics for Engineers With Focus on Differential Equations", 2017)

"Converting real life situations into mathematical concepts and symbols and thereby converting real life problems into mathematical problems." (G Udhaya Sankar & C Ganesa Moorthy, "Network Modelling on Tropical Diseases vs. Climate Change", 2020)