This work presents a mathematically proven approach to scientific field research. It is an attempt that elaborates philosophical principles so as to mark scientific research and technological innovation. For that, this work is focusing on exploring the ‘mechanisms’ of innovation, within the causes, logics or laws of innovation, as well as in the nature of the actors involved and the role and functionality of an entrepreneurship activity. In order to achieve that, the current work proposes the introduction of ‘new productive combinations’, made possible by utilizing previous knowledge in a well-defined analytical-combinatorial way. Such derived innovations, may evidently, sweep away the old in favor of a newly defined approach, fill-in the research-based knowledge gaps and, eventually, provide a cognitive completion of knowledge. Although via a rather different approach, the dynamics of innovation and the notion of the entrepreneur researcher as the key actor, seem to have been already present in a Tarde’s previous work. On the other hand, we are not standing behind Tarde’s position that invention is the (new and original) result of an (originally) combined imitation of previously existing inventions. But then, we try to identify the procedure towards novelty or originality, via a non-static circular process where production functions constantly change in a Centrifugal mode. Research and Development is essentially the outcome following the introduction into such a ‘circular flow’ of a ‘new combination’ of existing knowledge and cognition. This work may technically be described as a "classification-transformation method” (CTM), which classifies experiences, qualities, properties and characteristics of the inputs, processes and outcomes, related with a phenomenon taking place in a specific system of the Euclidean & Newtonian world, and mathematically transforms them through levels that is said to represent the complexity in the description of the system.