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This study is part of a research project that analyzes the processes of conceptualization of the notion of infinitesimals in college students majoring in Mathematics. The research project originates from an interest in understanding the processes of teaching and learning key concepts of Mathematical Analysis such as limit, real numbers, and continuity among others. From mathematical and cognition points of view, these notions are recognized as complex. In order to conceptualize them, students rely on an intuitive understanding of infinitesimals. In this paper, we describe, analyze, and characterize the epistemological conceptual frameworks associated with the historical evolution of the notion of infinitesimals. We identify seven epistemological concept frameworks: The infinitesimal as a ratio, as an indeterminate, as a difference, as an increment, as an arithmetic ratio, as a symbol, and as a function. Furthermore, ideas, methods, representations, and problems that mathematicians use in specific contexts are presented. [ABSTRACT FROM AUTHOR]