Andrea F. de Donato

The contemporary debate on the problem of style is mainly developed along two lines: foremost, the logic argumentation and the discursive modes of literary writing, namely the style understood as the formal analysis of a work intertwined with the content it conveys (stylistics); secondly, the paradigms of scientific expressivity in the formation of epistemological domains (style of scientific thinking). This article studies the philosophical problem of style in the field of mathematics through three steps. At first, starting with the debate on mathematical aesthetics and tracing the aesthetic residue in the operators of calculation, demonstration and resolution, it will be investigated how a mathematical formula could be analysed aesthetically. Subsequently, studying the category of style, the relationship between thinkability, formalisation and understanding of a mathematical problem will be investigated, in order to propose some general elements of a mathematical stylistic. Finally, starting from the case study of the term transcendence in the thought of G. Deleuze and in the Abelian theory of functions, it will be argued that, by thinking the problem of style, it is not merely indicated the formal analysis of an argument, nor merely it is proposed to recognise historically epistemic models of knowledge: the problem of style allows to trigger virtualities in order to create new conceptual environments and new epistemic practices, or to free thought from dogmatisms. This metaphysics of style will be introduced by the notion of stylology.

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