THOMAS KUHN ȘI GEOMETRIA HIPERBOLICĂ

Abstract

In the present study, we propose a discussion from a Kuhnian perspective on the status of revolutions in mathematics in general; and in particular, we will query to what extent we can say that hyperbolic geometry produces such a scientific revolution. Given that this debate already possesses its own intellectual history, we will attempt to substantiate the proposed thesis – namely, that the emergence of hyperbolic geometry indeed triggered a revolution within mathematics, though one that must be interpreted in a particular way – by pursuing four specific objectives: (1) an exposition of Euclid’s ideas; (2) an overview of several historical leaps in the attempt to prove Euclid’s fifth postulate; (3) an incursion into Kuhn’s views on the structure of scientific revolutions; and (4) a reflection on whether Kuhn’s concepts are applicable to the development of hyperbolic geometry. As the nature of this work is both historical and philosophical, we will approach the aforementioned ideas and concepts through descriptive and hermeneutic methods. Furthermore, the present study is significant within the broader landscape of philosophical inquiry as, on the one hand, it not only interrogates the role of scientific revolutions within mathematics but, on the other hand, also offers an opportunity to highlight the philosophical importance of hyperbolic geometry in shaping the very way that people perceive space.