The Kuhnian Agenda and the History of Mathematics

Kuhn’s account of the development of science, together with its associated concepts of paradigm, normal science an scientific revolutions, has been the focus of intensive debate ever since its first publication in 1962.2 As a subsidiary issue in this debate the question has been raised as to the applicability of Kuhn’s theory or of Kuhn’s concepts to the history of individual scientific disciplines, and naturally the question has also been addressed by historians of mathematics concerning their own field of research. The debate concerning revolutions in the history of mathematics was opened by Michael Crowe (1975), who claimed that there have been no revolutions in the history of mathematics. Crowe was soon followed by Herbert Mehrtens (1976) who claimed the opposite. In a recently published volume (Gillies (ed.) 1992) an attempt has been made to assess the present state of that debate. This volume gathers contributions of twelve authors, including the original articles of Crowe and of Mehrtens, as well as both authors’ respective present views on the issue. Thus, about thirty years after Kuhn’s book on paradigms and scientific revolutions first appeared in print, and about twenty years after a debate on related issues was opened for the case of the history of mathematics, it makes sense to attempt to evaluate, from a critical perspective, the specific contribution of this debate to the historiography of mathematics.