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  1. Incomplete understanding of complex numbers Girolamo Cardano: a case study in the acquisition of mathematical concepts.Denis Buehler - 2014 - Synthese 191 (17):4231-4252.
    In this paper, I present the case of the discovery of complex numbers by Girolamo Cardano. Cardano acquires the concepts of (specific) complex numbers, complex addition, and complex multiplication. His understanding of these concepts is incomplete. I show that his acquisition of these concepts cannot be explained on the basis of Christopher Peacocke’s Conceptual Role Theory of concept possession. I argue that Strong Conceptual Role Theories that are committed to specifying a set of transitions that is both necessary and sufficient (...)
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  • A Historically and Philosophically Informed Approach to Mathematical Metaphors.Roy Wagner - 2013 - International Studies in the Philosophy of Science 27 (2):109-135.
    This article discusses the concept of mathematical metaphor as a tool for analyzing the formation of mathematical knowledge. It reflects on the work of Lakoff and Núñez as a reference point against which to rearticulate a richer notion of mathematical metaphor that can account for actual mathematical evolution. To reach its goal this article analyzes historical case studies, draws on cognitive research, and applies lessons from the history of metaphors in philosophy as analyzed by Derrida and de Man.
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  • Quelques conceptions de la théorie des proportions dans des traités de la seconde moitié du dix septième siècle.Pierre Lamandé - 2013 - Archive for History of Exact Sciences 67 (6):595-636.
    This article examines how the theory of proportions was explained during the second half of the seventeenth century in the works of Andreas Tacquet, Antoine Arnauld, Ignace Gaston Pardies, Bernard Lamy, and Jacques Rohault. These five authors had very different conceptions of this subject, and on one hand, they show that this question was not forgotten, even after the Geometry of Descartes, and on the other hand, their work displays the progressive transformation of mathematical objects. While Tacquet deepened Euclidean thought, (...)
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  • The six books of Diophantus’ Arithmetic increased and reduced to specious: the lost manuscript of Jacques Ozanam.Francisco Gómez-García, Pedro J. Herrero-Piñeyro, Antonio Linero-Bas, Ma Rosa Massa-Esteve & Antonio Mellado-Romero - 2021 - Archive for History of Exact Sciences 75 (5):557-611.
    The introduction of a new analytical method, due fundamentally to François Viète and René Descartes and the later dissemination of their works, resulted in a profound change in the way of thinking and doing mathematics. This change, known as process of algebrization, occurred during the seventeenth and early eighteenth centuries and led to a great transformation in mathematics. Among many other consequences, this process gave rise to the treatment of the results in the classic treatises with the new analytical method, (...)
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