Le mathématicien André Weil rappelle dans son œuvre que certaines surfaces mathématiques connues en géométrie algébrique, les surfaces K3, ont été ainsi nommées d’après trois mathématiciens (Kummer, Kähler et Kodaira) et une montagne du Pakistan, le K2.L’auteur du présent ouvrage a pris le prétexte de ce rapprochement pour réfléchir sur les mathématiques et la montagne, les variétés de Calabi-Yau, la théorie des cordes, la géométrie tropicale ou la recherche opérationnelle, domaine...

La notion classique de « crise » désigne au départ une période troublée marquant une discontinuité ou une rupture dans un contexte plus ou moins homogène (cadre de référence). Elle appelle une « stratégie » de résolution, terme d’origine militaire désignant un art ou une science substituant aux approches empiriques de l’action humaine des décisions conscientes et calculées. Alors que divers modèles (continus ou discrets) des crises classiques ont pu être proposés – tous se heurtant à l’imp...

From Pythagoreans to Hegel, and beyond, this book gives a brief overview of the history of the notion of graphs and introduces the main concepts of graph theory in order to apply them to philosophy. In addition, this book presents how philosophers can use various mathematical notions of order. Throughout the book, philosophical operations and concepts are defined through examining questions relating the two kinds of known infinities – discrete and continuous – and how Woodin's approach can...

This book, which studies the links between mathematics and philosophy, highlights a reversal. Initially, the (Greek) philosophers were also mathematicians (geometers). Their vision of the world stemmed from their research in this field (rational and irrational numbers, problem of duplicating the cube, trisection of the angle...). Subsequently, mathematicians freed themselves from philosophy (with Analysis, differential Calculus, Algebra, Topology, etc.), but their researches continued to i...

An English translation of Bachelard's sixth book, in which he seeks to develop a metaphysical context for modern atomistic science.French philosopher Gaston Bachelard (1884–1962) is best known in the English-speaking world for his work on poetics and the literary imagination, but much of his oeuvre is devoted to epistemology and the philosophy of science. Like Thomas Kuhn, whose work he anticipates by three decades, Bachelard examines the revolution taking place in...

This book is an essay on the epistemology of classifications. Its main purpose is not to provide an exposition of an actual mathematical theory of classifications, that is, a general theory which would be available to any kind of them: hierarchical or non-hierarchical, ordinary or fuzzy, overlapping or non-overlapping, finite or infinite, and so on, establishing a basis for all possible divisions of the real world. For the moment, such a theory remains nothing but a dream. Instead, the aut...