Une Histoire de L’universalité des Matrices Mathématiques

International matrix theory of the 1930s is influenced by multiple phenomena and may be analyzed by looking at how local practices were globalized via pathways which manifested a short-term reappropriation between the two world wars of work developed over the long term. This article interrogates the constitution of the universality of matrix terminology and focuses particularly on phenomena of the collective circulation of texts which present cultural aspects proper to networks with complex identities.     

Experts en Sciences Mathématiques et Projets Impériaux sous le Règne de Kangxi

In 1713 the Kangxi emperor commissioned the compilation of a treatise on mathematics, astronomy, and harmonics. For this project, he recruited literati, selecting them by special examination and closely supervising their work. Only two of them went on to have careers as high officials. In the middle of the 18th century, mathematics began to be taught at the Imperial University. Thus the Qing dynasty established the transmission of a degree of expertise in this field as part of the training of certain literati who aimed at a civil service career.     

La réflexion Benthamienne sur les mathématiques

In 1814, Jeremy Bentham began to writeChrestomathia; this work is a presentation of what is useful to learn. However this text is, more generally, an entire organization of the knowledge of his time, through developing a «theory of fictions», which is a reflexion on concepts and a critics of nomenclatures. The following essay focuses on the fifty pages refering to mathematics in a work that considers the integrality of sciences at the beginning of the xix^th century and criticizes the FrenchEncyclopédie of Diderot and D’Alembert. A most singular idea expressed by the author, indirectly echoed by Gaston Bachelard through some books, is the conflict between concepts and their being designated by words. Signified, signifying entities and concepts are reciprocally adrift so that nobody, even the scholar, can keep control of these motions; what makes education unceasingly difficult.     

Questions ethnographiques et mathématiques de la préhistoire

The study of the mathematics of prehistory cannot be founded on bare archeological data alone; it may be useful to set the archeological documents in context, with the help of comparative ethnography, according to which our own contemporaray or near-contemporary primitive societies can help us understand our prehistoric ancestors. Although once used spontaneously by several historians of mathematics, this approach has been rejected on principle by the recent school of ethnomathematicians. This paper sets out to show, by means of a certain number of examples, that the method can nonetheless yield rewards: on the one hand because it demolishes the fantastic theories so fondly constructed by certain mathematicians, and on the other because it opens up a vast field of research which has so far been vitually unexplored.     

L’histoire des mathématiques de l’Antiquité

Historical research, during the last half-century, has improved our knowledge of the mathematics of Antiquity. Texts from Egypt and Mesopotamia have been better understood and their elucidation has left behind the crude alternative between empricism and rationalism. The landscape offered by Greek science grew richer and became more varied: it is no longer possible to reduce it to the sole geometrical theory. The main problems which were raised by its history have been deeply discussed. Things being so, more general questions arise, from an epistemological or philosophical point of view. Does the search into some far past of a single «birth» of mathematics make any sense? What link, if any, is there between the form of mathematics in such and such a civilization and its social structure? Can cultural anthropology help to elucidate the variety and unity of mathematics among various peoples? From what time and under what conditions is it possible for a single united historical progress of mathematics to begin?     

La genèse des concepts mathématiques

Counter to the standard viewpoint which tends to dismiss history and intersubjectivity when dealing with mathematical cognition, the article shows that taking them into account is the only way to overcome a certain number of aporias related to mathematical objectivity, especially psychologism and relativism. Resting upon the conceptual framework devised by Ernst Cassirer under the name «symbolic form», the article shows that the fictional and the scientific stance must be located along the same meaning continuum and that it is only the collective elaboration of individual representations which can account for cultural productions.     

Paul Bernays et la rénovation des fondements philosophiques des mathématiques

The history of the foundations of mathematics in the XX^th century leads to a revision of the meaning of traditional philosophical notions such as «evidence», «experience» or «rationality». This paper focuses on the influence of Ferdinand Gonseth's «open philosophy» on Paul Bernays' philosophical interpretations of the technical results in the foundations. Familiar with the ideas of Jacob Friedrich Fries and Léonard Nelson, the logician Bernays turns at the middle of the century more and more towards Gonseth's ideas. Quite before Thomas Kuhn, Bernays considers the revisions under consideration not simply as a problem of truth and falsehood, but as a task requiring the introduction of a new conceptual system. Indeed, in opposition to Kuhn, according to Bernays, the necessary change is less the consequence from a change of paradigm and methodological incommensurability as a epistemological necessity.     

Fédération et/ou confédération

A concern to pin ideological labels on Morris has obscured the continuing importance of romanticism and Protestantism for his socialist politics. Romanticism led him to seek self-realisation in an art based on naturalness and harmony, and Protestantism led him to do so in the everyday worlds of work and domestic life. From Ruskin, he took a sociology linking the quality of art to the extent of such self-realisation in daily life. Even after he turned to Marxism, he still defined his socialist vision in terms of good art produced and enjoyed within daily life. Moreover, his over-riding concern to promote a new spirit of art, not his dislike of Hyndman, led him to a purist politics, that is, to look with suspicion on almost all forms of political action.