This massive two-volume reference presents a comprehensive selection of the most important works on the foundations of mathematics. While the volumes include important forerunners like Berkeley, MacLaurin, and D'Alembert, as well as such followers as Hilbert and Bourbaki, their emphasis is on the mathematical and philosophical developments of the nineteenth century. Besides reproducing reliable English translations of classics works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare, William Ewald also includes selections from Gauss, Cantor, Kronecker, and Zermelo, all translated here for (...) the first time. (shrink)

ArgumentThis article offers a social history of the “Galois Affair,” which arose in 1831 when the French Academy of Sciences decided to reject a paper presented by an aspiring mathematician, Évariste Galois. In order to historicize the meaning of Galois's work at the time he tried to earn recognition for his research on the algebraic solution of equations, this paper explores two interrelated questions. First, it analyzes scholarly algebraic practices and the way mathematicians were trained in the nineteenth century to (...) reconstruct the scientific meaning of Galois's research. By emphasizing the historically contingent nature of scientific debates, the paper argues that to historicize the work of a mathematician, we must historicize the scientific world as well. The second part of this article goes further to seek a fresh perspective on Galois's short career by analyzing the cultural, social, and institutional dynamics that governed how the mathematical community came to recognize an aspiring mathematician as one of its own. (shrink)

This review of peter hodgson's new english translation of hegel's "lectures on the philosophy of religion", Part iii, And of two other books on hegel, Includes a report on plans for retranslating the entire "lectures". A new edition is made feasible by the hegel archiv's ability to construct a superior critical text of each of the four lecture series (1821, 1824, 1827, 1831) from lasson plus additional recently-Discovered auditors' transcripts. Stephen dunning's book on hegel and hamann, And james yerkes' on (...) hegel's christology, Disagree emphatically on the suitability of hegel's conceptual framework for doing justice to the nature of christianity. (shrink)

Cari Friedrich Hindenburg (1741-1808), le fondateur de la « prétendue Ecole combinatoire » (Eugen Netto), est un personnage largement oublié aujourd’hui. Pourtant, le Dictionary of Scientific Biography lui consacre un article. Il est vrai que l’Ecole combinatoire eut un grand succès en Allemagne à la fin du 18ème siècle, mais seulement en Allemagne, puis elle tomba en discrédit.En fait, l’Ecole combinatoire ne se proposait rien moins que de fonder l’analyse — et si possible toutes les mathématiques — sur l’analyse combinatoire, (...) une nouvelle branche des mathématiques qui était la création de Hindenburg : la problématique des fondements était au cœur de cette tentative. (shrink)