El presente artículo intenta ofrecer un marco documental para la discusión sobre la estructura cosmológica de Ferecides de Siros. Partiendo de la polémica entre quienes le adjudican un cosmograma quinario y aquellos que lo interpretan septenario, proponemos un recorrido por las antiguas doctrinas cosmológicas quinarias, tanto griegas como orientales, a fin de explorar su recurrencia y variedad. Se constata que la disputa religiosa entre los apologetas del cinco y los del siete existía ya en la antigüedad, pudiendo haber afectado a (...) la lectura que los doxógrafos hicieron entonces de la obra de Ferecides. Se expone la teoría de Nick Allen sobre la existencia de una «ideología pentádica» indoeuropea y se critica su sesgo idealista (pitagórico en la línea de Dumézil). Finalmente, se suscribe la hipótesis del origen «protogeométrico» de muchos de estos mapas ontológicos quinarios y se recapitulan las posibles referencias que manejaba el maestro de Pitágoras cuando ideó su teogonía. (shrink)

Mathematicians use theological metaphors when they talk in the kitchen of mathematics. How essential is this talk? Have theological considerations and religious concepts influenced mathematics? Can mathematical models illuminate theology? Some authors have given positive answers to these questions, but they do not seem final. It is unclear how religious views influenced the work of those mathematicians who were also theologians. Religious background of some mathematical concepts could have been inessential. Mathematical models in theology have no predictive value. It is, (...) however, important to continue the recently initiated search for the mutual influences of mathematics and theology., 2016.). (shrink)

Examples of possible theological influences upon the development of mathematics are indicated. The best known connection can be found in the realm of infinite sets treated by us as known or graspable, which constitutes a divine-like approach. Also the move to treat infinite processes as if they were one finished object that can be identified with its limits is routine in mathematicians, but refers to seemingly super-human power. For centuries this was seen as wrong and even today some philosophers, for (...) example Brian Rotman, talk critically about “theological mathematics”. Theological metaphors, like “God’s view”, are used even by contemporary mathematicians. While rarely appearing in official texts they are rather easily invoked in “the kitchen of mathematics”. There exist theories developing without the assumption of actual infinity the tools of classical mathematics needed for applications (For instance, Mycielski’s approach). Conclusion: mathematics could have developed in another way. Finally, several specific examples of historical situations are mentioned where, according to some authors, direct theological input into mathematics appeared: the possibility of the ritual genesis of arithmetic and geometry, the importance of the Indian religious background for the emergence of zero, the genesis of the theories of Cantor and Brouwer, the role of Name-worshipping for the research of the Moscow school of topology. Neither these examples nor the previous illustrations of theological metaphors provide a certain proof that religion or theology was directly influencing the development of mathematical ideas. They do suggest, however, common points and connections that merit further exploration. (shrink)

L'étude des mathématiques de la préhistoire ne peut être fondée uniquement sur les documents archéologiques bruts, sous peine de stérilité ; elle a tout intérêt à les mettre en situation grâce au comparatisme ethnographique, selon lequel les sociétés primitives actuelles ou récemment disparues nous renseignent sur nos ancêtres de la préhistoire. D'abord utilisée spontanément par quelques historiens des mathématiques, cette méthode est de nos jours rejetée en principe par le courant récent des ethnomathématiciens. Il s'agit de montrer par quelques exemples (...) que la méthode est pourtant féconde, d'une part parce qu'elle ruine les constructions fantastiques dont raffolent certains mathématiciens, et d'autre part parce qu'elle ouvre un vaste champ de recherches pratiquement inexploré. (shrink)