A calculating prodigy, or mental calculator, is someone who can mentally perform mathematical operations involving very large numbers or very fast mental calculations. From the nineteenth to the beginning of the twentieth century, this phenomenon met with considerable interest, and several calculating prodigies became famous enough for us to trace their careers. They found themselves at the crossroads of three worlds: the world of entertainment, where their skill at juggling numbers was admired; the world of the brain and psyche, where their peculiarities were explained and used to better understand how the brain functions; and finally, the world of mathematics, where the reproducibility of their methods and their potential as future scientists were of interest. By examining the commonalities in their trajectories, this article explores the images and practices behind the development of numeracy, at the intersection of reasoning and calculation, in nineteenth- and early twentieth-century Western societies.

En examinant le travail du conseil des mathématiciens formé au sein de la Compagnie d'assurances générales sur la vie des hommes à sa création en 1819, cet article aborde la dimension professionnelle que revêtent les applications des statistiques et des probabilités pour les questions d'assurance et de prévoyance. Ce domaine, que l'on appellera l'actuariat plus tard au xixe siècle, constitue un objet privilégié pour étudier la pratique des mathématiques comme technique nécessaire à la conduite d'activités économiques, mais aussi les dispositifs sur lesquels repose une telle pratique, les actions concrètes de travail intellectuel qu'elle induit, ou encore les interactions qu'elle suppose entre des acteurs « mathématiciens » et des acteurs appartenant au champ politique ou économique.

This paper analyses the program of "concrete history of abstraction" formulated by Jean-Claude Perrot in the 1990s to show how this program could contribute to the history of mathematics. As a matter of fact, while emphasizing the social, cultural, and material dynamics in which knowledge is produced, this program provides tools to analyze not only the ways in which mathematics circulate, but also the concrete effects of symbolical practices, which are often ignored by historical studies of science. Moreover, this program offers the possibility to historicize the process during which the material traces of learned activities, and the modes of reasoning they carry on, can reach us, and thus transcend their initial circumstances of production. Therefore, the concrete history of abstraction offers an analytical frame to study the relationship between mathematics and historical time.

Résumé Cet article propose de revenir sur le programme d’histoire concrète de l’abstraction proposé par Jean-Claude Perrot dans les années 1990, pour montrer quels en sont les apports pour l’histoire des mathématiques. En mettant l’accent sur les dynamiques sociales, culturelles et matérielles dans lesquelles s’élaborent les connaissances, ce programme fournit en effet des outils pour analyser non seulement les modalités de circulation des mathématiques, mais surtout les effets concrets des pratiques symboliques, souvent laissées de côtés dans les travaux historiens sur les sciences. Plus encore, le programme d’histoire concrète de l’abstraction constitue en objet d’histoire le processus qui permet aux traces matérielles des activités savantes passées et aux modalités de raisonnements qu’elles véhiculent de parvenir jusqu’à nous tout en transcendant leurs conditions initiales de production. Il offre ainsi un cadre analytique pour étudier le rapport des mathématiques au temps historique.

The focus of this chapter is the French Subcommission of the International Commission on Mathematical Instruction, particularly its commitment to modernizing teaching practices and its fight for the democratization of the teaching of mathematics in France. The chapter shows that the subcommission totally supported the reforms introduced in the teaching of mathematics in France in the early twentieth century. The first part of the chapter studies the French subcommission and the authors of the series of reports that were compiled in preparation for a general report on progress in the teaching of mathematics in the various countries of the world presented at the 1912 International Congress of Mathematicians. Analysis thus shows a pluralist, open mathematical environment that was not restricted to learned elite groups. It also demonstrates that the members were not only experts in the field of teaching but also keen to make the work of the International Commission on Mathematical Instruction more widely known. The second part of the chapter analyzes the nature of the mathematics promoted by the French Subcommission, as presented in the reports mentioned above. It highlights the determination of the members to promote a common – and resolutely modern – mathematical culture for all the sectors making up the education system in France at the time.

L'article presente la copie rendue par le mathematicien Evariste Galois a l'epreuve de mathematiques du concours d'admission a l'Ecole preparatoire en 1829. La confrontation de ce document meconnu, temoignage des annees d'apprentissage du mathematicien Galois, aux copies des autres candidats de 1829 et aux archives relatives au concours d'admission pour la periode 1826-1830 permet de decrypter les pratiques concretes d'enseignement des mathematiques et les capacites developpees par les etudiants au debut du XIX e siecle. Cette analyse ouvre ainsi des pistes quant au lien entre la formation scolaire et le savoir-faire savant.

This article traces the beginnings of the Revue du mois, a journal created in 1905 by the mathematician Emile Borel to address scientific topics for the general public. Although at this time similar periodicals were becoming common, la Revue du mois stood out because it offered articles dealing with recent scientific questions, and made forays in the artistic world by reporting on theater and literature. Based on Borel’s personal papers, the article documents the making of the first issues. It analyzes how the editorial policy of the journal was formulated, how the contradictory goals of high quality and publishing for the general public were met, and how the journal gradually came to develop a stable readership.

While there were a few mathematical journals aimed at teachers and students as early as the 1840s, it was only in the late 19th century that they became more numerous in Europe. This article is based on the analysis of a corpus of European mathematical journals published between the 1860s and World War I, selected in the first place because they were aimed at high school teachers and high school or/and first two years university students, which are often referred to as "intermediate journals". All these journals had focused on the teaching of mathematics and, as such, they were shaped by the educational context of the country in which they were published. However, leafing through theses journals, one is struck by the fact that the mathematics they published was in fact highly commensurable, and can see that they were the locus of transnational exchanges on mathematical knowledge. This article shows that several aspects of "internationalisation" were in fact at stake in mathematical journals for students: making knowledge from elsewhere available and of publicizing to the whole world the mathematics produced in one country; making people from different countries collaborate. Finally, it focuses on the effects of transnational exchanges between journals for teachers and students: what was the mathematical knowledge that was circulated through them, and in what respect was it different from that published in other mathematical journals? (C) 2018 Elsevier Inc. All rights reserved.

This paper tackles the history of tactics, a field of investigation at the crossroads of algebra, combinatorics and recreational mathematics. Tactics was only taken up by mathematicians now and then between the 1850s and the 1900s, and its emergence was a process of mathematization of questions linked to the notions of "order" and "position". To understand the long-term history of this field of investigation-one that became neither a theory nor a discipline-the paper analyzes the different historical configurations in which tactics took on its scientific meaning. It thus investigates how, under the banner of tactics, a continuity could be claimed by mathematicians that were, finally, working in very different scientific and historical context. (C) 2015 Elsevier Inc. All rights reserved.

Cet article considère l'enquête sur les écoles centrales lancée le 20 floréal an VII (9 mai 1799) par le ministre de l'Intérieur, N.-L. François de Neufchâteau, comme un objet statistique en soi, historiquement situé, ceci à partir des mathématiques. Il s'agit, d'une part, de comprendre la genèse et la logique de l'enquête en tant qu'outil de gouvernement, et d'autre part, de reconstituer les modalités de son exploitation, c'est-à-dire les pratiques statistiques mises en œuvre dans son traitement. Après s'être placé du côté des enquêteurs pour mettre au jour la grille selon laquelle ils cherchaient à interpréter l'enseignement secondaire de leur temps, on s'attachera à saisir, symétriquement, le sens qu'a pu prendre cette enquête pour les enquêtés eux-mêmes.

Apres s’etre interesse dans ses precedents ouvrages a un mathematicien, a une institution d’enseignement scientifique et au systeme d’enseignement des sciences au XIXe siecle, Bruno Belhoste tourne le regard vers une autre periode – celle des Lumieres – et elargit son terrain d’enquete a une ville tout entiere – Paris. Paris savant s’ouvre sur un chapitre consacre a l’Academie des sciences, avant de parcourir les differentes institutions scientifiques de la capitale (chap. II) et de reconstit...

Evariste Galois est une veritable legende en mathematiques, voire bien au-dela. Mort a 21 ans, en ayant laisse une production breve et enigmatique largement inedite, il a pourtant donne son nom a l’une des theories mathematiques les plus importantes du xxe siecle. Mais, au-dela du mythe, que reste-t-il exactement du travail de Galois dans cette theorie ? En retracant l’itineraire qu’a suivi l’un des rares manuscrits acheves de Galois, depuis son elaboration et son refus par l’Academie des sciences au debut des annees 1830 jusqu’aux reelaborations qui en furent faites tout au long du xixe siecle aux quatre coins de l’Europe, ce livre nous convie a explorer le cœur meme de l’activite mathematique : la fabrication concrete d’une theorie par les mathematiciens. En s’attachant a des mathematiciens celebres ou aujourd’hui oublies, en examinant les environnements sociaux et culturels multiples dans lesquels ils travaillent, cet ouvrage fait revivre un monde mathematique dans lequel la preservation d’une memoire mathematicienne du texte de Galois va de pair avec l’effacement du contexte qui l’a vu naitre. Ainsi, si Galois est devenu Galois, c’est parce qu’il a appartenu a un present des mathematiques sans cesse renouvele, depuis 1832.