Les Debuts De L'histoire Des Mathematiques Sur Les Scenes Internationales Et Le Cas De L'entreprise Encyclopedique De Felix

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Les Debuts De L'histoire Des Mathematiques Sur Les Scenes Internationales Et Le Cas De L'entreprise Encyclopedique De Felix Historia Mathematica 26 (1999), 344–360 Article ID hmat.1999.2260, available online at http://www.idealibrary.com on Les d´ebuts de l’histoire des math´ematiquessur les sc`enes View metadata, citation and similar papersinternationales at core.ac.uk et le cas de l’entreprise encyclop´edique brought to you by CORE provided by Elsevier - Publisher Connector de Felix Klein et Jules Molk H´el`eneGispert1 Groupe d’histoire et de diffusion des sciences d’Orsay, Institut universitaire de formation des maˆıtres de Versailles, Batimentˆ 407, Centre universitaire, F-91405 Orsay Cedex, France At the beginning of the 20th century, the history of mathematics first appeared on different inter- national scenes as a result of different initiatives of mathematicians, historians, and philosophers. By studying the way in which historians of mathematics took advantage of these opportunities, we have sought the contours, the lines of force, and the equilibria of this process of the internationalization of the history of mathematics on an institutional as well as intellectual plane. This search was focused through the study of the German- and French-language editions of the En- cyklopadie¨ der mathematischen Wissenschaften, which is one of the most remarkable examples dating from this period of an international collaboration for mathematics and its history. C 1999 Academic Press Au d´ebut du vingti`emesi`eclel’histoire des math´ematiquesfait ses d´ebuts sur diff´erentessc`enes internationales `al’occasion de diff´erentesinitiatives de math´ematiciens,d’historiens, de philosophes. En ´etudiantla fa¸condont les historiens des math´ematiquesse saisirent de ces opportunit´es,nous avons cherch´e`a comprendre les contours, les lignes de force, les ´equilibresde ce processus d’internationalisa- tion de l’histoire des math´ematiques,tant sur le plan institutionnel qu’intellectuel. Cette enquˆetea ´et´epr´ecis´eepar l’´etudedes ´editionsen langues allemande et fran¸caisede l’Encyklopa-¨ die der mathematischen Wissenschaften qui est un des exemples les plus marquant de cette p´eriode d’une collaboration internationale, tant pour les math´ematiquesque leur histoire. C 1999 Academic Press MSC subject classifications: 01A60, 01A74. Key Words: historiography; internationalization; Encyklopadie¨ der mathematischen Wissenschaften; Encyclopedie´ des sciences mathematiques´ pures et appliquees´ ; Felix Klein; Jules Molk. INTRODUCTION Pr´esentant,lors d’une des s´eancesg´en´eralesdu deuxi`emecongr`esinternational des math´ematiciens`aParis en 1900, une conf´erenceintitul´ee“l’historiographie des math´e- matiques,” Moritz Cantor remarquait `aquel point “cette branche [qui] n’a jamais ´et´eaussi 1 Cet article a ´et´er´edig´e`a l’origine dans le cadre du ICHM Working Group “Historiography of Mathematics” qui se r´eunitdepuis plusieurs ann´eespour la r´ealisationde l’ouvrage collectif Writing the History of Mathematics: Its Historical Development r´ealis´esous la direction de Joseph W. Dauben et Christoph. J. Scriba, `aparaˆıtrechez Birkh¨auserdans ‹‹ Science Network›› series. Je tiens ici `aexprimer ma gratitude `al’ensemble des coll`eguesdu Working Group pour les ´echangesdont j’ai b´en´efici´e,et tout particuli`erement`aJeanne Peiffer, auteur du chapitre sur la France, dont l’aide m’a ´et´epr´ecieuse. Catherine Goldstein, lectrice d’une premi`ereversion de ce texte, doit egalement´ etre ˆ remerci´eepour ses critiques stimulantes. Enfin, je suis redevable aux referees pour leurs remarques que j’ai tent´ede prendre en compte dans cette pr´esenteversion. 344 0315-0860/99 $30.00 Copyright C 1999 by Academic Press All rights of reproduction in any form reserved. HMAT 26 L’ENCYCLOPEDIE´ DE KLEIN ET MOLK 345 d´elaiss´eequ’on le croyait, n’a jamais eu pourtant autant de succ`esque depuis une vingtaine d’ann´ees`apeu pr`es”[1, 40]. La science, continuait-il en ´elargissant son constat, aime se mettre `ala mode et aujourd’hui l’historiographie scientifique a su entrer en faveur. Rien d’´etonnant,alors, `ace que les premi`eresinitiatives internationales qui mobilis`erent les savants de diff´erentschamps au tournant du si`ecleaient pris en compte l’histoire des math´ematiques,soit comme domaine propre, soit comme composante de l’histoire des sciences. Les math´ematiciens,les historiens, les philosophes allaient ouvrir leurs premiers congr`esinternationaux `al’histoire des sciences et des math´ematiques.La fa¸condont ils le firent, et dont les historiens des math´ematiquesse servirent de ces diff´erentesopportunit´es ou les provoqu`erent,nous donne des indications int´eressantessur les d´ebuts de l’histoire des math´ematiquessur la sc`eneinternationale, ses contours, ses lignes de force, ses ´equilibres, tant sur le plan institutionnel qu’intellectuel. Cette enquˆetepeut ˆetrepr´ecis´eegrˆace`al’´etude de l’Encyklopadie¨ der mathematischen Wissenschaften, con¸cuepar Felix Klein comme une œuvre de collaboration internationale,2 et de son ´editionen langue fran¸caisedirig´eepar Jules Molk.3 Elles sont en effet une des illus- trations les plus fameuses de la nature et de la solidit´edu lien de l’histoire des math´ematiques aux milieux math´ematiciens,lien qui s’av`erealors privil´egi´e`al’´echelle internationale. Cette entreprise encyclop´ediquedont la publication d´ebuta en 1898 chez Teubner et `alaquelle particip`erentune centaine et plus de r´edacteursdont plus d’une trentaine n’´etaientpas allemands, fut en effet en partie une entreprise d’histoire des math´ematiques:il s’agissait, comme cela est expliqu´edans l’avant propos du premier volume [4, i–xx] et repris bri`evement dans [5, 123], de faire connaˆıtrel’´etatdes math´ematiquescontemporaines en rendant compte de leur d´eveloppement historique. Cette initiative fut ainsi une des premi`eresmanifesta- tions d’une vie scientifique qui commen¸cait`as’organiser `aune ´echelleinternationale,ala ` fois dans le domaine des math´ematiques,de l’histoire des math´ematiqueset de l’histoire des sciences. Quoiqu’exceptionnel, l’exemple de l’Encyklopadie¨ n’est pas isol´e.D’autres initiatives ´editorialesdans le domaine de l’histoire des math´ematiques,issues du milieu math´ematique, connurent alors un succ`es remarquable. Citons la nouvelle revue internationale L’Enseignement mathematique´ , lanc´eeen 1898, qui faisait une large part `al’histoire des math´ematiques,et des initiatives individuelles sp´ecialis´eeslargement ouvertes aux contribu- tions de tous pays comme le Bulletino di bibliografia e di storia delle scienze mathematiche e fisiche de Boncompagni, les Abhandlungen zur Geschichte der Mathematik,´edit´espar Moritz Cantor, qui devinrent alors ind´ependantesdu Zeitschrift fur¨ Mathematik und Physik, ou le journal de Gustav Enestr¨om, Bibliotheca Mathematica, dont le nombre de pages fit plus que quadrupler `apartir de 1900. 2 Il est hautement symbolique qu’une s´eancepleini`eredu quatri`emecongr`esinternational des math´ematiciens en 1908 ait ´et´econsacr´ee`al’Encyklopadie¨ . En remplacement de Klein, excus´e,Walter von Dyck, pr´esental’´etat d’avancement de l’Encyklopadie¨ et en souligna le caract`ereinternational exemplaire, conforme aux diff´erentes r´esolutions prises durant les pr´ec´edentscongr`eset indispensable `ala bonne r´ealisationde l’entreprise [5]. 3 Jules Molk (1857–1914), math´ematicienfran¸caisn´e`a Strasbourg, ´etudiant`aZ¨urich puis `aParis, auteur d’une th`esede th´eoriedes nombres qu’il pr´eparaaupr`esde Leopold Kronecker, professeur `al’universit´ede Nancy `a partir de 1890, eut la charge de l’´editionfran¸caisedont la publication commen¸caen 1904. Voir `ason propos la notice n´ecrologiquequ’´ecrivit Gustav Enestr¨om`ala mort de Molk [7]. Nous d´esigneronsici cette ´editionpar l’Encyclopedie´ ,`aladiff´erence de l’´editionoriginale not´eel’Encyklopadie¨ . 346 HEL´ ENE` GISPERT HMAT 26 L’HISTOIRE DES MATHEMATIQUES´ SUR LA SCENE` MATHEMATIQUE´ INTERNATIONALE D`es le premier congr`esinternational des math´ematiciens`aZurich, en 1897, l’histoire des math´ematiques,coupl´eeavec la bibliographie, est l’objet d’une section. Dans les congr`es suivants, c’est au cˆot´ede la didactique ou p´edagogie,de la philosophie, ou des deux `ala fois que figure l’histoire des math´ematiques.La pr´esencede l’histoire dans ces congr`es,puis son int´egrationdans une trinit´e“histoire, philosophie, didactique,” est en fait le reflet d’une caract´eristiquede la production math´ematiqued’alors telle qu’elle est recens´eedans le Jahrbuch uber¨ die Fortschritte der Mathematik: depuis 1870, de fa¸con`apeu pr`esconstante, 9`a 10% de l’ensemble des titres mentionn´esdans les Fortschritte figurent dans la premi`ere section dont rel`eve l’histoire, associ´eetout d’abord `ala philosophie, puis `ala philosophie et la p´edagogie.4 La stabilit´edu pourcentage ne saurait cependant occulter l’accroissement du nombre des contributions auquel se r´ef´eraitMoritz Cantor au congr`esde Paris dans la citation ci-dessus. Le nombre annuel des articles class´essp´ecifiquementdans le chapitre “histoire” des Fortschritte, inf´erieur`aune cinquantaine dans les premi`eresann´ees,d´epassait 150 dans la derni`ered´ecenniedu 19e si`ecleet atteignait, voir d´epassait,200 autour de 1905. Les sections des congr`esinternationaux des math´ematiciensconsacr´ees`al’histoire des math´ematiquespr´esententcependant une caract´eristiqueremarquable. D`esZurich et au fil des diff´erentscongr`esqui suivirent, d´epassantle simple cadre des confrontations ´erudites, des congressistes s’attach`erent`al’avenir de leur discipline, l’histoire des math´ematiques, et `al’organisation de leur domaine intellectuel. Cette question d’actualit´edans la r´eflexion des historiens des math´ematiques,dont t´emoignentnombre d’articles alors recens´espar exemple par les Fortschritte, se trouva ainsi port´eesur une sc`enecollective d’une ampleur nouvelle. Avant ces congr`esdes propositions furent avanc´ees,leurs auteurs insistant souvent sur l’´etapenouvelle que connaissait ce champ de recherches, tant au plan quantitatif que qualitatif, et sur la n´ecessit´ed’une coop´erationinternationale. Citant une appr´eciationd’Enestr¨omquant au nombre “consid´erable”de personnes qui s’occupaient d’histoire des math´ematiques[22, 541].
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