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Mathematicians and the Nation in the Second Half of the Nineteenth Century as Reflected in the Luigi Cremona Correspondence

Published online by Cambridge University Press:  03 February 2011

Ana Millán Gasca
Ana Millán Gasca*
Affiliation:
University of Roma Tre
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Argument

Up until the French Revolution, European mathematics was an “aristocratic” activity, the intellectual pastime of a small circle of men who were convinced they were collaborating on a universal undertaking free of all space-time constraints, as they believed they were ideally in dialogue with the Greek founders and with mathematicians of all languages and eras. The nineteenth century saw its transformation into a “democratic” but also “patriotic” activity: the dominant tendency, as shown by recent research to analyze this transformation, seems to be the national one, albeit accompanied by numerous analogies from the point of view of the processes of national evolution, possibly staggered in time. Nevertheless, the very homogeneity of the individual national processes leads us to view mathematics in the context of the national-universal tension that the spread of liberal democracy was subjected to over the past two centuries. In order to analyze national-universal tension in mathematics, viewed as an intellectual undertaking and a profession of the new bourgeois society, it is necessary to investigate whether the network of international communication survived the political, social, and cultural upheavals of the French Revolution and the European wars waged in the early nineteenth century, whether national passions have transformed this network, and if so, in what way. Luigi Cremona's international correspondence indicates that relationships among individuals have been restructured by the force of national membership, but that the universal nature of mathematics has actually been boosted by a vision shared by mathematicians from all countries concerning the role of their discipline in democratic and liberal society as the basis of scientific culture and technological innovation, as well as a basic component of public education.

Type
Research Article
Information
Science in Context , Volume 24 , Issue 1 , March 2011 , pp. 43 - 72
Copyright
Copyright © Cambridge University Press 2011

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References

Archibald, Thomas. 2002. “Charles Hermite and German Mathematics in France.” In Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800–1945, edited by Parshall, Karen Hunger and Rice, Adrian C., 122–137. Providence RI: American Mathematical Society and London Mathematical Society.Google Scholar
Arendt, Hannah. 1968. Between Past and Future: Eight Exercises in Political Thought. New York: Penguin.Google Scholar
Ausejo, Elena and Hormigón, Mariano eds. 1993. Messengers of Mathematics: European Mathematical Journals (1800–1946). Madrid: Siglo XXI.Google Scholar
Baltzer, Richard. 1865–1868. Elementi di matematica. Genova: Tipografia del Reale Istituto dei Sordo-muti, 6 vol. Translated by Cremona, Luigi.Google Scholar
Barrow-Green, June E. 2002. “Gösta Mittag-Leffler and the Foundation and Administration of Acta Mathematica.” In Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800–1945, edited by Parshall, Karen Hunger and Rice, Adrian C., 139–164. Providence RI: American Mathematical Society and London Mathematical Society.Google Scholar
Battimelli, Giovanni and Gagliasso, Elena, eds. 1993. Le comunità scientifiche tra storia e sociologia della scienza. Atti del Workshop, Roma 18–20 aprile 1991. Roma: Università di Roma “La Sapienza.” “Quaderni della Rivista di Storia della Scienza.”Google Scholar
Becvár, Jindrich and Becvárová, Martina. 2006. “Emil Weyr e Luigi Cremona.” Bollettino di Storia delle Scienze Mathematical 26 (2).Google Scholar
Bergier, Jacques. 1969. L'espionnage industriel. Paris: Hachette.Google Scholar
Blay, Michel and Nicolaïdis, Efthymios, eds. 2001. L'Europe des sciences. Constitution d'un espace scientifique. Paris: Seuil.Google Scholar
Bottazzini, Umberto. 1994. “The Italian States.” In Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, edited by Grattan-Guinness, Ivor 2:1499. London: Routledge.Google Scholar
Bottazzini, Umberto. 1998. “Francesco Brioschi and Scientific Culture in Post-Union Italy.” (Italian). Bollettino della Unione Matematica Italiana – Sez. A La matematica nella società e nella cultura, 8th series 1 (1):59–78.Google Scholar
Bottazzini, Umberto, and Rossi, Arcangelo. 1984. “Luigi Cremona.” In Dizionario matematico degli italiani 30:606–611.Google Scholar
Brigaglia, Aldo. 1991. “Lettere di Julius Plücker a Luigi Cremona (1867–1868).” In LCC 1:153–158.Google Scholar
Brigaglia, Aldo. 1993. “Il ‘Circolo Matematico di Palermo’ and Its ‘Rendiconti.’ The Contribution of Italian Mathematical Community to the Diffusion of International Mathematical Journals, 1884–1914.” In Messengers of Mathematics. European Mathematical Journals 1800–1946, edited by Ausejo, Elena and Hormigón, Mariano, 71–93. Madrid: Siglo XXI de España.Google Scholar
Brigaglia, Aldo. 2000. “Brioschi, Cremona e l'insegnamento della Geometria nel Politecnico.” In Francesco Brioschi e il suo tempo (1824–1897), 2 vols., 2000–2003, edited by Lacaita, Carlo G. and Silvestri, Andrea, vol. 1, 403–418. Milano: Franco Angeli.Google Scholar
Brigaglia, Aldo. 2006. “Da Cremona a Castelnuovo. Continuità e discontinuità nella visione della scuola.” In Da Casati a Gentile. Momenti di storia dell'insegnamento secondario della matematica in Italia, edited by Giacardi, Livia, 159–179. La Spezia: Pubblicazioni del Centro Studi Enriques–Agorà Edizioni.Google Scholar
Brigaglia, Aldo and Di Sieno, Simonetta. 2009. “L'opera politica di Luigi Cremona attraverso la sua corrispondenza. Prima parte. Gli anni dell'entusiasmo e della creatività,” La matematica nella società e nella cultura. Rivista della Unione Matematica Italiana, Series I, 2: 353–388.Google Scholar
Brigaglia, Aldo, Ciliberto, Ciro and Sernesi, Edoardo. 1994. Algebra e geometria (1860–1940): Il contributo italiano. Supplemento ai Rendiconti del Circolo matematico di Palermo, 36. Palermo: Circolo matematico di Palermo.Google Scholar
Brigaglia, Aldo and Masotto, Guido. 1982. Il Circolo Matematico di Palermo. Bari: Dedalo.Google Scholar
Brisse, Charles and André, Charles. 1873. Cours de physique à l'usage des élèves de la classe de mathématiques spéciales. Paris: Dunod.Google Scholar
Cassirer, Ernst. 1931. “Enlightenment.” In Enciclopedia of Social Sciences 547–552. New York: Macmillan.Google Scholar
Cremona, Luigi. [1861] 1914. “Prolusione ad un corso di geometria superiore, letta nell'Università di Bologna. Novembre 1860,” Il Politecnico 10:22–42. Also in Cremona 1914. Opere matematiche di Luigi Cremona, edited by Luigi Cremona I:237–253. Milano: Hoepli.Google Scholar
Cremona, Luigi. 1873. Elementi di geometria projettiva ad uso degli istituti tecnici del Regno di Italia, vol. I (con Atlante separato), contenente la material assegnata dal Programma dell'ottobre 1871 al 1° corso del 2° biennio. Roma-Torino-Milano-Firenze: G. B. Paravia.Google Scholar
Curbera, Guillermo P. 2009. Mathematicians of the World, Unite! The International Congress of Mathematicians: A Human Endeavor. Wellesley: A. K. Peters.CrossRefGoogle Scholar
Dell'Aglio, Luca, ed. 1992a. “Lettere di Charles Hermite a Luigi Cremona (1867–1878).” In LCC, vol. 1:89–94.Google Scholar
Dell'Aglio, Luca, ed. 1992b. “Lettera di Carl A. Bjerknes a Luigi Cremona (1872).” In LCC, vol. 1:173–174.Google Scholar
Dell'Aglio, Luca, ed. 1992c. “Lettere di Lorenz L. Lindelöf a Luigi Cremona (1880–1889).” In LCC, vol. 1:175–177.Google Scholar
Di Sieno, Simonetta. 2006. “Luigi Cremona e la formazione tecnica pre-universitaria nella seconda metà dell'Ottocento.” In Da Casati a Gentile. Momenti di storia dell'insegnamento secondario della matematica in Italia, edited by Giacardi, Livia, 99–124. La Spezia: Pubblicazioni del Centro Studi Enriques–Agorà Edizioni.Google Scholar
Fletcher, Colin. 1996. “Mersenne: sa correspondance et l'academia parisiensis.” In Mathematical Europe, edited by Goldstein, Gray, and Ritter, 143–153.Google Scholar
Furet, François. 1995. Le passé d'une illusion. Essai sur l'idée comuniste au XXe siècle. Paris: Robert Laffont/Calmann-Lévy.Google Scholar
Gario, Paola, ed. 1994a. “Lettere di G. Henri Halphen a Luigi Cremona (1876–1886).” In LCC, vol. 2:21–25.Google Scholar
Gario, Paola, ed. 1994b. “Lettere di Hieronymus Georg Zeuthen a Luigi Cremona (1866–1898).” In LCC, vol. 2:107–128.Google Scholar
Gario, Paola, ed. 1994c. “Lettere di Charles Brisse a Luigi Cremona (1873–1885).” In LCC, vol. 2:9–11.Google Scholar
Gario, Paola, ed. 1994d. “Lettere di Georges Fouret a Luigi Cremona (1875–1880).” In LCC, vol. 2:17–18.Google Scholar
Gerö, András. 2006. Imagined History: Chapters from 19th and 20th-century Hungarian Symbolic Politics. Wayne: Center for Hungarian Studies and Publications, Budapest: Institute of Habsburg History.Google Scholar
Giacardi, Livia, ed. 1994. “Lettere di Eugène Prouhet a Luigi Cremona 1861–1867.” In LCC, vol. 2:37–47.Google Scholar
Giacardi, Livia. 2004. “I manuali per l'insegnamento della geometria elementare in Italia fra Otto e Novecento.” In Teseo. Tipografia e editori scolastico-educativi dell'Ottocento, edited by Giorgio Chiosso, 97–123. Milano: Editrice Bibliografica.Google Scholar
Giacardi, Livia, ed. 2006. Da Casati a Gentile. Momenti di storia dell'insegnamento secondario della matematica in Italia. La Spezia: Pubblicazioni del Centro Studi Enriques–Agorà Edizioni.Google Scholar
Giusti, Enrico. 1993. Euclides reformatus. La teoria delle proporzioni nella scuola galileiana. Torino: Bollatin Boringhieri.Google Scholar
Goldstein, Cathérine, Gray, Jeremy, and Ritter, Jim. 1996. L'Europe mathématique/Mathematical Europe. Paris: Éditions de la maison des sciences dell'homme.Google Scholar
Grattan-Guinness, Ivor. 1993. “The ingénieur-savant, 1800–1830: A Neglected Figure in the History of French Mathematics and Science.” Science in Context 6:405–433.CrossRefGoogle Scholar
Grattan-Guinness, Ivor, ed. 1994. Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, 2 vols. London: Routledge.Google Scholar
Grattan-Guinness, Ivor. 2002. “The End of Dominance: The Diffusion of French Mathematics Elsewhere, 1820–1870.” In Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800–1945, edited by Parshall, Karen Hunger and Rice, Adrian C., 17–44. Providence RI: American Mathematical Society and London Mathematical Society.Google Scholar
Greitzer, Samuel L. “Luigi Cremona.” In Dictionary of Scientific Biography, edited by Gillispie, Charles C., ad vocem. New York: Scribner.Google Scholar
Harrison, Carol E. and Johnson, Ann, eds. 2009. National Identity. The Role of Science and Technology. Osiris 24. Chicago: University of Chicago Press.Google Scholar
Harvey, Penelope. 1996. Hybrids of Modernity: Anthropology, The Nation State and the Universal Exhibition. London: Routledge.Google Scholar
Hormigón, Mariano and Gasca, Ana Millán. 1992. “Projective Geometry and Applications in the Second Half of the Nineteenth Century.” Archives Internationales d'Histoire des Sciences 42 (129):269–289.Google Scholar
Israel, Giorgio. 2004. “Italian Mathematics, Fascism and Racial Policy.” In Mathematics and Culture I, edited by Michele Emmer, 21–48. Berlin-Heidelberg: Springer-Verlag.Google Scholar
Israel, Giorgio and Gasca, Ana Millán. 2009. The World as a Mathematical Game. John von Neumann in 20th Century Science. Basel: Birkhäuser.Google Scholar
Israel, Giorgio and Nurzia, Laura. 1983. “Correspondence and Manuscripts Recovered at the Istituto Matematico ‘G. Castelnuovo’ of the University of Rome.” Historia Mathematica 10:93–97.CrossRefGoogle Scholar
Israel, Giorgio and Nurzia, Laura. 1989. “Fundamental Trends and Conflicts in Italian Mathematics between the Two World Wars.” Archives Internationales d'Histoire des Sciences 39 (122):111–143.Google Scholar
Knobloch, Eberhard and Rowe, David E., eds. 1994. History of Modern Mathematics, vol. 3, Images, Ideas, and Communities. Boston: Academic Press.Google Scholar
Lacaita, Carlo G. and Silvestri, Andrea, eds. 2000–2003. Francesco Brioschi e il suo tempo (1824–1897), 2 vols. Milano: Franco Angeli.Google Scholar
LCC. 1992–1999. La corrispondenza di Luigi Cremona (1830–1903). Directed by Giorgio Israel, 4 vols. Roma-Palermo: Università di Roma “La Sapienza”/Università Bocconi. Vol. 1, edited by Ana Millán Gasca, 1992, Roma: Università di Roma “La Sapienza”; vol. 2, edited by Marta Menghini, 1994, Roma: Università di Roma “La Sapienza”; vol. 3, edited by Marta Menghini, 1996, Palermo: Università Bocconi; vol. 4, edited by Laura Nurzia, 1999. Palermo: Università Bocconi.Google Scholar
Lehto, Olli. 1998. Mathematics without Borders: A History of the International Mathematical Union. New York: Springer.Google Scholar
Loria, Gino. 1904. “Luigi Cremona et son oeuvre mathématique.” Bibliotheca mathematica, 125–195.Google Scholar
Lützen, Jesper. 2002. “International Participation in Liouville's Journal de Mathématiques Pures et Appliquées.” In Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800–1945, edited by Parshall, Karen Hunger and Rice, Adrian C., 89–104.Google Scholar
Menghini, Marta. 1986. “Notes on the correspondence between Luigi Cremona and Max Noether.” Historia Mathematica 13:341–351.Google Scholar
Menghini, Marta 1993. “Il ruolo di capiscuola di Felix Klein e Luigi Cremona alla luce della loro corrispondenza.” Rivista di Storia della Scienza (2nd series) 1:183–225.Google Scholar
Millán Gasca, Ana, ed. 1992. “I corrispondenti spagnoli di Luigi Cremona.” In LCC, vol. 1:165–172.Google Scholar
Millán Gasca, Ana. 2006. “Mainardi, Gaspare.” In Dizionario Biografico degli Italiani, vol. 57:560–561. Roma: Istituto della Enciclopedia Italiana.Google Scholar
Millán Gasca, Ana and Nastasi, Pietro, eds. 1994. “Lettere di Olry Terquem a Luigi Cremona (1861–1862).” In LCC, vol. 2:49–51.Google Scholar
Morrell, Jack and Thackray, Arnold. 1981. Gentlemen of Science: Early Years of the British Association for the Advancement of Science. Oxford: Clarendon Press.Google Scholar
Nastasi, Pietro, ed. 1994. “Lettere di François Folie a Luigi Cremona (1879).” In LCC, vol. 2: 133–135.Google Scholar
Nastasi, Pietro and Nurzia, Laura, eds. 1994. “Lettere di Charles-Antoine de Cyuper a Luigi Cremona (1877–1878).” In LCC, vol. 2:129–131.Google Scholar
Nurzia, Laura. 1984. “Materiali di archivio rinvenuti presso l'Istituto ‘G. Castelnuovo’ dell'Università di Roma.” Rivista di Storia della Scienza 1:107–114.Google Scholar
Nurzia, Laura, ed. 1996. “Lettere di Thomas Hudson Beare, Charles Edward Doble, Horace Hart e Olaus Henrici a Luigi Cremona (1886–1888).” In LCC, vol. 3:179–195.Google Scholar
Nurzia, Laura, ed. 1999. “La corrispondenza tra Luigi Cremona e Thomas Archer Hirst (1864–1892).” In LCC 1999, vol. 4:1–224.Google Scholar
Palladino, Nicla, Mercurio, Anna Maria, and Palladino, Franco, eds. 2009. Per la costruzione dell'Unità d'Italia. Le corrispondenze epistolari Brioschi-Cremona e Betti-Genocchi. Firenze: Leo S. Olschki.Google Scholar
Parshall, Karen H. 1996. “How We Got Where We Are: An International Overview of Mathematics in National Contexts (1875–1900).” Notices of the American Mathematical Society 43:287–296.Google Scholar
Parshall, Karen H., and Rice, Adrian C., eds. 2002. Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800–1945. Providence RI: American Mathematical Society and London Mathematical Society.Google Scholar
Parshall, Karen H. 2009. “The Internationalization of Mathematics in a World of Nations, 1800–1960.” In The Oxford Handbook in the History of Mathematics, edited by Robson, E. and Stedall, J., 85–104. Oxford-New York: Oxford University Press.Google Scholar
Pepe, Luigi. 2007. Rinascita di una scienza. Matematica e matematici in Italia (1715–1814). Bologna: Clueb.Google Scholar
Rédei, Miklós, ed. 2005. John von Neumann: Selected letters. Providence R I: American Mathematical Society.CrossRefGoogle Scholar
Rowe, David. 1989. “Klein, Hilbert, and the Göttingen Mathematical Tradition.” Osiris 5:186–213.CrossRefGoogle Scholar
Sasaki, Chikara. 2002. “The Emergence of the Japanese Mathematical Community in the Modern Western Style, 1855–1945.” In Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800–1945, edited by Parshall, Karen Hunger and Rice, Adrian C., 229–252. Providence RI: American Mathematical Society and London Mathematical Society.Google Scholar
Turner, R. Steven. 1971. “The Growth of Professional Research in Prussia, 1818 to 1848: Causes and Context.” Historical Studies in the Physical Sciences 3:137–182.Google Scholar