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Mathematical Correspondences and Critical Editions pp 247–269Cite as

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Democratization of Mathematics Through Cremona’s Correspondence with Foreign Colleagues (1860–1901)

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Part of the book series: Trends in the History of Science ((TRENDSHISTORYSCIENCE))

Abstract

From the mid-nineteenth to the early twentieth century, many common traits were shared by national mathematical communities, which were not only separated geographically (from the Czech lands to Japan), and culturally (from northern to southern Europe), but which also varied from the point of view of the dynamism of original research (from Germany to the United States). Societies and journals were launched in the national languages, thanks to the widening of the social platform of mathematics and the emergence of a national leadership; the development of state school systems increased mathematical knowledge; and furthermore, mathematics played a role in and received encouragement from the processes of social and economic modernization and the evolution of state institutions. Intellectual competition among nations, very much a part of the spirit of the nineteenth century, seems to prevail over early Modern European universalism. A panorama of almost planetary dissemination of Western mathematics resulted from this evolution, leading eventually to a reinforcement of the international circulation of knowledge, which survived two world wars.

The collection of letters written to Luigi Cremona conserved at the Sapienza University of Rome casts light on several aspects of this evolution. The letters offer a “backstage” point of view, in contrast with official proclamations; they show the interplay between national leaders and the mathematical circles in the capitals as well as mathematicians working in isolation; moreover, they show a variety of connected activities—research, institutional commitments, and the fostering of culture, including translations and textbooks. International dialogue grew out of this hive of initiatives, driven by both national passion and philosophical and political convictions, in contrast with the present European trend of entrusting the circulation of ideas—and the production of knowledge—to initiatives governed from the top, standardized (design, funding and assessment) far beyond what is needed. The edition (in the Académie Internationale d’Histoire des Sciences series “De diversis artibus”) has been carried out by a European team directed by Giorgio Israel.

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Notes

  1. 1.

    A first overall presentation of this edition was discussed by the first two authors with the title “Luigi Cremona’s network of foreign correspondents (1860–1901): a testimony to the evolution of the “Europe of science” in the late nineteenth century” at the International Conference Mathematical Schools and National Identity (sixteenth to twentieth cent.), Turin, October 10–12, 2013.

  2. 2.

    For a biographical profile of Luigi Cremona, see Israel (2016) and the bibliography therein.

  3. 3.

    Prouhet to Cremona, Paris, May 29th 1861; for further details, see Millán Gasca (2011, pp. 52 ff). Letters from Amédée Mannheim (1831–1906) can be found in the Genova Cremona Archive (see note 8).

  4. 4.

    Terquem to Cremona, Paris, March 11, 1862. On Cremona’s political evolution, see Brigaglia and Di Sieno (2009, 2010, 2017); see also Rossi 1984.

  5. 5.

    He was offered the ministry of education twice: in 1881, by Quintino Sella, a request he turned down, and in 1898, this time accepting, although he only remained in office for the month of June, owing to the political crisis within the government. In 1880, the minister Francesco De Sanctis appointed him government commissioner for the reorganization of the “Vittorio Emanuele” National Library in Rome housed in the Collegio Romano.

  6. 6.

    For example, letters from Sturm initially addressed geometrical issues, but then turned towards institutional aspects; letters from German correspondents were edited in the CLC by Eberhard Knobloch and Karin Reich.

  7. 7.

    Academy of Sciences of Lisbon (1867), Mathematical Society of London (1871), Society of Sciences of Bohemia (1872), Danish Academy of Sciences (1876), Cambridge Philosophical Society (1877), the Academy of Science of Munich (1878), the Royal Society of London (1879), the Society of Sciences of Göttingen (1880), the Dutch Academy of Sciences (1881), the Mathematical Society of Prague (1881), the Royal Society of Edinburgh (1883), the Prussian Academy of Berlin (1886), the Physico-Medical Society of Erlangen (1896), the Irish Academy of Dublin (1898), the Academy of Belgium (1899), the Institut de France (1899), the Swedish Academy (1901), and finally, the American Academy of Washington (1902).

  8. 8.

    In Genoa there are letters from 22 non-Italian correspondents included in the Sapienza Cremona Archive: Arthur Cayley (4 letters); Eugène Dewulf (2 letters); Lewis Carroll–Charles Dodgson (1 letter); James Glaisher (4 letters); Charles Hermite (1 letter); Thomas Archer Hirst (86 letters); Felix Klein (4 letters); Leopold Kronecker (1 letter); Ernst Eduard Kummer (1 letter); Sophus Lie (1 letter); Max Noether (1 letter); Emile Picard (1 letter); Eugène Prouhet (1 letter); Theodor Reye (1 letter); George Salmon (3 letters); Ludwig Schläfli (1 letter); Kyparissos Stephanos (1 letter); Rudolf Sturm (4 letters); James Sylvester (1 letter); Peter Tait (5 letters); Emil Weyr (1 letter); and Hieronymus Georg Zeuthen (1 letter). There are also letters from the following additional 12 foreign correspondents: James Booth (1806–1878) (4 letters); Maurice D’Ocagne (1862–1938) (1 letter); Morgan Jenkins (1 letter); Seligmann Kantor (1857–1902) (8 letters); Jacob Lüroth (1844–1910) (7 letters); Gösta Mittag Leffler (1846–1927) (2 letters); Amédée Mannheim (1831–1906) (55 letters); Henri Poincaré (1854–1912) (3 letters); Henry Smith (1826–1883) (9 letters); William Spottiswoode (1825–1883) (16 letters); J. Vanecek (7 letters); and Gustav Wolff (1834–1913) (20 letters, 1883). Data from Brigaglia and Di Sieno (2011a); the study of this collection is ongoing (see website www.luigi-cremona.it).

  9. 9.

    See Carbone et al. (2001, 2002), Cerroni (2014), Cerroni and Fenaroli (2007), Enea and Gatto (2009) and Palladino et al. (2009). All of the publications are included on the web site www.luigi-cremona.it

  10. 10.

    In fact, the overall research into Cremona’s letters to every correspondent was so immense that it soon became obvious that the project would inevitably remain incomplete and that failure to acknowledge this fact would postpone the conclusion of the book indefinitely.

  11. 11.

    Louise Palmyre Gaudin (1813–1889).

  12. 12.

    Ettore Caporali (2 letters), Valentino Cerruti (1 letter), and Carlo Saviotti (6 letters, referring to Louis Bossut's French translation of his 1872 essay Le figure reciproche nella statica grafica).

  13. 13.

    See Table 1.

  14. 14.

    Four letters from Martin Krause (1851–1920) to Eugenio Beltrami (written in 1898–1899); a letter from Rudolf Clausius (1822–1888) and 5 letters from a certain Heinrich Schramm to Francesco Brioschi dating back to the years 1867–1869; and three letters from Édouard Combescure (1824–1889) to an unidentified member of the editorial office of the journal Annali di matematica, written in 1871–1872.

  15. 15.

    See Israel (2016).

  16. 16.

    These booklets have been useful for obtaining a better understanding of the general historical meaning of this archival material and establishing the final criteria for the edition (Millán Gasca 1992a, b; Menghini 1994, 1996; Nurzia 1999).

  17. 17.

    Edited by G. Israel and L. Regoliosi.

  18. 18.

    For example: at bbf.dipf.de (German Institute for International Educational Research (DIPF), Bibliothek für Bildungsgeschichte Forschung, Germany), the BBF/DIPF/Archiv, Gutachterstelle des BIL—Personalbögen der Lehrer höherer Schulen Preußens; at www.culture.gouv.fr/public/mistral/leonore_fr. The database Léonore (Légion d’honneur), Archives Nationales (France).

  19. 19.

    Knobloch, Reich, in CLC, pp. 1651–1652. This letter, written in Italian and dated March 25, 1867, in Berlin, was found together with two letters from Weierstrass to Cremona dated 1874 (and two letters from Weierstrass’s sister Clara). See Casorati’s letter published in Neuenschwander (1978, p. 72 ff). We have already mentioned the letters from Prouhet, showing shared political feelings; also Neuenschwander (1986).

  20. 20.

    For its influence in Spain, see Millán Gasca (2012).

  21. 21.

    The break-up of the Soviet Union brought to a close a cycle of development of modernity that began with the French Revolution and had as its guiding principle the development of democracy, enveloped as this was in the tension between universal aspiration and national dimension.

  22. 22.

    “The boundless number of editions, translations and reprints that followed each other throughout the sixteenth century bears witness to the circulation at all levels of Euclid’s works, the assimilation of which was to make a substantial contribution to a unitary mathematical culture, and thus to the formation of a universal scientific community.” (Giusti 1993, p. 2). Euclid’s Book V theory of proportions became the universal language of natural philosophy, “almost a metageometry, or better a mathesis universalis” (ibid.).

  23. 23.

    Fletcher (1996).

  24. 24.

    Euler, L. 1975. Opera Omnia. Series quarta A, Commerciumepistolicum, vol. 1. Basel: Birkhäuser.

  25. 25.

    This is accurately summed up in the declaration of November 11, 1997, of UNESCO support for the IMU’s decision to declare 2000 the International Year of Mathematics on the basis of the role of mathematics and its current applications in science, technology, communications and economy; of its ancient roots and universal character; and of the importance of a mathematical education for the development of rational thinking.

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Authors and Affiliations

  1. Department of Education, Università Roma Tre, Roma, Italy

    Giorgio Israel, Ana Millán Gasca & Luigi Regoliosi

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  1. Giorgio Israel
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  2. Ana Millán Gasca
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  3. Luigi Regoliosi
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Correspondence to Ana Millán Gasca .

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Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Ferrara, Ferrara, Italy

    Maria Teresa Borgato

  2. Institute of Mathematics, University of Zurich, Zurich, Switzerland

    Erwin Neuenschwander

  3. Institut de Mathématiques de Jussieu-Paris, Rive Gauche, CNRS, Sorbonne Université, Paris, France

    Irène Passeron

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Israel, G., Millán Gasca, A., Regoliosi, L. (2018). Democratization of Mathematics Through Cremona’s Correspondence with Foreign Colleagues (1860–1901). In: Borgato, M., Neuenschwander, E., Passeron, I. (eds) Mathematical Correspondences and Critical Editions. Trends in the History of Science. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-73577-1_13

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