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The Edition of the Bernoulli Correspondence: A Historical Overview and Insights into the Most Recent Developments

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Mathematical Correspondences and Critical Editions

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

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Abstract

The aim of the online Basler Edition der Bernoulli-Briefwechsel (BEBB) is to make all as-of-yet unpublished letter exchanges of the seventeenth- and eighteenth-century mathematicians Daniel Bernoulli, Jacob II Bernoulli, Johann I Bernoulli, Johann II Bernoulli, Nicolaus I Bernoulli, Nicolaus II Bernoulli and Jacob Hermann available to the scientific community. Some of their correspondents were outstanding scientists. The edition of the Bernoulli correspondence has a long history that goes back to the eighteenth century, when the edition of the Commercium epistolicum between Johann I Bernoulli and Leibniz was prepared under the supervision of the Bernoullis. Despite the early interest in a scholarly edition of large parts of the Bernoulli correspondence and the repeated attempts by historians of mathematics to realize such a project, the undertaking experienced numerous setbacks. However, the digital age seems to provide the necessary conditions for a complete edition of the correspondence. In the context of the BEBB, around 1500 letters have been edited and published online in the last 10 years. In the next 10 years, another 2505 edited letters will be made available online. The present paper focuses on the main phases of the history of the Bernoulli letter edition and aims to give an overview of the on-going preparation of a modern online edition. This will include all related data, such as metadata, critical, emended transcriptions, digital facsimiles, commentaries, and indices, accessible through new technologies and tools that are currently being developed for the project.

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Notes

  1. 1.

    For their valuable advice and information, I wish to express my sincere thanks to Martin Mattmüller, Erwin Neuenschwander and Tobias Schweizer.

  2. 2.

    A complete list of the correspondents can be found at http://www.ub.unibas.ch/bernoulli/index.php/Suchbaum. This and all further websites referred to in the following were last consulted on 12/31/2017.

  3. 3.

    Individual phases of the history of the Bernoulli letter Edition between 1936 and 2005 are described in the introduction of Spiess (1955, pp. 9–85), and in Truesdell (1958, pp. 54–62), and Fellmann and Mikhajlov (1998, pp. 18–28). For the history of publication of the correspondence between the Bernoullis and Euler, see Neuenschwander (2002, pp. 103–105) and Nagel (2005, pp. 173–175).

  4. 4.

    The edition of the correspondence between Johann I Bernoulli and Pierre Varignon is still in progress. The third volume is in preparation, and will be published in 2019.

  5. 5.

    www.ub.unibas.ch/bernoulli

  6. 6.

    For the role of scientific correspondence in the eighteenth century, see Peiffer (1998).

  7. 7.

    The text is printed in Wolf (1859, pp. 71–94).

  8. 8.

    On the edition of the correspondence between Johann I Bernoulli and Leibniz, see Nagel (1989, pp. 167–174).

  9. 9.

    Christian Wolff asks Bernoulli for information about this rumour in his letter of October 11, 1717 (Basel UB, Ms. L Ia 671, Nr.14*). In his answer of April 13, 1718 (Basel UB, Ms. L Ia 671, Nr.10), Bernoulli admits having already spoken with a publisher about the edition of his correspondence with Leibniz, but denies the rumours of an actual project dedicated to the edition.

  10. 10.

    On Bourguet’s plan for an edition of Bernoulli’s and Hermann’s letter exchanges with Leibniz, see Nagel (1994, pp. 525–528), and Bovet (1905, pp. 255–259). The correspondence of Bernoulli and Hermann with Bourguet, in which the topic of the edition of the Leibniz correspondence is addressed, is housed at the Bibliothèque publique et universitaire de Neuchâtel (Suisse), Ms 1267 and Ms 1272. The letters will be published in 2020 as part of the BEBB.

  11. 11.

    Johann I Bernoulli sent his manuscripts to Bourguet with his letter of June 11, 1731. See Nagel (1994, p. 528). In December 1731, Hermann sent a small parcel from Basel to Neuchâtel that probably contained his Leibniz manuscripts. See Bovet (1905, p. 258), and Nagel (1994, p. 527).

  12. 12.

    Nagel (1994, p. 528).

  13. 13.

    On Kortholt’s project, see Nagel (1994, p. 529). The only sources of information on this project are a letter from Johann I Bernoulli to Bourguet of November 7, 1733, and a letter from Kortholt to Johann I Bernoulli of October 14, 1738.

  14. 14.

    Kortholt (1734–1742).

  15. 15.

    On the history of the Commercium philosophicum et mathematicum, see Nagel (1994, pp. 529–531).

  16. 16.

    Bernoulli and Cramer (1742).

  17. 17.

    Bernoulli et al. (1745).

  18. 18.

    See Cantor (1898, p. 486).

  19. 19.

    Bernoulli et al. (1745, pp. II–III).

  20. 20.

    Genève, BGE, Ms. Suppl. 384, fo. 14r-15v.

  21. 21.

    For an overview of Johann III Bernoulli’s plans, see Spiess (1955, pp. 27–31).

  22. 22.

    The sales offer of approximately 1700 letters was made anonymously in Bernoulli Jo III (1796).

  23. 23.

    A detailed account of the rediscovery of the Bernoulli manuscripts can be found in Spiess (1955, pp. 31–38).

  24. 24.

    At present, the manuscripts are located at the St. Petersburg branch of the Archive of the Russian Academy of Science.

  25. 25.

    Fuss (1842).

  26. 26.

    An account of the history of this edition is given in Fuss (1842, 1843 I, pp. IXX–XXXV) and in Fellmann and Mikhajlov (1998, pp. 21–23).

  27. 27.

    Fellmann and Mikhajlov (1998, p. 23).

  28. 28.

    These letters are edited in Fellmann and Mikhajlov (1998, 2016).

  29. 29.

    Gerhardt (1855–1856) and (1859). For an overview and description of Gerhardt’s editorial work, see Hess (1986). The edition of Leibniz’s mathematical correspondence with the Bernoulli is addressed on pp. 35–38.

  30. 30.

    Gerhardt (1855, p. 132).

  31. 31.

    The original letters sent by Leibniz to the Bernoullis were, at the time, kept at the University Library of Basel.

  32. 32.

    See below (p. 12).

  33. 33.

    Wolf (1858–1862).

  34. 34.

    The discovery is reported in Wolf (1876).

  35. 35.

    Eneström (1880).

  36. 36.

    See Spiess (1955 pp. 40–41).

  37. 37.

    Eneström (1903–1905) and (1906).

  38. 38.

    Fellmann and Mikhajlov (2016, p. 16).

  39. 39.

    Fellmann and Mikhajlov (1998; 2016).

  40. 40.

    Spiess (1955, pp. 44–45).

  41. 41.

    For an overview, see Spiess (1955, pp. 9–85).

  42. 42.

    Wollenschläger (1933). The need for a re-edition of this correspondence, due to the inadequate standard of the Wollenschlägers edition, is pointed out in Spiess (1955, pp. 47–48). Moivre’s correspondence will be edited anew within the BEBB.

  43. 43.

    Rebel (1934).

  44. 44.

    Fedel (1934).

  45. 45.

    Stieda (1926).

  46. 46.

    An overview of the Euler-Edition is given in Kleinert (2015, 2017), and Kleinert and Mattmüller (2007).

  47. 47.

    For more detailed information on Spiess, see Neuenschwander (2013) and Dauben and Scriba (2002, p. 526).

  48. 48.

    In 1935, Spiess managed to bring the project under the patronage of the Naturforschende Gesellschaft Basel and to create a foundation supervised by the Bernoulli-Kommission. See Spiess (1955, p. 49).

  49. 49.

    The University Library of Basel obtained the manuscripts conserved at the Royal Academy of Stockholm on a loan basis in 1935 for the purpose of their edition, and finally acquired them in 1965. See Spiess (1955, p. 29, 50), and Fellmann and Mikhajlov (1998, p. 25).

  50. 50.

    Spiess (1955, p. 10).

  51. 51.

    Spiess (1955, p. 75).

  52. 52.

    Spiess (1955, p. 58). The typewritten transcriptions prepared by Spiess still form the basis of the Bernoulli letter edition. They are conserved, together with the card index, at the Bernoulli-Euler-Zentrum in the University Library of Basel.

  53. 53.

    Spiess (1955, pp. 95–485).

  54. 54.

    Spiess (1955, pp. 87–92).

  55. 55.

    See Costabel and Peiffer (1988, p. IX).

  56. 56.

    On the history of the correspondence between Bernoulli and Varignon, see Costabel and Peiffer (1988, pp. 3–4).

  57. 57.

    Costabel and Peiffer (1988–1992).

  58. 58.

    Weil (1993).

  59. 59.

    See above (p. 8).

  60. 60.

    Ljubimenko (1937). See Fellmann and Mikhajlov (2016, p. 16).

  61. 61.

    Fellmann’s work is credited in Neuenschwander (2018).

  62. 62.

    Fellmann and Mikhajlov (1998).

  63. 63.

    On the history of the Leibniz edition see inter alia Wahl (2013), Folkerts (2008), Lorenz (2007), Poser (2000), and Schepers (1999).

  64. 64.

    Leibniz-Archiv, Leibniz-Forschungsstelle Hannover (eds) (1976–). Volumes 4-8 were published between 1995 and 2015. Volume 9 is still in progress, but a preliminary version is already available on the webpage of the Leibniz edition (http://www.gwlb.de/Leibniz/Leibnizarchiv/Veroeffentlichungen/III9.pdf).

  65. 65.

    Berlin-Brandenburgische Akademie der Wissenschaften/Akademie der Wissenschaften zu Göttingen (eds) (2017–) Personen- und Korrespondenz-Datenbank der Leibniz-Edition (https://leibniz.uni-goettingen.de/pages/index). At present, the database is not yet completely accessible to the public; the remaining parts will be released in stages.

  66. 66.

    The published letters are edited in Mazzone and Roero (1992, 1997), and Grugnetti (1986).

  67. 67.

    It can be consulted at http://aleph.unibas.ch/F/func=option-update-lng&file_name=find-b&p_con_lng=GER&local_base=bernoulli_edition

  68. 68.

    The edited letters can be consulted at http://www.ub.unibas.ch/bernoulli/index.php/Briefe_im_Volltext.

  69. 69.

    The Bernoulli-wiki was developed by Andreas Bigger, at the time, the coordinator of the digitalisation team of the University Library.

  70. 70.

    The presentation of digital images of the manuscript is particularly useful in editions of mathematical texts, since the editorial representation of mathematical formulae or figures sometimes implies a loss of information. For the problems related to the representation of mathematical figures in editions, see Beeley (2007, p. 106).

  71. 71.

    The guidelines containing a detailed documentation of the editorial rules can be consulted at http://www.ub.unibas.ch/bernoulli/images/e/e0/Richtlinien_2011.pdf

  72. 72.

    For more detailed information on the correspondents, see www.ub.unibas.ch/bernoulli

  73. 73.

    The Bernoulli Scheuchzer edition benefited from the cooperation of the following experts: Daniel Bernoulli, professor of geology, ETH Zürich; Ulrich Gäbler, professor of church and dogma history, University of Basel; Ernst Jenni, professor of Old Testament and Semitic linguistics, University of Basel; Paul Michel, professor for older German literature, University of Zürich; Rebekka Schifferle, cultural historian, University of Basel; Martin Rickenbacher, historian of geography, Swisstopo Bern; Andreas Verdun, historian of astronomy, University of Bern.

  74. 74.

    Jeanne Peiffer participated in the publication of the previous two volumes of the correspondence, which appeared in 1988 and 1992 as volumes 2 and 3 of Der Briefwechsel von Johann Bernoulli.

  75. 75.

    The Bernoulli-Euler-Zentrum was established by the University of Basel in 2012 and is hosted on the premises of the Basel University Library. The pivotal aims of the Centre are the maintenance of the heritage of the “Basel school” of mathematicians in the seventeenth and eighteenth centuries, the edition of their works and correspondence, and the promotion of international research cooperation. More information can be found online at: https://bez.unibas.ch

  76. 76.

    The work on BEOL is funded by the Swiss National Foundation and currently stands under the direction of Lukas Rosenthaler and Helmut Harbrecht, the actual director of the BEZ.

  77. 77.

    The VRE used here is based on the Knora/SALSAH platform developed by Lukas Rosenthaler at the DHLab. Knora stands for Knowledge Organization, Representation, and Annotation. It is an open, modular, extensible and flexible platform on which the data are stored and processed. In order to represent data, Knora uses industry standards such as the Resource Description Framework (RDF). A description of the platform with a graphical representation of its architecture is given in SAGW (2015).

  78. 78.

    Lemmermeyer and Mattmüller (2015).

  79. 79.

    The Bernoulli-Varignon edition is a hybrid edition, having been elaborated in parallel for publication in print and online. For more information on the project, see above (pp. 15–16).

  80. 80.

    A link to the beta release can be found on the BEZ website (https://www.bez.unibas.ch/beol.php).

  81. 81.

    Immenhauser (2017, p. 27).

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    Sulamith Gehr

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Correspondence to Sulamith Gehr .

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  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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Gehr, S. (2018). The Edition of the Bernoulli Correspondence: A Historical Overview and Insights into the Most Recent Developments. 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_3

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