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From Graz to Göttingen: Neugebauer’s Early Intellectual Journey

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A Mathematician's Journeys

Part of the book series: Archimedes ((ARIM,volume 45))

Abstract

Otto Neugebauer’s early academic career was marked by a series of transitions. His interests shifted from physics to mathematics, and finally to the history of ancient mathematics and exact sciences. Yet even from his early years in Graz, Neugebauer was strongly attracted to the mathematical culture of Göttingen. When he arrived there in 1922, he quickly established a strong personal friendship with Richard Courant, the newly appointed Director of the Mathematics Institute. Neugebauer and Courant worked together closely up until 1933, when the Nazi government decimated the Göttingen scientific community. In this essay, Neugebauer’s historical work and his vision for a new approach to the study of the exact sciences are viewed through the prism of these events. By so doing, one can easily appreciate how Neugebauer’s scholarship reflects the ideals he and Courant shared as leading representatives of the Göttingen mathematical tradition.

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Notes

  1. 1.

    For a brief account of Courant’s deep identification with Göttingen mathematics, see (Rowe 2015).

  2. 2.

    Schoenflies to Hilbert, 1919, Hilbert Nachlass 355, Niedersächsische Staats- und Universitätsbibliothek Göttingen.

  3. 3.

    Courant’s appointment in Münster thus helped pave the way for his return to Göttingen in 1920.

  4. 4.

    Einstein to Klein, 27 December 1918, Collected Papers of Albert Einstein, vol. 8B (Princeton: Princeton University Press, 1998), pp. 975–976.

  5. 5.

    Born to C. H. Becker, 1919, Geheimes Staatsarchiv Preußischer Kulturbesitz, Berlin, I.HA.Rep.92. C. H. Becker.7919.

  6. 6.

    It is possible, though, that Schur may have been offered this position; in 1919 he attained a long-sought promotion to full professor in Berlin, where he had been the star pupil of Frobenius.

  7. 7.

    Hilbert to Toeplitz, 8 February 1920. Universitäts- und Landesbibliothek Bonn, Toeplitz B: Dokument 47. Hilbert mistakenly thought that Hausdorff, too, was of non-Jewish background.

  8. 8.

    Einstein to Hilbert, 21 February 1920, Collected Papers of Albert Einstein, vol. 9, (Princeton: Princeton University Press, 2004), p. 440.

  9. 9.

    Hilbert to Hermann Wagner, 1926, Cod. Ms. H. Wagner 27, Niedersächsische Staats- und Universitätsbibliothek Göttingen.

  10. 10.

    One of his admirers, Albert Einstein, wrote on the occasion of Hilbert’s 60th birthday: “Nur ein Zipfel Ihres gewaltigen Lebenswerkes kann ich Beschränkter (und Fauler) überschauen, aber gerade genug, um das Format Ihres schaffenden Geistes zu ahnen. Dazu den Humor und den sicheren, selbständigen Blick in alle Dinge und—einen harten Schädel wie kein zweiter nebst zwei starken Armen, um von Zeit zu Zeit den Fakultätsstall auszumisten.” (Einstein to Hilbert, 18 February 1922, Collected Papers of Albert Einstein, vol. 13, (Princeton: Princeton University Press, 2012), p. 92).

  11. 11.

    For much of the information relating to Neugebauer’s training and educational activities in Graz, Munich, and Göttingen I have drawn heavily on sources that can be found in the Otto Neugebauer Papers, The Shelby White and Leon Levy Archives Center, Institute for Advanced Study, Princeton, NJ, USA, cited hereafter as “Neugebauer Papers, IAS”.

  12. 12.

    Neugebauer Papers, IAS, Box 13, Tagebuch, 1917–1919.

  13. 13.

    Neugebauer Papers, IAS, Box 7.

  14. 14.

    Neugebauer Papers, IAS, Box 13, Vortrag über A.R.T. und (Weyl 1921).

  15. 15.

    Presumably Neugebauer had read Hilbert’s 1917 lecture on “Axiomatisches Denken” (Hilbert 1917), which suggests a very similar viewpoint.

  16. 16.

    Neugebauer Papers, IAS, Box 7.

  17. 17.

    Neugebauer Papers, IAS, Box 7. Neugebauer once made reference to Poincaré’s theory of lunar motion to refute standard teleological views of astronomers in the sixteenth century: “The investigations of Hill and Poincaré have demonstrated that only slightly different initial conditions would have caused the moon to travel around the earth in a curve [with nodal loops and] … with a speed exceedingly low in the outermost quadratures as compared with the motion at new and full moon. Nobody would have had the idea that the moon could rotate on a circle around the earth and all philosophers would have declared it as a logical necessity that a moon shows six half moons between two full moons. And what could have happened with our concepts of time if we were members of a double-star system (perhaps with some uneven distribution of mass in our little satellite) is something that may be left to the imagination.” He even drew a figure to illustrate this (Neugebauer 1969, 152–153).

  18. 18.

    Neugebauer Papers, IAS, Box 7, Drei Vorträge aus dem Gebiet der algebraischen Funktionen.

  19. 19.

    Young Friedrich Hund described this atmosphere many years later, see (Mehra and Rechenberg 1982, 345).

  20. 20.

    The famous “yellow series” founded by Courant in 1920 continues to occupy a central niche in Springer’s publishing program, though its character changed quite dramatically after 1945 when English became the dominant language for international publications in mathematics.

  21. 21.

    Hurwitz’s original Ausarbeitungen from that time can still be found among his scientific papers: they are numbers 112, 113, and 115 in the Hurwitz Nachlass, ETH Bibliothek, Zürich.

  22. 22.

    Born also related that he gave Courant his notebook for use in preparing the Hurwitz-Courant volume.

  23. 23.

    Another influential figure for the reception of Weierstrass’ theory in Italy was Salvatore Pincherle.

  24. 24.

    Bei aller inneren Konsequenz des so errichteten Gebäudes kann der Lernende sich heute mit den Gesichtspunkten der Weierstraßschen Theorie allein nicht mehr begnügen. (Hurwitz and Courant 1922, v).

  25. 25.

    “Ohne Zweifel liegt in dieser Tendenz eine Bedrohung für die Wissenschaft überhaupt; der Strom der wissenschaftlichen Entwicklung ist in Gefahr, sich weiter und weiter zu verästeln, zu versickern und auszutrocknen.” (Courant and Hilbert 1924, vi).

  26. 26.

    Courant-Hilbert II was not listed in the bibliography of the Deutsche Bücherei. It was still listed in the Springer catalogues, however, in 1940. The Sicherheitsamt of the Reichsführer of the SS established a liaison office in the Deutsche Bücherei in 1934 to oversee the listing of books by Jewish authors. See (Sarkowski 1996, 353).

  27. 27.

    See (Born 1978, 79–80).

  28. 28.

    In the same text, he later went on to admit that his own theory starts from precisely the opposite standpoint as that taken by Frege and Dedekind (Hilbert 1922, 163).

  29. 29.

    For a detailed account of Hilbert’s work on foundations during the final decades of his productive career, see (Hilbert 2013).

  30. 30.

    Neugebauer Papers, IAS, Box 7.

  31. 31.

    See Neugebauer’s letter to Erich Bessel-Hagen, 21 April, 1924, cited in Siegmund-Schultze’s paper for this volume.

  32. 32.

    A copy of (Neugebauer 1925) can be found in Neugebauer Papers, IAS, Box 14, item 1.

  33. 33.

    This fascination actually began with J. J. Sylvester, who called attention to the mysteries of unit fractions soon after publication of the Rhind papyrus.

  34. 34.

    Neugebauer ended his tribute to Courant on his 75th birthday with some moving remarks about how he had made it possible for him to pursue his chosen career (Neugebauer 1963, 9).

  35. 35.

    Neugebauer’s Rigorosum took place on 21 April, 1926. Promotionsverfahren Otto Neugebauer, Universitätsarchiv Göttingen, Math. Nat. Prom. Spec. N.I.

  36. 36.

    These documents are located in Cod. Ms. F. Klein 21 F, Niedersächsische Staats- und Universitätsbibliothek Göttingen.

  37. 37.

    On Neugebauer’s relationship with Bessel-Hagen, see Reinhard Siegmund-Schultze’s contribution to this volume.

  38. 38.

    A copy of this early essay can be found in Neugebauer Papers, IAS, Box 14, item 9.

  39. 39.

    Lecture in Kiel, “Über die Mathematik im alten Ägypten,” 11 December 1926, in Neugebauer Papers, IAS, Box 14, item 5.

  40. 40.

    “Diese Arbeitsrichtung, die seit einigen Jahren immer mehr zur Geltung kommt, bedeutet hoffentlich das Ende eines Zustandes in der Geschichte der Mathematik den man – jedenfalls was die Geschichte der vorgriechischen Mathematik anlangt – manchmal nur mit dem Faustrecht vergleichen kann, wo es mehr auf Kühnheit des Behauptens als auf Gründlichkeit der Untersuchung ankommt.” (S. 1). As a representative of the earlier tradition, he no doubt thought of Hermann Hilprecht, who speculated about the connection between certain numbers found on cuneiform tablets and Plato’s number mysticism, about which see (Neugebauer 1957, 27).

  41. 41.

    In view of this, one might wonder why this text does not appear in the three volumes of Hilbert’s Gesammelte Abhandlungen. Presumably, he and the editors chose to leave it out because the latter part of the text sketches a faulty proof of Cantor’s continuum hypothesis.

  42. 42.

    In (Hilbert 1925) he explicitly identified with Kant’s epistemology, while noting that Kant’s position already spelled doom for the logicist theories of Frege and Dedekind. This brought him closer to Brouwer’s intuitionism, but it was left to Brouwer to point this out in (Brouwer 1928).

  43. 43.

    Neugebauer Papers, IAS, Box 1, Geschichte der Geometrie bis Euclid 1929.

  44. 44.

    Neugebauer Papers, IAS, Box 1, Geschichte der Geometrie nach Euclid 1932.

  45. 45.

    Neugebauer Papers, IAS, Box 1, Ausgewählte Kapitel der Geschichte der antiken Mathematik.

  46. 46.

    For insight into Klein’s interests in technology and his impact on Göttingen and beyond, see (Eckert 2013, 67–193).

  47. 47.

    For a detailed analysis of the scope and impact of the IEB, see (Siegmund-Schultze 2001).

  48. 48.

    https://www.uni-goettingen.de/de/brief-von-james-franck-an-den-rektor-der-georg-august-universitaet-vom-17-april-1933/85743.html.

  49. 49.

    Details about this case, which was dismissed in court, can be found in Universitätsarchiv Göttingen, UAG.Kur.PA.Courant, Richard; Bd.1.

  50. 50.

    A copy of this newspaper article can be found in the Universitätsarchiv Göttingen, UAG.Sek.299.e.

  51. 51.

    Dekanatsakten, “Spaltung der Fakultat,” II Ph/lk, Uuniversitätsarchiv Göttingen.

  52. 52.

    Fakultatsakten IIPh Nr. 4e, Universitätsarchiv Göttingen.

  53. 53.

    Memorandum of 10 Aug. 1918, sent by the historische-philologische Abteilung to the Ministry, Rep. 76 Va Sekt. 6, Tit. IV, 1, Vol. XXV, Bi. 400–402, Geheimes Staatsarchiv Preußischer Kulturbesitz.

  54. 54.

    For Hilbert’s campaign against the appointment of Stark, see the documentation in Rep. 76 Va Sekt. 6, Tit. IV, 1, Vol. XXIV, Bi. 341–376, Geheimes Staatsarchiv Preußischer Kulturbesitz. This contains a letter from Stark, dated 1 Feb. 1915, from which it is clear that he would have accepted the call had he received it.

  55. 55.

    After the war, Hilbert pointedly attacked the conservative Germanist Eduard Schröder for his role in the persecution of pacifists on the faculty during wartime. Hilbert refused to attend meetings of the Göttingen Academy so long as Schröder presided (see Hilbert to Carl Runge, Cod. Ms. D. Hilbert 457: 13).

  56. 56.

    On Neugebauer’s role with both Zentralblatt and Mathematical Reviews, see Siegmund-Schultze’s paper in this volume.

  57. 57.

    This viewpoint was no mere rhetorical stance; in The Exact Sciences in Antiquity (Neugebauer 1957) he illustrated what he meant by discussing the number systems that appear in the famous Book of Hours of the Duc de Berry in order to show that “[f]or the history of mathematics and astronomy the traditional division of political history into Antiquity and Middle Ages is of no significance” (Neugebauer 1957, 3).

  58. 58.

    See (Christianidis 2004) for a recent account of older as well as the newer historiography on Greek mathematics.

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Acknowledgements

This paper was made possible by support from the Johannes Gutenberg University, Mainz, and the Institute for Studies of the Ancient World. My work on the Otto Neugebauer Papers, part of The Shelby White and Leon Levy Archives Center at the Institute for Advanced Study in Princeton, was very ably assisted by the archivists there, Jillian Matos Wolf and Erica Mosner. I also benefitted from input on and criticisms of earlier drafts from Alexander Jones, Norbert Schappacher, Erhard Scholz, Reinhard Siegmund-Schultze, and Noel Swerdlow.

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  1. Johannes Gutenberg Universität, Mainz, Germany

    David E. Rowe

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  1. David E. Rowe
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  1. Inst for Study of the Ancient World, New York University, New York, New York, USA

    Alexander Jones

  2. CNRS & Université Paris Diderot, Laboratoire SPHERE, Paris CX 05, France

    Christine Proust

  3. Brown University, Department of Egyptology and Assyriology, Providence, Rhode Island, USA

    John M. Steele

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Rowe, D.E. (2016). From Graz to Göttingen: Neugebauer’s Early Intellectual Journey. In: Jones, A., Proust, C., Steele, J. (eds) A Mathematician's Journeys. Archimedes, vol 45. Springer, Cham. https://doi.org/10.1007/978-3-319-25865-2_1

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