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Hermann Minkowski’s Cologne Lecture, “Raum und Zeit”

(Mathematical Intelligencer 31(2)(2009): 27–39)

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Abstract

A century ago, David Hilbert stepped to the podium at a special meeting of the Göttingen Academy of Sciences to recall the achievements of his close friend Hermann Minkowski. Just one month earlier, on 12 January 1909, the 43-year-old Minkowski had died unexpectedly after suffering a ruptured appendix, leaving those close to him in a state of shock. None was more deeply affected than Hilbert, whose memorial lecture (Hilbert 1910) reflects the deep sense of personal loss he felt at that time:

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Notes

  1. 1.

    Born recalled attending Minkowski’s lecture in his autobiography (Born 1978, 131); Sommerfeld was listed as one of the discussants after the lecture in Wangerin (1909, 9).

  2. 2.

    Hilbert took charge of publishing Minkowski’s collected works (Minkowski 1911) soon after the latter’s death.

  3. 3.

    Hermann Weyl to Auguste Minkowski, March 1943; transcription courtesy of Gunther Rüdenberg.

  4. 4.

    For a thoughtful assessment of how Hilbert’s views on axiomatics related to Minkowski’s approach to the foundations of physics, see Corry (1997, 2004).

  5. 5.

    Here, the example of Peter Gustav Lejeune-Dirichlet readily comes to mind. As the successor of C. F. Gauss in Göttingen, Dirichlet managed to combine his research interests in number theory with impressive contributions to mathematical physics. Minkowski documented his close affinity with Dirichlet in Minkowski (1905), a glowing tribute delivered before the Göttingen Academy to celebrate the centenary of his birth.

  6. 6.

    Hilbert also noted that Lindemann failed to appear at the Munich meeting, even though it was held in the city where he taught. Hilbert to Hurwitz, 5–12 November 1899, Mathematisches Archiv 76, 975, SUB Göttingen.

  7. 7.

    Scott Walter has pointed out that Minkowski paid very close attention to Poincaré’s publications (Walter 2008, 223).

  8. 8.

    Klein’s notes are in the Mathematisches Archiv, Niedersächsische Staats- und Universitätsbibliothek, Göttingen. In the second volume of his lectures on nineteenth-century mathematics, Klein noted how Schütz had managed to clarify the relationships between the 10 first integrals of classical mechanics (Klein 1927, 58). Klein went further, enlisting the support of Friedrich Engel, who published two papers on applications of Lie’s theory of infinitesimally generated groups to classical mechanics.

  9. 9.

    One could also cite Wolfgang Pauli, who in his report on relativity theory for the German encyclopedia (Pauli 1921) noted that similar consequences can be drawn for Minkowskian electrodynamics. Felix Klein also alluded to this in his commentary on Hilbert’s first note on the foundations of physics. Klein thereby launched the investigations into the status of energy conservation theorems in special and general relativity, the topic that led to Emmy Noether’s fundamental theorems on invariant variational problems (see Rowe 1999).

  10. 10.

    He emphasized this distinction, for example, in his widely read article for the Times (London), Einstein (1919b).

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Acknowledgments

This paper is based on a lecture delivered at the conference “Space and Time 100 Years after Minkowski,” held from 7–12 September 2008 at the Physics Center in Bad Honnef, Germany. My thanks go to the conference organizers, Claus Kiefer and Klaus Volkert, as well as the other participants, especially Engelbert Schücking and Scott Walter, who offered several insightful remarks.

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  1. Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Mainz, Rheinland-Pfalz, Germany

    David E. Rowe

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Rowe, D.E. (2018). Hermann Minkowski’s Cologne Lecture, “Raum und Zeit”. In: A Richer Picture of Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-67819-1_18

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