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Poincaré in Göttingen

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Book cover Poincaré, Philosopher of Science

Part of the book series: The Western Ontario Series in Philosophy of Science ((WONS,volume 79))

Abstract

In this paper we discuss the relation between Henri Poincaré and the Göttingen mathematician David Hilbert , in particular, in connection with Poincaré’s visit to Göttingen in 1909.

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Notes

  1. 1.

    For a general view on Poincaré , his life and his work see the two recent books Verhulst 2012 and Gray 2013.

  2. 2.

    See the more than 2,000 letters documented and partly digitalized by the Archives Henri Poincaré in Nancy at http://www.univ-nancy2.fr/poincare/chp/hpcoalpha.xml.

  3. 3.

    See Klein ’s exposition in the closing chapter on automorphic functions in Klein 1927, Vol. 1 (English translation in Klein 1979). He opens the report thus: “It is now time for me to tell of the appearance of H. Poincaré and of the personal relations which developed between us and which laid the foundations for the further development of the whole subject” (Klein 1979, 355).

  4. 4.

    By this time, Klein was still in Leipzig; he moved to Göttingen in 1886. Poincaré was already since 1884, i.e., before the arrival of Klein, corresponding member of the (Hanover) Royal Society of Sciences in Göttingen; he became foreign member in 1892.

  5. 5.

    It is a known story that Klein ’s mathematical work stopped after he collapsed during some kind of competition with Poincaré ; here his own words (Klein 1979, 360):

    In fact, I was again able to precede Poincaré by a little, for my offprints were sent off at the end of November 1882; while the first issue of the Acta, which contains Poincaré’s first paper, appeared at the beginning of December 1882 […]

    The price I had to pay for my work was extraordinarily high –my health completely collapsed. In the next years I had to take long leaves and to renounce all productive activity. […] My real productive activity in theoretical mathematics parished in 1882.

    Thus Poincaré had a free field and, until 1884, went on to publish his five great papers on the new functions. […]

  6. 6.

    The visit to Halle is documented in a letter from Cantor to Poincaré from 15.12.1895 (Poincaré 1986; Cantor 1991). See also Décaillot 2011, 30.

  7. 7.

    Undated letters from Poincaré to Klein (Poincaré 1989, XXVII and XXVIII).

  8. 8.

    See the letter of Klein to Poincaré from 14.1.1902 (Poincaré 1989, XXXII) and the one from Karl Schwarzschild to Poincaré from 22.4.1902 (Poincaré 1989, footnote 120, 138; a scan of the letter is available at the webpage mentioned in footnote 2) and the report of the meeting (Kreutz 1902).

  9. 9.

    Cf. http://www.univ-nancy2.fr/poincare/chp/text/hilbert05.xml, Poincaré a Hilbert , Ca. 1899-début 1900:

    Mon cher Collègue,

    Nous serons très heureux d’entendre votre communication. Nous vous accordons volontiers trois quarts d’heure; seulement ne le racontez pas, tout le monde ferait la même demande. Pour ce que vient de vous-plus on aura, plus on sera content.

    Votre bien dévoué,

    Poincaré .

    (Cod. Ms. D. Hilbert 312, Handschriftenabteilung, Niedersächsische Staats- und Universitätsbibliothek. A transcription and commentary appeared in Poincaré 1986, 208).

  10. 10.

    In this context, it is worth mentioning that Poincaré reviewed in 1902 (Poincaré 1902), Hilbert ’s famous book Grundlagen der Geometrie which acquainted Poincaré with Hilbert’s axiomatic method.

  11. 11.

    Poincaré was present in Rome, but due to his poor health during the conference, the talk was, in fact, read by Gaston Darboux , cf. Gray 1991 and Verhulst 2012, 50.

  12. 12.

    More information about the Bolyai prize ––which vanished with World War I, and which was revived only in 2000–– one may find at the site of the Hungarian Academy of Science, http://www.mathe.bme.hu/akademia/jbimp.html. It contains a link to an interesting historical note (cf. Szénássy) where one reads: “I also mention that Poincaré and Hilbert did not receive the award in Budapest: instead, it was delivered to them by official channels. As far as I know, Hilbert had never been to Budapest; […]”.

  13. 13.

    It was awarded, in 1997 just 10 years before a 100 year limit expired, to Andrew Wiles. The amount was no longer comparable with the original value but still around 75,000 DM (German Marks). For more about the history of Paul Wolfskehl and the Wolfskehl Prize, see Barner 1997. In addition to the story that the money of the Wolfskehl donation melted during the German hyperinflation and two monetary reforms, we learned once (without being able to recall the source) that the Wolfskehl commission was forced to invest their money in German war bonds, which, of course, were completely worthless after the war. However, infracting the order some money was kept aside.

  14. 14.

    About the following years we know from Reid (1970, 1351), that in 1910 H. A. Lorentz was invited; in 1911 no lecturer was invited but Zermelo received a prize of 5,000 Marks; in 1912 Sommerfeld was invited; and in 1913 a conference on the Kinetic Theory of Matter was organized; finally, in 1914 Haar and Debye were invited as guest professors. Hilbert also planned to invite Bertrand Russell , whose visit due to World War I never materialized (Sieg 1999, Appendix B).

  15. 15.

    We thank the Archives Henri Poincaré , UMR 7117 CNRS – Nancy-Université, Université Nancy 2, France (Prof. Gerhard Heinzmann) for the permission of the reprint.

  16. 16.

    A scanned version of the chapters of the book is available under http://projecteuclid.org/euclid.chmm/1263313049, a text version under http://www.univ-nancy2.fr/poincare/bhp/hp1910sv.xml.

  17. 17.

    For more information about all talks, see Gray 2013, 416 ff.

  18. 18.

    Here, and at many other places, one may ask how good Hilbert was in mentioning work of others. In his lecture notes he was usually sparingly in the bibliography and one gets the impression that he was not too much concerned with references.

  19. 19.

    These papers are reprinted in English translations, together with indications of the changes made in the book edition in Ewald 1996, 22.D-F.

  20. 20.

    We are indebted to William B. Ewald for the permission to reprint his translation. The paragraph numbers are additions of the translation.

  21. 21.

    See Sieg 1999, 7.

  22. 22.

    The original German reads: “Ein actual Unendliches gibt es jedenfalls nicht”.

  23. 23.

    Also Barrow-Green 2011, 41f refers to this quotation, but remarks “Courant ’s memory –he was recalling events that had taken more than fifty years earlier– might not have been entirely reliable”.

  24. 24.

    For a detailed discussion of his work in relation to the Principia see Linsky 2011.

  25. 25.

    This aspect was, with more emphasize on the paradoxes, already highlighted in Kahle 2011; the current section reuses, in particular, the marginals of Hilbert in his lecture notes from 1905.

  26. 26.

    Addressing Howard Stein, Sieg sees one of the reasons for the postponement of Hilbert ’s work in Proof Theory in Poincaré ’s criticism of the potential vicious circle in the approach concerning induction (Sieg 1999, footnote 15, p. 7). This, however, should not be extended to foundational work in general.

  27. 27.

    For instance, the draft notes for a lecture in 1914/15 contain an explicit reference for them.

  28. 28.

    We are indebted to the Mathematical Institute of the University of Göttingen (Prof. Jörg Brüdern) for the permission to use here copies of the original lecture notes kept in the library of the Mathematical Institute.

  29. 29.

    We follow Ewald in translating “Tafel” by “table” although “blackboard” would be a more literally translation.

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Acknowledgments

I would like to thank again the Archives Henri Poincaré , the Mathematical Institute of the University of Göttingen, and William B. Ewald for the permission to reprint material of which they hold the copyright. I also thank Hassan Tahiri, the editor of Kahle 2011, for the suggestion to include here the scans of Hilbert ’s original texts. Finally, I’m indebted to Jesse Alama, Gerhard Heinzmann, Ferdinand Verhulst, and Wilfried Sieg for comments on earlier versions of this paper.

The author was partially supported by the ESF research project Dialogical Foundations of Semantics within the ESF Eurocores program LogICCC (funded by the Portuguese Science Foundation, FCT LogICCC/0001/2007) and the FCT-projects Hilbert ’s Legacy in the Philosophy of Mathematics, PTDC/FIL-FCI/109991/2009 and The Notion of Mathematical Proof , PTDC/MHC-FIL/5363/2012.

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  1. CENTRIA and DM, FCT, Department of Mathematics, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    Reinhard Kahle

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Correspondence to Reinhard Kahle .

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  1. Centre for Philosophy of Science at the University of Lisbon (CFCUL), University of Lisbon, Lisbon, Portugal

    María de Paz

  2. Department of Philosophy, University of Western Ontario, London, Ontario, Canada

    Robert DiSalle

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Kahle, R. (2014). Poincaré in Göttingen. In: de Paz, M., DiSalle, R. (eds) Poincaré, Philosopher of Science. The Western Ontario Series in Philosophy of Science, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8780-2_5

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