Skip to main content

Kummer and Kronecker

  • Chapter

Abstract

Ernst Eduard Kummer was the senior member of the triumvirate — Kummer, Weierstrass, Kronecker — that dominated mathematics in Berlin, and in Germany, during much of the second half of the 19th Century. He probably is best known today for an incident that never happened.

Keywords

  • Private Tutor
  • Bernoulli Number
  • Abelian Extension
  • Algebraic Number Theory
  • Kummer Surface

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-0348-8787-8_8
  • Chapter length: 9 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   44.99
Price excludes VAT (USA)
  • ISBN: 978-3-0348-8787-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   59.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Biermann, K.-R., Die Mathematik und ihre Dozenten an der Berliner Universität 1810-1933, Akademie Verlag, Berlin, 1988.

    MATH  Google Scholar 

  2. Biermann, K.-R., E.E. Kummer, in Dictionary of Scientific Biography.

    Google Scholar 

  3. Biermann, K.-R., Leopold Kronecker, in Dictionary of Scientific Biography.

    Google Scholar 

  4. Edwards, H. M., The background of Rummer’s proof of Fermat’s Last Theorem for regular primes, Arch. Hist. Exact Sci. 14 (1975), 219–236.

    MATH  CrossRef  Google Scholar 

  5. Edwards, H.M., Postscript to “The background of Rummer’s proof of Fermat’s Last Theorem for regular primes”, Arch. Hist. Exact Sci. 17 (1977), 381–394.

    CrossRef  Google Scholar 

  6. Edwards, H.M., Fermat’s Last Theorem, A genetic introduction to algebraic number theory, Graduate Texts in Math. 50, Springer-Verlag, Berlin, 1977.

    Google Scholar 

  7. Edwards, H.M., Kronecker on the Foundations of Mathematics, in: Jaakko Hintikka (ed.), From Dedekind to Goedel, Kluwer, Dordrecht, 1995, 45–52.

    Google Scholar 

  8. Edwards, H. M., On the Kronecker Nachlass, Hist. Math. 5 (1978), 419–429.

    CrossRef  Google Scholar 

  9. Frobenius, G. F., Gedächtnisrede auf Leopold Kronecker, Abhandlungen der Königlich Preussischen Akademie der Wissenschaften zu Berlin, 1893, also in: Collected works, vol. 3, 705–724.

    Google Scholar 

  10. Hensel, K., Gedächtnisrede auf Ernst Eduard Kummer, in: Festschrift zur Feier des 100. Geburtstages Eduard Kummers, Teubner, Leipzig und Berlin, 1910, also in: Weil, A. (ed.), E.E. Kummer, Collected Papers, vol. I, Springer-Verlag, Berlin, 1975, 33–69.

    Google Scholar 

  11. Hilbert, D., Neubegründung der Mathematik, Erste Mitteilung, Abh. Math. Sem. Hamburg 1 (1922), 157–177, also in: Gesammelte Abhandlungen, vol. III, Springer-Verlag, Berlin, 1935, 157-177.

    MATH  CrossRef  Google Scholar 

  12. Kneser, A., Leopold Kronecker, Rede, gehalten bei der Hundertjahrfeier seines Geburtstages in der Berliner Mathematischen Gesellschaft am 19. Dezember 1923, Jber. dt. Math.-Verein. 33 (1925), 210–228.

    MATH  Google Scholar 

  13. Kronecker, L., Auszug aus einem Briefe von L. Kronecker an G. Cantor, in: Hensel, K. (ed.), Leopold Kroneckers Werke, vol. V, Leipzig, 1930.

    Google Scholar 

  14. Lampe, E., Nachruf für Ernst Eduard Kummer, Jber. dt. Math.-Verein. 3 (1893), 13–28, also in: Weil, A. (ed.), E.E. Kummer, Collected Papers, vol. I, Springer-Verlag, Berlin, 1975, 15-30.

    Google Scholar 

  15. Lifschitz, R., Briefwechsel mit Cantor, Dedekind, Helmholtz, Kronecker, Weierstrass und anderen, bearbeitet von W. Scharlau, Dokumente zur Geschichte der Mathematik, Band 2, DMV, Vieweg Verlag, 1986.

    Google Scholar 

  16. Meth, B., Ernst Eduard Kummer als Lehrer, Mathematischer Verein Berlin, 1910, unpublished.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1998 Springer Basel AG

About this chapter

Cite this chapter

Edwards, H.M. (1998). Kummer and Kronecker. In: Begehr, H., Koch, H., Kramer, J., Schappacher, N., Thiele, EJ. (eds) Mathematics in Berlin. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8787-8_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8787-8_8

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-5943-0

  • Online ISBN: 978-3-0348-8787-8

  • eBook Packages: Springer Book Archive