Gerhard Hessenberg

Gerhard Hessenberg (German: [ˈgɛʁ.hart ˈhɛsənˌbɛrk]; 16 August 1874 – 16 November 1925) was a German mathematician who worked in projective geometry, differential geometry, and set theory.

Gerhard Hessenberg
Hessenberg in May 1921
Born(1874-08-16)16 August 1874
Frankfurt
Died16 November 1925(1925-11-16) (aged 51)
Berlin
NationalityGerman
Alma materUniversity of Berlin
Known forHessenberg sum and product
Scientific career
FieldsMathematics
InstitutionsUniversity of Breslau
ThesisÜber die Invarianten linearer und quadratischer binärer Differentialformen und ihre Anwendung auf die Deformation der Flächen (1899)
Doctoral advisorHermann Schwarz
Lazarus Fuchs

Career

Hessenberg received his Ph.D. from the University of Berlin in 1899 under the guidance of Hermann Schwarz and Lazarus Fuchs.

His name is usually associated with projective geometry, where he is known for proving that Desargues' theorem is a consequence of Pappus's hexagon theorem,[1] and differential geometry where he is known for introducing the concept of a connection.[2][3] He was also a set theorist: the Hessenberg sum and product of ordinals are named after him. However, Hessenberg matrices are named for Karl Hessenberg, a near relative.

In 1908 Gerhard Hessenberg was an Invited Speaker of the International Congress of Mathematicians in Rome.[4]

Publications
  • Ebene und sphärische Trigonometrie ((several editions) ed.). Berlin: de Gruyter.
  • "Grundbegriffe der Mengenlehre". Abhandlungen der Friesschen Schule. Neue Folge. 1: 478–706. (also in book form as a separate publication from Verlag Vandenhoeck und Ruprecht, Göttingen 1906).
  • Grundlagen der Geometrie (2nd ed.). Berlin: de Gruyter. 1967.1st ed. Leipzig: B. G. Teubner. 1930.[5]
  • Transzendenz von e und π. Ein Beitrag zur höheren Mathematik vom elementaren Standpunkte aus. New York. 1965.{{cite book}}: CS1 maint: location missing publisher (link) (unaltered reprint of the Teubner edition of 1912).[6]
  • Vom Sinn der Zahlen. Tübingen/ Leipzig. 1922.{{cite book}}: CS1 maint: location missing publisher (link)

Notes
  1. Hessenberg, Gerhard (1905), "Beweis des Desarguesschen Satzes aus dem Pascalschen", Mathematische Annalen (in German), 61 (2): 161–172, doi:10.1007/BF01457558, S2CID 120456855.
  2. Hessenberg, Gerhard (1917), "Vektorielle Begründung der Differentialgeometrie", Mathematische Annalen (in German), 78 (1): 187–217, doi:10.1007/bf01457097, S2CID 123915533.
  3. Hessenberg, Gerhard (1874-1925) from Eric Weisstein's World of Scientific Biography
  4. Hessenberg, G. "Zaehlen und Anschauung". Atti del IV Congresso internazionale dei matematici (Roma, 6–11 Aprile 1908). Vol. 3. pp. 377–379.
  5. Allen, Edward Switzer (1931). "Review: Grundlagen der Geometrie, by Gerhard Hessenberg, ed. by W. Schwan; Vorlesungen über Grundlagen der Geometrie, by Kurt Reidemeister". Bull. Amer. Math. Soc. 37 (11): 798–802. doi:10.1090/S0002-9904-1931-05254-X.
  6. Gronwall, T. H. (1914). "Review: Transzendenz von e und π. Ein Beitrag zur höheren Mathematik vom elementaren Standpunkte aus, by Gerhard Hessenberg". Bull. Amer. Math. Soc. 20 (8): 421–422. doi:10.1090/s0002-9904-1914-02517-0.


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