Gerhard Hessenberg

Gerhard Hessenberg (born August 16, 1874 in Frankfurt am Main , † November 16, 1925 in Berlin ) was a German mathematician .

Live and act

Gerhard Hessenberg studied in Strasbourg and Berlin. Doctorate in 1899. Habilitation in 1901 at the Technical University of Berlin . In 1907 he became a professor at the Agricultural Academy in Bonn, and in 1910 at the Technical University in Breslau . In 1919 he was appointed to the University of Tübingen .

Hessenberg occupied himself in his work a. a. with differential geometry ( geodetic lines ) and basic questions of geometry . He developed u. a. a system of axioms of elliptical geometry . For the synthetic investigation of projective planes and spaces , the theorem, which he proved in 1905, is important that in every plane in which the projective incidence axioms and the Pappos theorem apply, the Desargues theorem also applies. He is named Satz von Hessenberg in his honor .

He was also known for his 1906 published treatise on set theory , in which he completely that - also as a set of Hessenberg proved statement that for all infinite cardinal numbers - known applies: . Even if, from a mathematical point of view, this paper has to be seen as outdated to a large extent, according to Oliver Deiser it deserves the predicate "historically particularly valuable". Furthermore, Hessenberg's natural operations are named after Hessenberg in set theory . ${\displaystyle \,{\mathfrak {a}}}$ ${\displaystyle \,{\mathfrak {a}}^{n}={\mathfrak {a}}}$

In 1916 Hessenberg was elected a member of the Leopoldina .

Works (selection)

• Plane and spherical trigonometry . de Gruyter, Berlin (various editions).
• Basic concepts of set theory . Treatises of the Friesschen Schule, New Series, Volume 1, pp. 478–706 (also in book form as a special edition published by Verlag Vandenhoeck and Ruprecht, Göttingen 1906).
• Basics of geometry . 2nd Edition. de Gruyter, Berlin 1967. (EA 1930)
• Transcendence of e and π. A contribution to higher mathematics from an elementary point of view . New York 1965, unmodified reprint of 1912 EA.
• The meaning of numbers . Tübingen / Leipzig 1922.

literature

• Rudolf Rothe : Gerhard Hessenberg , DMV annual report, 1912, uni-goettingen.de
• Walter Benz :  Hessenberg, Gerhard. In: New German Biography (NDB). Volume 9, Duncker & Humblot, Berlin 1972, ISBN 3-428-00190-7 , p. 24 ( digitized version ).
• Oliver Deiser : Introduction to set theory . 2nd Edition. Springer, Berlin 2004, ISBN 978-3-540-20401-5 .
• Karin Reich : The Desarguessche and the Pascalsche theorem: Hessenberg's contribution to Hilbert's foundations of geometry . In: Hartmut Hecht (ed.): Cosmos and number. Contributions to the history of mathematics and astronomy, to Alexander von Humboldt and Leibniz . Boethius (58), Stuttgart 2008, pp. 377-393

Web links

• Literature by and about Gerhard Hessenberg in the catalog of the German National Library

Individual evidence

1. ^ H. Meschkowski: Mathematicians Lexicon . BI, Mannheim 1964, p. 119.
2. ↑ O. Deiser: Introduction to set theory . 2nd Edition. Springer, Berlin 2004, p. 502.
3. ↑ O. Deiser: Introduction to set theory . 2nd Edition. Springer, Berlin 2004, p. 510.