Sophus Lie

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Sophus Lie (1842-1899)

Marius Sophus Lie [ liː ] (born December 17, 1842 in Nordfjordeid , † February 18, 1899 in Kristiania, now Oslo ) was a Norwegian mathematician .


Lie studied from 1859 to 1865 in Christiania (later Kristiania, now Oslo) natural sciences and in 1862 heard lectures on group theory from Peter Ludwig Mejdell Sylow . In 1865 he passed the real teacher examination and was initially undecided about his further career. It was not until 1868 that he turned to mathematics . His first mathematical publication, which appeared in 1869, earned him a travel grant . He used this for stays a. a. in Berlin , Göttingen and Paris . The acquaintance and friendship with Felix Klein , with whom he traveled to Paris in 1870 and wrote joint works on transformation groups, was decisive for Lie's further career . In 1872 Lie became a professor in Christiania, and in 1886 he was appointed to Leipzig as Klein's successor (who moved to Göttingen) . Lie suffered - as was later diagnosed - from pernicious anemia , which together with difficulties in the scientific environment led to a nervous breakdown in 1889 . In addition, Lie fell out with his colleagues Friedrich Engel and Klein over priority issues. From 1892 Norwegian personalities, above all Nansen , Björnson and Elling Holst, tried to get Lie back, on the one hand out of concern for him, on the other hand for reasons of national patriotism. In 1894 the Norwegian parliament gave him a personal professorship with a corresponding increase in salary in Christiania. However, Lie did not return to Norway until 1898, seriously ill , and privately taught a few of his mostly succeeded students. He died in February 1899 of pernicious anemia, which was incurable at the time .

Lie was made a Knight of the Order of Saint Olav in 1886 . In 1895 he was elected to the National Academy of Sciences and as a foreign member of the Royal Society . In 1892 he became a corresponding member of the Académie des Sciences in Paris and in 1896 of the Russian Academy of Sciences in St. Petersburg .


His parents were Johann Lie , from 1851 pastor in Moss on the Kristianiafjord, and his wife Mette Stabell . Sophus Lie married Anna Birk (1854–1920) in 1874 ; she was the daughter of the chief customs officer Gottfried Jörgen Stenersen Birk and his wife Marie Elisabeth Simonsen . The couple had a son Herman (1884–1960) and two daughters. Marie (* May 21, 1877) married the later ophthalmologist Friedrich Leskien, son of August Leskien in 1905 ; together with her husband she translated works by Alexander Lange Kielland into German. Dagny Lie (born July 5, 1880, † December 28, 1945) was married to the pharmacologist Walther Straub (1874–1944).


Lie established the theory of continuous symmetry and used it to study differential equations and geometric structures. Continuous or constant symmetry operations are, for example, displacements and rotations by any amount, including infinitesimal, in contrast to discrete symmetry operations such as mirroring. On the basis of his work, u. a. developed an algorithm for the numerical integration of differential equations ( Lie integration ) or the method of base point transformation .

In order to investigate and apply continuous transformation groups (today called Lie groups ), he linearized the transformations and examined the infinitesimal generators. The connection properties of the Lie group can be expressed by commutators of the generators; the commutator algebra of generators is now called Lie algebra .

Many other terms and phrases are associated with Lie's name, including a. Lie bracket , Lie's sentences , Lie theorem , Lie product formula .


Monument in Nordfjordeid, 2019

His place of birth, Nordfjordeid, erected a memorial for him and named a street after him.


  • Moritz CantorLie, Sophus . In: Allgemeine Deutsche Biographie (ADB). Volume 51, Duncker & Humblot, Leipzig 1906, pp. 695-698.
  • Nils A. Baas: Sophus Lie. In: Det Kongelige Norske Videnskabers Selskabs Forhandlinger. 1992, pp. 43–48 ( PDF file )
  • Karl StrubeckerLie, Sophus. In: New German Biography (NDB). Volume 14, Duncker & Humblot, Berlin 1985, ISBN 3-428-00195-8 , pp. 470-472 ( digitized version ).
  • Arild Stubhaug : It was the boldness of my thoughts. The mathematician Sophus Lie. Springer, Berlin a. a. 2003, ISBN 3-540-43657-X .
  • Gösta Mittag-Leffler : Obituary. In Acta Mathematica. 1899.
  • Max Noether : Obituary. In mathematical annals. Volume 53, 1901, pp. 1-41 ( online ).
  • Friedrich Engel : Obituary. In the DMV annual report. Volume 8, 1900 ( online ).
  • Hans Freudenthal : Lie, Marius Sophus . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography . tape 8 : Jonathan Homer Lane - Pierre Joseph Macquer . Charles Scribner's Sons, New York 1973, p. 323-327 .
  • Bernd Fritzsche: Life and Work of Sophus Lies. A sketch. In: Seminar Sophus Lie. 2, 1992, pp. 235-261.
  • Bernd Fritzsche: Sophus Lie. A sketch of his life and work. In: Journal of Lie theory. Volume 9, 1999, pp. 1-38.
  • Poul Heegaard in Norsk Biografisk Leksikon. Oslo 1938.
  • Sigurdur Helgason : Sophus Lie, the Mathematician. In: O. Laudal, B. Years: Proc. Sophus Lie Memorial Conference (Oslo 1992). Oslo 1994.
  • Felix Klein : Sophus Lie. Evanston Colloquium 1893, Macmillan 1894, pp. 9–24 ( French translation in Nouvelle Annales de Mathematique. )
  • Sophus Lie: Kjaere Ernst. 60 letters from Sophus Lie to Ernst Motzfeld. Edited by Marianne Kern and Elin Ström. Vitenskapshistorisk Skriftreihe, Nr. 4, Mathematisches Institut Oslo 1997.
  • Thomas W. Hawkins : The birth of Lie's theory of groups. In: Mathematical Intelligencer. 16, 1994, No. 2, pp. 6-17.
  • Thomas Hawkins: The emergence of the theory of Lie groups. Springer 2000.
  • David E. Rowe : The correspondence between Sophus Lie and Felix Klein. An insight into their personal and scientific relationships, In: NTM Series History of Natural Sciences. 1988, pp. 37-47.
  • Eldar Straume: Sophus Lie. In: Newsletter European Mathematical Society. No. 3, 1992.
  • Isaak Moissejewitsch Jaglom : Felix Klein and Sophus Lie. Evolution of the idea of ​​symmetry in the 19th century. Birkhäuser, 1988.
  • Paul Günther : Sophus Lie. In: Herbert Beckert , Horst Schumann (Hrsg.): 100 Years of Mathematical Seminar at the Karl Marx University of Leipzig. German Science Publishers, Berlin 1981.


  • Collected papers, Leipzig (Teubner), Oslo, 7 volumes, 1922 to 1960 (editors Friedrich Engel and Poul Heegaard )
  • Theory of Transformation Groups, 3 volumes, Leipzig: Teubner 1888 to 1893, online
  • Sophus Lie: About the influence of geometry on the development of mathematics (Leipzig inaugural lecture 1886) in: Herbert Beckert, Walter Purkert Leipzig mathematical inaugural lectures. Selection from the years 1869-1922 , BG Teubner, Leipzig 1987 (with biography)
  • G. Czichowski, Bernd Fritzsche (editor): Contributions to the theory of differential invariants (Sophus Lie, Friedrich Engel, Eduard Study ), Teubner Archive for Mathematics, Volume 17, 1993 (therein by Fritzsche: Biographical Notes on the Relationships between Sophus Lie, Friedrich Engel and Eduard Study)
  • Geometry of contact transformations, Leipzig: Teubner 1896 (editor Georg Scheffers )
  • Lectures on differential equations with known infinitesimal transformations, Teubner 1912 (editor Scheffers), online
  • About the basics of geometry, Wissenschaftliche Buchgesellschaft Darmstadt 1967 (originally reports Abh. Kgl. Sächs. Ges. Wiss. Leipzig, Math.-Naturwiss. Klasse, Volume 42, 1890)
  • About integral variants and differential equations, Vid. Selskab, Mat.-Naturv. Skrifter 1, Oslo 1902, Gutenberg project

Web links

Wikisource: Sophus Lie  - Sources and full texts

Individual evidence

  1. ^ Entry on Lie, Marius Sophus (1842 - 1899) in the archives of the Royal Society , London
  2. ^ List of members since 1666: Letter L. Académie des sciences, accessed on January 13, 2020 (French).
  3. ^ Foreign members of the Russian Academy of Sciences since 1724: Lie, Marius Sophus. Russian Academy of Sciences, accessed January 13, 2020 (Russian).