Ernst Schröder (mathematician)

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Ernst Schröder

Ernst Schröder (born November 25, 1841 in Mannheim , † June 16, 1902 in Karlsruhe ; full name Ernst Friedrich Wilhelm Karl Schröder ) was a German mathematician and logician .

life and work

After studying mathematics and physics at the Ruprecht-Karls-Universität Heidelberg and Albertus-Universität Königsberg , Schröder completed his habilitation at the University of Zurich in 1865. After completing school service, he became professor of mathematics in 1874 at the TH Darmstadt , then in 1876 at the TH Karlsruhe , where he also acted as director in 1890/91.

Title page of the first edition of On the Formal Elements of Absolute Algebra

His main areas of work were the basics of mathematics, function theory and combinatorial analysis. In his work on iterated functions from 1871 he examined Schröder's functional equation , which is named after him today and which plays an important role in complex dynamics. The fact that logic became an independent discipline is thanks to his work on theoretical algebra and symbolic logic. With his work on the algebra of logic he achieved international recognition. He optimized the logic of George Boole and in 1877 developed the first complete system of axioms in Boolean algebra . In his three-volume Algebra der Logic from 1890–1895, in contrast to Boole, who based his calculation on the identity of classes, he assumed the inclusion of classes. Schröder also developed relational algebra (see relational theory ), introduced the term normal form and discovered the principle of duality in class logic (see Boolean algebra ). Furthermore, he solved special cases of the decision problem by eliminating the quantifiers .

Giuseppe Peano built on Schröder's logic; also tied Norbert Wiener in his dissertation A comparison between the treatment of the algebra of relatives by Schröder and did by Whitehead and Russell to work on Schroeder. For Alfred Tarski , his work was the basis for a modern theory of algebra and the history of logic.

He is one of the namesake for the Cantor-Bernstein-Schröder theorem . The Schröder numbers are also named after him. With his three-volume main work on the algebra of logic, Ernst Schröder created one of the foundations for conceptual knowledge processing. This is why the Ernst Schröder Center for Conceptual Knowledge Processing also bears his name. It promotes training, research and development in the field of conceptual knowledge processing and its application.


  • Text-book of arithmetic and algebra , 1873
  • On the formal elements of absolute algebra , 31 p., Stuttgart, 1874
  • The logic calculus operating circle , 1877
  • Lectures on the algebra of logic (exact logic) , 3 volumes, Leipzig 1890–1905
Volume 1. Teubner, Leipzig 1890. ( digitized , digitized and full text in the German text archive )
Volume 2, Dept. 1. Teubner, Leipzig 1891 ( digitized , digitized and full text in the German text archive )
Volume 2, Dept. 2. Teubner, Leipzig 1905. ( digitized , digitized and full text in the German text archive )
Volume 3. Teubner, Leipzig 1895 ( digitized and full text in the German text archive )
  • Algebra and Logic of Relatives, Lectures on Algebra of Logic 3  : Volume 3, Dept. 1 , Leipzig, BG Teubner, 1890–1905
  • About the sign , Karlsruhe, 1890
  • About two definitions of finiteness and G. Cantor's sentences - treatise in the series Imperial Leopoldino-Carolinische Deutsche Akademie der Naturforscher Vol. 71, pp. 301–362, Halle, 1898
  • Outline of the Algebra of Logic , 2 parts, Leipzig, 1909/1910


  • I. Grattan-Guinness: Wiener on the logics of Russell and Schröder. An account of his doctoral thesis, and of his discussion of it with Russell , in: Annals of Science, Vol 32, 1975, No. 2, pp. 102-132
  • Daniel S. Alexander: A history of complex dynamics: from Schröder to Fatou and Julia. (Aspects of Mathematics), Vieweg, Braunschweig 1994, ISBN 3-528-06520-6 . Sections 1.1–1.7 give a detailed account of Schröder’s contributions to iteration theory.
  • Davide Bondoni: La teoria delle relazioni nell'algebra della logica schroederiana, Led Edizioni, Milan, 2007, ISBN 978-88-7916-349-1 .
  • D. Bondoni: Parafrasi schröderiane, ovvero, Ernst Schröder: Le operazioni del calcolo logico (Original: Operationskreis des Logic Calculus (1877) with parallel Italian translation; in appendix, extracts from works by Boole, Frege and Peirce), Led Edizioni, Milan, 2010, ISBN 978-88-7916-474-0 .
  • Ernst Schröder: On the Formal Elements of the Absolute Algebra (Original: Ueber the formal elements of absolute Algebra (1874) by Davide Bondoni with an introductory essay), Led Edizioni, Milan, 2012, ISBN 978-88-7916-516-7 .
  • D. Bondoni: Structural Features in Ernst Schröder's Work, Part I , in: Logic and Logical Philosophy, Vol 20, 2011, No. 4, pp. 327-359
  • D. Bondoni: Structural Features in Ernst Schröder's Work, Part II , in: Logic and Logical Philosophy, Vol 21, 2012, No. 3, pp. 271-315

Web links

Wikisource: Ernst Schröder  - Sources and full texts