Heinrich Martin Weber

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Heinrich Martin Weber
Born(1842-03-05)5 March 1842
Died17 May 1913(1913-05-17) (aged 71)
Alma materUniversity of Erlangen
University of Heidelberg
Known forAbstract algebra
Class field theory
Group theory
Number theory
Weber functions
Weber vector
Weber modular function
Weber's theorem
Kronecker–Weber theorem
AwardsICM Speaker (1897)
Scientific career
Doctoral advisorOtto Hesse
Doctoral studentsHeinrich Brandt
E. V. Huntington
Louis Karpinski
Friedrich Levi

Heinrich Martin Weber (5 March 1842, Heidelberg, Germany – 17 May 1913, Straßburg, Alsace-Lorraine, German Empire, now Strasbourg, France) was a German mathematician.[1] Weber's main work was in algebra, number theory, and analysis. He is best known for his text Lehrbuch der Algebra published in 1895 and much of it is his original research in algebra and number theory. His work Theorie der algebraischen Functionen einer Veränderlichen (with Dedekind) established an algebraic foundation for Riemann surfaces, allowing a purely algebraic formulation of the Riemann–Roch theorem. Weber's research papers were numerous, most of them appearing in Crelle's Journal or Mathematische Annalen. He was the editor of Riemann's collected works.

Weber was born in Heidelberg, Baden, and entered the University of Heidelberg in 1860. In 1866 he became a privatdozent, and in 1869 he was appointed as extraordinary professor at that school. Weber also taught in Zurich at the Federal Polytechnic Institute (today the ETH Zurich), at the University of Königsberg, and at the Technische Hochschule in Charlottenburg. His final post was at the Kaiser-Wilhelm-Universität Straßburg, Alsace-Lorraine, where he died.

In 1893 in Chicago, his paper Zur Theorie der ganzzahligen algebraischen Gleichungen was read (but not by him) at the International Mathematical Congress held in connection with the World's Columbian Exposition.[2] In 1895 and in 1904 he was president of the Deutsche Mathematiker-Vereinigung. His doctoral students include Heinrich Brandt, E. V. Huntington, Louis Karpinski, and Friedrich Levi.


  • with Richard Dedekind: Theorie der algebraischen Functionen einer Veränderlichen. J. Reine Angew. Math. 92 (1882) 181–290
  • Elliptische Functionen und algebraische Zahlen. Braunschweig 1891
  • Encyklopädie der Elementar-Mathematik. Ein Handbuch für Lehrer und Studierende. Leipzig 1903/07, (Vol. 1, Vol. 2, Vol. 3) (in German)
  • with Bernhard Riemann (i.e. partly based on Riemann's lectures): Die partiellen Differential-Gleichungen der mathematischen Physik. Braunschweig 1900-01[3]
  • Lehrbuch der Algebra. Braunschweig 1924, ed. Robert Fricke
  • Weber, Heinrich Martin (1981) [1895], Lehrbuch der Algebra (in German), vol. 1 (3rd ed.), New York: AMS Chelsea Publishing, ISBN 978-0-8218-3258-5
  • Weber, Heinrich Martin (1981) [1895], Lehrbuch der Algebra (in German), vol. 2 (3rd ed.), New York: AMS Chelsea Publishing, ISBN 978-0-8218-2647-8
  • Weber, Heinrich Martin (1981) [1898], Lehrbuch der Algebra (in German), vol. 3 (3rd ed.), New York: AMS Chelsea Publishing, ISBN 978-0-8218-2971-4 The third volume is an expanded version of his earlier book "Elliptische Functionen und algebraische Zahlen".


  1. ^ Archibald, R. C. (1913). "Review: Festschrift Heinrich Weber zu seinem siebzigsten Geburtstag am 5 März 1912". Bull. Amer. Math. Soc. 20 (3): 152–155. doi:10.1090/s0002-9904-1913-02453-4.
  2. ^ "Zur Theorie der ganzzahlingen algebraischen Gleichungen by Heinrich Martin Weber". Mathematical papers read at the International Mathematical Congress held in connection with the World's Columbian Exposition. Papers published by the American Mathematical Society, v. I. NY: Macmillan as publisher for the AMS. 1896. pp. 401–407.
  3. ^ Ames, J. S. (1901). "Riemann–Weber: Partial Differential Equations of Mathematical Physics". Bull. Amer. Math. Soc. 8 (2): 81–85. doi:10.1090/S0002-9904-1901-00858-0.