Paul Gustav Heinrich Bachmann

Paul Gustav Heinrich Bachmann ( born June 22, 1837 in Berlin, † March 31, 1920 in Weimar ) was a German mathematician who is best known for his textbooks on number theory.


Bachmann was the son of a Protestant pastor, and showed in his youth musical inclinations. He studied mathematics at the University of Berlin where he received his doctorate in 1862 with a dissertation in the field of group theory at Ernst Eduard Kummer. In between, he had studied from 1856 in Göttingen in the exchanged recently there from Berlin Peter Gustav Lejeune Dirichlet, and there became a friend of Richard Dedekind. After his dissertation, he went to the University of Breslau, where in 1864 he studied with a number-theoretic work habilitated to complex units and 1867 was an associate professor. In 1875, he accepted a professorship at the Royal Academy of Philosophy and Theology in Münster. In 1890 he gave up his chair after his divorce from his wife and moved with his second wife to Weimar, to devote himself entirely to music ( as a pianist and critic) and the writing of his famous books on number theory, in five volumes from 1892 to 1923 ( 1872 ) published. Bachmann also wrote the biographical section about Carl Friedrich Gauss as a number theorist in his collected works.

A grandson Paul Bachmann, Friedrich Bachmann, worked from 1949 as a professor of mathematics at the Christian- Albrechts- University of Kiel.


  • Elements of Number Theory 1892
  • Arithmetic of quadratic forms, 1898
  • The doctrine of the circular scale and its relationship to number theory in 1872
  • General arithmetic of number fields, 1923
  • Analytic Number Theory, 1894, (later called Landau notation symbols were first used in this work ).
  • Low Number Theory, 2 vols 1902, 1910
  • The Fermat problem in his development, 1919

A complete list of publications includes the Bachmann's written by Kurt Hensel Obituary ( DMV Annual Report 36 (1927 ) ).