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Paul Gustav Heinrich Bachmann (June 22, 1837 – March 31, 1920) was a German mathematician.

Bachmann studied mathematics at the University of his native city of Berlin and received his doctorate in 1862 for his thesis on group theory. He then went to Breslau to study for his habilitation, which he received in 1864 for his thesis on Complex Units.

Bachmann was a professor at Breslau and later at Münster.

His major works include

  • Analytische Zahlentheorie, a work on analytic number theory in which Big O notation was first introduced
  • Die Lehre von der Kreistheilung und ihre Beziehungen zur Zahlentheorie, Teubner, Leipzig, 1872
  • Niedere Zahlentheorie, a two-volume work on elementary number theory
  • Das Fermat-Problem in seiner bisherigen Entwicklung, a work about Fermat's Last Theorem

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