Bachmann, Paul Gustav Heinrich
Bachmann, Paul Gustav Heinrich
(b. Berlin, Germany, 22 June 1837; d. Weimar, Germany, 31 March 1920)
Bachmann’s father was pastor at the Jacobi Kirche, and from his home the young Paul inherited a pious Lutheran view of life, coupled with modesty and a great interest in music. During his early years in the Gymnasium he had some trouble with his mathematical studies, but his talent was discovered by the excellent teacher Karl Schellbach. After a stay in Switzerland for his health, presumably to recover from tuberculosis, Bachmann studied mathematics at the University of Berlin until he transferred to Göttingen in 1856 to attend Dirichlet’s lectures. Here he became a close friend of Dedekind, who was a fellow student.
From 1856 on, Bachmann’s interests were centered almost exclusively upon number theory. He completed his studies in Berlin, where in 1862 he received his doctorate under the guidance of Ernst Kummer for a thesis on group theory. Two years later he completed his habilitation in Breslau with a paper on complex units, a subject inspired by Dirichlet. After some years as extraordinary professor in Breslau, Bachmann was appointed to a professorship in Münster.
Around 1890 Bachmann divorced his wife and resigned his professorship. With his second wife he settled in Weimar, where he combined his mathematical writing with composing, playing the piano, and serving as music critic for various newspapers. His main project, however, was a complete survey of the state of number theory, Zahlentheorie. Versuch einer Gesamtdarstellung dieser Wissenschaft in ihren Hauptteilen (1892–1923). It includes not only a review of known results but also an evaluation of the various methods of proof and approach, labors for which his close association with Dirichlet, Kummer, Dedekind, and Hensel made him ideally suited.
Bachmann’s writings are Vorlesungen über die Natur der Irrationalzahlen (Leipzig, 1892); Zahlentheorie. Versuch einer Gesamtdarstellung dieser Wissenschaft in ihren Hauptteilen, 5 vols. (Leipzig, 1892–1923); Niedere Zahlentheorie, 2 vols. (Leipzig, 1902–1910); and Das Fermat-Problem in seiner bisherigan Entwicklung (Leipzig, 1919), which has stimulated much research in this field.
"Bachmann, Paul Gustav Heinrich." Complete Dictionary of Scientific Biography. . Encyclopedia.com. (October 23, 2018). https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/bachmann-paul-gustav-heinrich
"Bachmann, Paul Gustav Heinrich." Complete Dictionary of Scientific Biography. . Retrieved October 23, 2018 from Encyclopedia.com: https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/bachmann-paul-gustav-heinrich
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.