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Friedrich Engel was the son of a Lutheran pastor. He attended the Gymnasium at Greiz, one of the chief towns of Reuss Oberland, from 1872 to 1879. His university studies began in 1879 and he attended the University of Leipzig and the University of Berlin. He received his doctorate from Leipzig in 1883 having studied under Adolph Mayer working on contact transformations.
At Leipzig, Engel was taught by Klein who recognised that he was the right man to assist Lie. At Klein's suggestion Engel went to work with Lie in Christiania (now Oslo) from 1884 until 1885. In 1885 Engel's Habilitation thesis was accepted by Leipzig and he became a lecturer there. The year after Engel returned to Leipzig from Christiania, Lie was appointed to succeed Klein and the collaboration of Lie and Engel continued.
In 1889 Engel was promoted to assistant professor and, ten years later he was promoted to associate professor. In 1904 he accepted the chair of mathematics at Greifswald when his friend Eduard Study resigned the chair. Engel's final post was the chair of mathematics at Giessen which he accepted in 1913 and he remained there for the rest of his life. In 1931 he retired from the university but continued to work in Giessen.
The collaboration between Engel and Lie led to Theorie der Transformationsgruppen a work on three volumes published between 1888 and 1893. This work was:-
... prepared by S Lie with the cooperation of F Engel...In many ways it was Engel who put Lie's ideas into a coherent form and made them widely accessible. From 1922 to 1937 Engel published Lie's collected works in six volumes and prepared a seventh (which in fact was not published until 1960). In  Engel's efforts in producing Lie's collected works are described as:-
... an exceptional service to mathematics in particular, and scholarship in general. Lie's peculiar nature made it necessary for his works to be elucidated by one who knew them intimately and thus Engel's 'Annotations' completed in scope with the text itself.Engel also edited Hermann Grassmann's complete works and really only after this was published did Grassmann get the fame which his work deserved. Engel collaborated with Stäckel in studying the history of non-euclidean geometry. He also wrote on continuous groups and partial differential equations, translated works of Lobachevsky from Russian to German, wrote on discrete groups, Pfaffian equations and other topics.
He received many honours for his work including the Lobachevsky Gold Medal and the Norwegian Order of St Olaf. In addition he was awarded an honorary doctorate from the University of Oslo.
References (9 books/articles)
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