**Friedrich Engel** worked on Lie algebras as well as continuous groups and partial differential equations.

- Moritz Engel, as well as being a Lutheran pastor was the author of many religious books and a gymnasium teacher.
- Friedrich began his schooling in Greiz in 1868 and, four years later, he entered the Gymnasium at Greiz where he studied from 1872 to 1879.
- On 1 April 1883 Engel began a year of military service which he undertook in Dresden.
- Felix Klein and Adolph Mayer had realised that Lie needed assistance and that Engel was the right person to give it.
- Having received a scholarship from the University of Leipzig and the Royal Saxon Society of the Sciences in Leipzig to support his trip abroad, Engel went to work with Lie in Christiania (now Oslo) arriving in September 1884.
- Leaving Christiania in June 1885, Engel returned to Leipzig where he defended his Habilitation thesis Über die Definitionsgleichungen der continuirlichen Transformationsgruppen Ⓣ(On the defining equations of continuous transformation groups) on 15 July.
- The year after Engel returned to Leipzig from Christiania, Klein accepted a professorship at the University of Göttingen and Lie was appointed to succeed him in Leipzig becoming professor of geometry there in February 1886.
- This allowed the collaboration between Lie and Engel to continue and we give further details below.
- In 1889 Engel was promoted to assistant professor to fill the position which became vacant when Friedrich Schur moved to Dorpat.
- 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.
- The collaboration between Engel and Lie led to Theorie der Transformationsgruppen Ⓣ(Theory of transformation groups) a work of three volumes published between 1888 and 1893.
- In many ways it was Engel who put Lie's ideas into a coherent form and made them widely accessible.
- Lie had died in 1899 and, 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).
- Lie's peculiar nature made it necessary for his works to be elucidated by one who knew them intimately and thus Engel's 'Annotations' competed in scope with the text itself.
- Engel, who was pressing the undertaking, resorted to an unusual means.
- On 9 March 1913, the newspaper 'Tidens Tegn' of Christiania carried a short article by Engel with the title 'Sophus Lies samlede Afhandlinger' in which was emphasized the failure of Lie's homeland to respond with assistance in the work of printing his collected memoirs.
- Up to this time the work had been under the charge of Engel as editor.
- Accordingly, Poul Heegaard became associated with Engel as an editor.
- The work also contains a biography of Grassmann written by Engel.
- Engel's life of Grassmann is written in a sound critical spirit, there is neither laudation nor condemnation of its subject, merely a connected and sympathetic history of him, from which the reader may get instruction and interest and inspiration.
- We should all admit our deep obligations to Engel as editor and biographer.
- Engel collaborated with Paul Stäckel in studying the history of non-euclidean geometry.
- it is clear that Engel intended to publish a book not in the spirit of Weierstrass but in the spirit of Lie.
- Thus Engel has certainly been guided also by historical points of view.
- The book also contains some interesting, hitherto unpublished, investigations of Engel.
- Engel received many honours for his work including the Lobachevsky Gold Medal and the Norwegian Order of St Olaf.

Born 26 December 1861, Lugau (near Chemnitz), Germany. Died 29 September 1941, Giessen, Germany.

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Origin Germany

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive