# Friedrich Engel (mathematician)

Friedrich Engel ( born December 26, 1861 in Lugau, † September 29, 1941 in Gießen ) was a German mathematician.

Engel was the son of a Lutheran pastor and attended high school in Greiz. From 1879 he studied at the University of Leipzig, received his doctorate in 1883 at which Adolph Mayer ( On the theory of contact transformations ). He also studied at the University of Berlin. One of his teachers in Leipzig Felix Klein recommended Angel to his friend Sophus Lie, to assist it in the preparation / formulation of his work on continuous transformation groups ( now called Lie groups ). Lie himself always had difficulties in formulating its intuitive combined geometric ideas in analytical form, and both complemented each other well. Engel worked with Lie 1884/85 in Oslo (then Christiania ) and returned with him in 1886 back to Leipzig, where Lie became the successor of small as a professor. Your three -volume work on transformation groups appeared from 1888 to 1893. Later Angel was editor of the Collected Essays Lies ( 1922-1937 ). 1885 angel habilitated in Leipzig, where he became a lecturer, associate professor in 1889 and 1899 ordinary honorary professor. In 1904 he became a full professor at the University of Greifswald and 1913 at the University of Giessen, where he stayed until his retirement in 1931 as a successor to his friend Eduard Study. But he was also then still scientifically active.

In 1931, he published his doctoral Karl Faber published the book The Lie's first order partial differential equations ( a project that Lie planned but could no longer run ).

Angel helped Hermann Grassmann to recognition by issuing all of whose works, and made Nikolai Ivanovich Lobachevsky through the translation of his writings from Russian into German known. With Paul Stäckel he wrote a history of non-Euclidean geometry, and in addition to the work of Lobachevsky published other documents to non-Euclidean geometry ( Teubner, 1898 ) as described by Janos Bolyai Farkas Bolyai and his father. Angel even addressed, among others, partial differential equations of first order, contact transformations and finite continuous groups, the Pfaffian problem (see Johann Friedrich Pfaff ) and systems Pfaffian forms, surface theory, Invariantheorie of differential equations, theory of surfaces and the general integration of the n- body problem in mechanics.

He was in correspondence with Wilhelm Killing. and was involved in the Euler Complete Edition.

In 1910 he was president of the German Mathematical Society. The set of angels, which characterizes the finite dimensional nilpotent Lie algebras is connected with his name.

He was a member of the Saxon, Norwegian, Russian and Prussian Academy of Sciences, an honorary doctorate in Oslo and the recipient of the Lobachevsky gold medal in Kazan.