Friedrich Engel (26 December 1861 – 29 September 1941) was a German
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
.
Engel was born in
Lugau,
Saxony
Saxony, officially the Free State of Saxony, is a landlocked state of Germany, bordering the states of Brandenburg, Saxony-Anhalt, Thuringia, and Bavaria, as well as the countries of Poland and the Czech Republic. Its capital is Dresden, and ...
, as the son of a
Lutheran
Lutheranism is a major branch of Protestantism that emerged under the work of Martin Luther, the 16th-century German friar and Protestant Reformers, reformer whose efforts to reform the theology and practices of the Catholic Church launched ...
pastor. He attended the Universities of both
Leipzig
Leipzig (, ; ; Upper Saxon: ; ) is the most populous city in the States of Germany, German state of Saxony. The city has a population of 628,718 inhabitants as of 2023. It is the List of cities in Germany by population, eighth-largest city in Ge ...
and
Berlin
Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...
, before receiving his
doctorate
A doctorate (from Latin ''doctor'', meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' licentia docendi'' ("licence to teach ...
from Leipzig in 1883.
Engel studied under
Felix Klein
Felix Christian Klein (; ; 25 April 1849 – 22 June 1925) was a German mathematician and Mathematics education, mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and the associations betwe ...
at Leipzig, and collaborated with
Sophus Lie
Marius Sophus Lie ( ; ; 17 December 1842 – 18 February 1899) was a Norwegian mathematician. He largely created the theory of continuous symmetry and applied it to the study of geometry and differential equations. He also made substantial cont ...
for much of his life. He worked at Leipzig (1885–1904),
Greifswald
Greifswald (), officially the University and Hanseatic City of Greifswald (, Low German: ''Griepswoold'') is the fourth-largest city in the German state of Mecklenburg-Western Pomerania after Rostock, Schwerin and Neubrandenburg. In 2021 it surpa ...
(1904–1913), and
Giessen
Giessen, spelled in German (), is a town in the Germany, German States of Germany, state () of Hesse, capital of both the Giessen (district), district of Giessen and the Giessen (region), administrative region of Giessen. The population is appro ...
(1913–1931). He died in Giessen.
Engel was the co-author, with Sophus Lie, of the three volume work ''Theorie der Transformationsgruppen'' (publ. 1888–1893; tr., "Theory of transformation groups"). Engel was the editor of the collected works of Sophus Lie with six volumes published between 1922 and 1937; the seventh and final volume was prepared for publication but appeared almost twenty years after Engel's death. He was also the editor of the collected works of
Hermann Grassmann
Hermann Günther Grassmann (, ; 15 April 1809 – 26 September 1877) was a German polymath known in his day as a linguist and now also as a mathematician. He was also a physicist, general scholar, and publisher. His mathematical work was littl ...
. Engel translated the works of
Nikolai Lobachevski from Russian into German, thus making these works more accessible. With
Paul Stäckel he wrote a history of
non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean ge ...
(''Theorie der Parallellinien von Euklid bis auf Gauss'', 1895). With his former student Karl Faber, he wrote a book on the theory of
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.
The function is often thought of as an "unknown" that solves the equation, similar to ho ...
s of the first order using methods of
Lie group
In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable.
A manifold is a space that locally resembles Eucli ...
theory.
In 1910 Engel was the president of the
Deutsche Mathematiker-Vereinigung.
See also
*
Engel group
*
Engel expansion The Engel expansion of a positive real number ''x'' is the unique non-decreasing sequence of positive integers (a_1,a_2,a_3,\dots) such that
:x=\frac+\frac+\frac+\cdots = \frac\!\left(1 + \frac\!\left(1 + \frac\left(1+\cdots\right)\right)\right)
...
*
Engel's theorem
References
External links
*
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1861 births
1941 deaths
People from the Kingdom of Saxony
Humboldt University of Berlin alumni
Leipzig University alumni
Academic staff of Leipzig University
Academic staff of the University of Greifswald
Academic staff of the University of Giessen
19th-century German mathematicians
20th-century German mathematicians
German historians of mathematics
Mathematicians from the German Empire
Presidents of the German Mathematical Society
{{Germany-mathematician-stub