Background

Friedrich Engel was born on December 26, 1861 in Lugau, Germany. He was the son of Moritz Robert Engel, a Lutheran pastor, and of Marie Meissner.

Education

Engel attended the Gymnasium at Greiz from 1872 to 1879, studied mathematics in Leipzig and Berlin from 1879 to 1883, and received his doctorate in Leipzig in 1883 under Adolph Mayer. In 1884 and 1885 he studied with Sophus Lie in Christiania (now Oslo).

Career

In 1885 Engel qualified as a lecturer in pure mathematics at Leipzig and became an assistant professor there in 1889 and an associate professor in 1899. In 1904 he succeeded his friend Eduard Study as full professor at Greifswald, and in 1913 he went in the same capacity to Giessen, where, after his retirement in 1931, he continued to work until his death.

Engel was the closest student and the indispensable assistant of Sophus Lie. Lie was not capable of giving to the ideas that flowed inexhaustibly from his geometrical intuition the overall coherence and precise analytical form they needed in order to become accessible to the mathematical world. It was no less a mathematician than Felix Klein who recognized that the twenty-two-year-old Engel was the right man to assist Lie and who sent him to Christiania.

Shortly after Engel’s return to Leipzig in 1886, Lie succeeded Klein there, and the fruitful collaboration was continued. The result was the Theorie der Transformationsgruppen, which appeared from 1888 to 1893 in three volumes “prepared by S. Lie with the cooperation of F. Engel.”

Engel performed two further services for the great man long after the latter’s death in 1899. In 1932 there appeared Engel’s lectures Die Liesche Theorie der partiellen Differentialgleichungen: Ersler Ordnung, prepared for publication by Karl Faber. For Lie the transformation groups had only been an important aid in handling differential equations; however, he never succeeded in composing a work on his theory of these differential equations. In Faber the seventy-year-old Engel had found the right person to help him in completing this work of his teacher.

Between 1922 and 1937, Engel published six volumes and prepared the seventh of the seven-volume edition of Lie’s collected papers, 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 Anmerkungen (“Annotations”) competed in scope with the text itself. The seventh volume finally appeared in 1960.

Engel’s numerous independent works also are concerned primarily with topics in the fields of continuous groups and of partial differential equations: contact transformations (in his dissertation, before his meeting with Lie), Pfaffian equations, Lie’s element sets and higher differential quotients, and many others.

Engel also edited the collected works of Hermann Grassmann, thus bringing posthumous fame to this great mathematician. In addition, with his friend P. Stäckel, Engel investigated the history of non-Euclidean geometry; along with this study he translated the essential works of N. I. Lobachevsky from Russian into German, their first appearance in a Western language.

Achievements

• Engel was an important and productive mathematician who found his place in the history of mathematics mainly for his numerous publushed and edited works. The Engel group, the Engel expansion and the Engel's theorem were named after him.
  
  He received the Lobachevsky Gold Medal and the Norwegian Order of St. Olaf and was an honorary doctor of the University of Oslo.

Works

More photos

• book

  • Theorie Der Transformationsgruppen, Band 1 1888
  • Theorie Der Transformationsgruppen, Band 2 1890
  • Theorie Der Transformationsgruppen, Band 3 1893

Membership

Engel was a member of the Saxon, Russian, Norwegian, and Prussian academies.

• 

  Saxon Academy of Sciences , Germany

• 

  Saint Petersburg Academy of Sciences , Russia

• 

  Academy of Sciences of the Soviet Union , Russia

• 

  Russian Academy of Sciences , Russia

• 

  Royal Prussian Academy of Sciences , Germany

• 

  Norwegian Academy of Science and Letters , Norway

Connections

In 1899 Engel married Lina Ibbeken, the daughter of a Lutheran pastor. Their only child died very young.

Father:

Moritz Robert Engel

Mother:

Marie Meissner

Spouse:

Lina Ibbeken

teacher:

Adolph Mayer

colleague:

Sophus Lie

References

• Neue Deutsche Biographie, 4
  1959