Karl Dörge

circa 1930

Otto Martin Karl Dörge (born November 5, 1899 in Müllerdorf near Halle, † June 16, 1975 in Bensberg ) was a German mathematician with a research focus on algebra.

Life

Dörge received private lessons up to the age of 13, including from his father, a pastor in Müllerdorf (later in Seyda ). In 1915 he passed the secondary school diploma in Torgau and became a soldier (lieutenant, Iron Cross 1st and 2nd class).

In 1919 Dörge began studying mathematics and physics in Berlin at the Friedrich Wilhelms University (Humboldt University since 1949), mathematics with Issai Schur , Richard von Mises , Erhard Schmidt , Ludwig Bieberbach , physics with Albert Einstein , Max Planck and Heinrich Rubens . In 1925 he received his doctorate under Issai Schur with a thesis (only 15 pages long) on the entire rational solution pairs of algebraic equations in two variables .

Dörge received his habilitation in 1926, in 1932 as associate professor and in 1936 as full professor at the University of Cologne . His main research focus was algebra. He was in the tradition of David Hilbert and Emmy Noether (with whom he corresponded). In his last creative period he dealt with universal algebra (structures with any number of arbitrary operations). He retired in 1968.

Dörge was a passionate art collector (one of the most beautiful pieces in his collection is a contemporary copy of Annibale Carracci's “Mystical Marriage of Saint Catherine”, around 1600). He also collected works of classical modern art (e.g. Joan Miró ).

student

Dörge's students are the graph theorist Klaus Wagner , the head of the Cologne school of graph theory (Hans-Joachim Burscheid, Rudolf Halin, Egbert Harzheim , Heinz Adolf Jung, Wolfgang Mader, who are also Dörge's students in the second generation and have worked with him) as well as the Algebraist Bruno Bosbach.

Articles (chronological)

• A contribution to the theory of the Diophantine equations with two unknowns, Math. Zeitschrift 24, 1925 (a tight version of the dissertation) , as well as his dissertation here
• On Hilbert's principle of irreducibility, Math. Annalen Vol. 95, 1925
• About the rarity of the reducible polynomials and the normal equations, Math. Annalen Vol. 95, 1925
• Simple proof of Hilbert's irreducibility theorem, Math. Annalen Vol. 96, 1926
• On the Fundamental Theorem of Algebra, session reports of the Prussian Academy of Sciences, 1928
• Comment on Hilbert's theorem of irreducibility, Math. Annalen, Vol. 102, 1929
• For the distribution of the square remains, annual report of the German Mathematicians Association, Vol. 38, 1929
• About the reducibility of polynomials in the field of real numbers, Math. Annalen Vol. 102, 1930
• On the justification of the calculation of probability given by R. von Mises (first communication: Theory of Gambling), Math. Zeitschrift Vol. 32, 1930
• An axiomatization of von Miss's probability theory, annual report of the German Mathematicians Association, Vol. 43, 1933
• On the justification of the calculus of probability given by R. von Mises (second part: General Probability Theory), Math. Zeitschrift Vol 40, 1935
• Proof of the law of reciprocity for square residues, Math. Annalen 118, 1941/1943
• Comment on elimination in arbitrary quantities with operations (Erhard Schmidt on his 75th birthday), Math. Nachrichten, Volume 4, 1950
• Decision on the algebraic character of power series with algebraic coefficients on the basis of their value stock Math. Annalen Bd.122, 1950/1951
• Comment on the basic concepts of calculus, Math. Annalen 123, 1951 (together with Klaus Wagner)
• Estimation of the number of reducible polynomials, Math. Annalen 160, 1965
• About the solvability of general algebraic systems of equations and some other questions, Math. Annalen 171, 1967
• Completion in classes of structured sets, Math. Annalen 187, 1970 (together with Heinz Adolf Jung)

Textbooks

• Probability calculation for non-mathematicians (co-author Hans Klein), Verlag Walter de Gruyter, Berlin 1939 (2nd edition 1947)
• Differential and integral calculus, part I, Ferdinand Dümmlers Verlag, Bonn 1948

Footnotes

1. ^ University archive Cologne
2. ↑ On the solvability of general algebraic systems of equations and some other questions, Math. Annalen 171, 1967