Theodor Vahlen

Karl Theodor Vahlen (30 June 1869 in Vienna, Austria-Hungary – 16 November 1945 in Prague, Czechoslovakia) was an Austrian-born mathematician who was an ardent supporter of the Nazi Party. He was a member of both the SA and SS.

Karl Theodor Vahlen
Born(1869-06-30)30 June 1869
Vienna
Died16 November 1945(1945-11-16) (aged 76)
Prague
Known forJournal editor Deutsche Mathematik
Signature

Education

His father was German classical philologist Johannes Vahlen (1830–1911). Theodor studied in Berlin from 1889 and received his doctorate there in 1893.[1]

Career

From 1893, Vahlen was a Privatdozent in mathematics at the Königsberg Albertina University. In 1904, he began teaching at the University of Greifswald, and in 1911 he became an ordinarius professor there. Vahlen had joined the Nazi Party (NSDAP) in 1922. From 1924, he was the first Pomeranian district leader of the NSDAP. In 1924, Vahlen incited a crowd at the University against the Weimar Republic, which resulted in taking down flags of the Republic. The University placed him on leave for political abuse of his function, and in 1927 he was dismissed without a pension.[2]

Upon his dismissal, Friedrich Schmidt-Ott increased the funding Vahlen had been receiving for his work for the German Navy since 1922. Vahlen worked briefly as an assistant in Johannes Stark's private physics laboratory. In 1930 Vahlen returned to his birthplace and became a lecturer of mathematics at the Technische Hochschule Wien.[3][4]

Once Adolf Hitler became Chancellor of Germany on 30 January 1933, Vahlen's career gained momentum and flourished in Germany as a result of his support for the NSDAP. In that year, he became an ordinarius professor of mathematics at the Humboldt University of Berlin, as successor to Richard Edler von Mises,[5] who emigrated from Germany as a result of the Law for the Restoration of the Professional Civil Service, which was in part directed against professors with Jewish ancestry, which von Mises had. After 1933, Vahlen was a strong advocate of Deutsche Mathematik, a parallel movement to Deutsche Physik, advocated by the Nobel Laureate physicists Philipp Lenard and Johannes Stark; both movements were anti-Semitic. From 1934, he was ordinarius professor at the University of Berlin, a position he held until attaining emeritus status in 1937.[3]

During the period 1933 to 1937, Vahlen served as third vice president of the Kaiser-Wilhelm Gesellschaft. From May 1934, he was Assistant Secretary and head of the Science Office at the Reichserziehungsministerium (Acronym: REM, translation: Reich Education Ministry.). Actually, the Science Office was split into two components, WI, a continuation of the Prussian department, and WII, the army office for research. Vahlen was head of WI, but, in actuality, the deputy chief, the chemist Franz Bachér ran WI.[6] From this position, in 1936, Vahlen began publishing the journal Deutsche Mathematik, for which the Berlin mathematician Ludwig Bieberbach was the editor; in the journal, political articles preceded the scholarly articles. On 1 January 1937 Vahlen was relieved of his duties at the REM. Through a manipulation of the election process by Vahlen and his supporters, he became president of the Prussian Academy of Sciences in 1938.[2][3][7]

It was in 1933 that Vahlen joined the Sturmabteilung (SA), and in 1936 he switched to the Schutzstaffel (SS), in which he eventually held the rank of SS-Brigadeführer.[2][3]

Mathematics

Vahlen gained his doctorate with Beiträge zu einer additiven Zahlentheorie, and continued to specialise in number theory, but later turned to applied mathematics.

Theodor Vahlen was an early proponent of geometric algebra. His 1902 paper in Mathematische Annalen recounts William Kingdon Clifford's construction of his 2n dimensional algebra with n − 1 anti-commuting square roots of −1. Vahlen also recounts split-biquaternions and parabolic biquaternions originated by Clifford. But Vahlen cites Eduard Study most of all since Study also focussed on the geometric motions (translation and rotation) as implicit in algebra. Since Vahlen explores some of the fractional-linear transformations of Clifford algebras, he is sometimes remembered for the Vahlen matrices. These are matrices with coefficients in a Clifford algebra that act on a projective line over a ring. In 1985 Lars Ahlfors recalled the article as follows: "The method was introduced as early as 1901 by K.T. Vahlen in a rather short, but remarkable, paper. His motivation was to unify the theory of motions in Euclidean, hyperbolic, and elliptic space, which is obviously in the spirit of Clifford. In this respect the paper seems somewhat antiquated, but the essence is in the method it advocates."[8]

The subject of relativity was a polemical issue in Nazi Germany. As Mark Walker writes

Eventually Vahlen adopted the common tactic of ascribing the theory of relativity to other "Aryan" physicists, thereby accusing Einstein of plagiarism, but also making the theory palatable to the National Socialist state.[2]:97

Works
  • 1899: "Rationale Funktion der Wurzeln, symmetrische und Affektfunktionen", (i.e. "Rational functions of roots, symmetric and effect-functions") Klein's encyclopedia, 1–1.
  • 1900: "Arithmetische Theorie der Formen", (i.e. "Arithmetic Theory of Forms") Klein's encyclopedia, Volume 1-2
  • 1902: "Über Bewegungen und complexe Zahlen", (i.e. "On Motions and Complex Numbers") Mathematische Annalen 55:585–93
  • 1905: Abstrakte Geometrie. Untersuchungen über die Grundlagen der euklidischen und nicht-euklidischen Geometrie, (i.e. Arithmetic Geometry. Studies of the Foundations of Euclidean and Non-Euclidean Geometry), Leipzig, 2nd edition 1940, Deutsche Mathematik, 2nd supplement
  • 1911: Konstruktionen und Approximationen in systematischer Darstellung, (i.e. Systematic Representations of Constructions and Approximations) Teubner
  • 1922: Ballistik (i.e. Ballistics) de Gruyter[9] 2nd edition 1942
  • 1929: Deviation und Kompensation, (i.e. Deviation and Compensation) Vieweg-Verlag
  • 1942: "Die Paradoxien der relativen Mechanik", (i.e. "Paradoxes of relative mechanics") Leipzig, Deutsche Mathematik, 3rd supplement

Bibliography
  • Beyerchen, Alan D. (1977) Scientists Under Hitler: Politics and the Physics Community in the Third Reich (Yale) ISBN 0-300-01830-4
  • Hentschel, Klaus, editor and Ann M. Hentschel, editorial assistant and Translator (1996) Physics and National Socialism: An Anthology of Primary Sources (Birkhäuser) ISBN 0-8176-5312-0
  • Macrakis, Kristie (1993) Surviving the Swastika: Scientific Research in Nazi Germany (Oxford) ISBN 0-19-507010-0
gollark: This is still meant to be a straight line, right?
gollark: Seems right.
gollark: Also, the y intercept is just what value it has when x = 0.
gollark: In equations.
gollark: Usually gradient is m and y intercept is b or c or something.

References
  1. Theodor Vahlen at the Mathematics Genealogy Project
  2. Walker, Mark (1995) Nazi Science: Myth, Truth, and the German Atomic Bomb, pages 95–99, (Persius, 1995) ISBN 0-306-44941-2
  3. Hentschel, 1996, Appendix F; see entry for Vahlen.
  4. Macrakis, 1993, pp. 78-79.
  5. Richard von Mises and the economist Ludwig von Mises were brothers.
  6. Beyerchen, 1977, p. 57.
  7. Beyerchen, 1977, pp. 144-145.
  8. Lars Ahlfors (1985) "Mobius transformations and Clifford numbers", pages 65 to 73 in Differential Geometry and Complex Analysis, H.E. Rauch Memorial Volume, I. Chavel & H.M. Farkas editors, Springer books ISBN 3-540-13543-X
  9. Rowe, J. E. (1923). "Review: Ballistik, by Dr. Theodor Vahlen" (PDF). Bull. Amer. Math. Soc. 29 (4): 186–187. doi:10.1090/s0002-9904-1923-03703-8.

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