Theodor Vahlen
Encyclopedia
Karl Theodor Vahlen was an Austria
n-born mathematician
who was an ardent supporter of the Nazi Party. He was a member of both the SA
and SS
.
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 Pomerania
n 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.
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
.
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
, 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.
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. 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.
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-Oberführer
.
, 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 algebra
s, his work contributed to the development of inversive ring geometry
.
The subject of relativity was a polemical issue in Nazi Germany. As Mark Walker writes
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
n-born mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who was an ardent supporter of the Nazi Party. He was a member of both the SA
Sturmabteilung
The Sturmabteilung functioned as a paramilitary organization of the National Socialist German Workers' Party . It played a key role in Adolf Hitler's rise to power in the 1920s and 1930s...
and SS
Schutzstaffel
The Schutzstaffel |Sig runes]]) was a major paramilitary organization under Adolf Hitler and the Nazi Party. Built upon the Nazi ideology, the SS under Heinrich Himmler's command was responsible for many of the crimes against humanity during World War II...
.
Career
From 1883, Vahlen was a PrivatdozentPrivatdozent
Privatdozent or Private lecturer is a title conferred in some European university systems, especially in German-speaking countries, for someone who pursues an academic career and holds all formal qualifications to become a tenured university professor...
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 Pomerania
Pomerania
Pomerania is a historical region on the south shore of the Baltic Sea. Divided between Germany and Poland, it stretches roughly from the Recknitz River near Stralsund in the West, via the Oder River delta near Szczecin, to the mouth of the Vistula River near Gdańsk in the East...
n district leader of the NSDAP. In 1924, Vahlen incited a crowd at the University against the Weimar Republic
Weimar Republic
The Weimar Republic is the name given by historians to the parliamentary republic established in 1919 in Germany to replace the imperial form of government...
, 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.
Upon his dismissal, Friedrich Schmidt-Ott
Friedrich Schmidt-Ott
Friedrich Schmidt-Ott was a German lawyer, scientific organizer, and science policymaker...
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
Johannes Stark
Johannes Stark was a German physicist, and Physics Nobel Prize laureate who was closely involved with the Deutsche Physik movement under the Nazi regime.-Early years:...
private physics laboratory. In 1930 Vahlen returned to his birthplace and became a lecturer of mathematics at the Technische Hochschule Wien
Vienna University of Technology
Vienna University of Technology is one of the major universities in Vienna, the capital of Austria. Founded in 1815 as the "Imperial-Royal Polytechnic Institute" , it currently has about 26,200 students , 8 faculties and about 4,000 staff members...
.
Once Adolf Hitler
Adolf Hitler
Adolf Hitler was an Austrian-born German politician and the leader of the National Socialist German Workers Party , commonly referred to as the Nazi Party). He was Chancellor of Germany from 1933 to 1945, and head of state from 1934 to 1945...
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
Humboldt University of Berlin
The Humboldt University of Berlin is Berlin's oldest university, founded in 1810 as the University of Berlin by the liberal Prussian educational reformer and linguist Wilhelm von Humboldt, whose university model has strongly influenced other European and Western universities...
, as successor to Richard Edler von Mises
Richard Edler von Mises
Richard Edler von Mises was a scientist and mathematician who worked on solid mechanics, fluid mechanics, aerodynamics, aeronautics, statistics and probability theory. He held the position of Gordon-McKay Professor of Aerodynamics and Applied Mathematics at Harvard University...
, who emigrated from Germany as a result of the Law for the Restoration of the Professional Civil Service
Law for the Restoration of the Professional Civil Service
The Law for the Restoration of the Professional Civil Service , also known as Civil Service Law, Civil Service Restoration Act, and Law to Re-establish the Civil Service, was a law passed by the National Socialist regime on April 7, 1933, two months after Adolf...
, 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
Deutsche Physik
Deutsche Physik or Aryan Physics was a nationalist movement in the German physics community in the early 1930s against the work of Albert Einstein, labeled "Jewish Physics"...
, advocated by the Nobel Laureate physicists Philipp Lenard
Philipp Lenard
Philipp Eduard Anton von Lenard , known in Hungarian as Lénárd Fülöp Eduárd Antal, was a Hungarian - German physicist and the winner of the Nobel Prize for Physics in 1905 for his research on cathode rays and the discovery of many of their properties...
and Johannes Stark
Johannes Stark
Johannes Stark was a German physicist, and Physics Nobel Prize laureate who was closely involved with the Deutsche Physik movement under the Nazi regime.-Early years:...
; 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.
During the period 1933 to 1937, Vahlen served as third vice president of the Kaiser-Wilhelm Gesellschaft
Kaiser Wilhelm Institute
The Kaiser Wilhelm Society for the Advancement of Science was a German scientific institution established in 1911. It was implicated in Nazi science, and after the Second World War was wound up and its functions replaced by the Max Planck Society...
. From May 1934, he was Assistant Secretary and head of the Science Office at the Reichserziehungsministerium
Reichserziehungsministerium
The Reichserziehungsministerium was officially known as the Reichsministerium für Wissenschaft, Erziehung und Volksbildung .-Background:...
(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. From this position, in 1936, Vahlen began publishing the journal Deutsche Mathematik
Deutsche Mathematik
Deutsche Mathematik was a mathematics journal founded by Ludwig Bieberbach and Theodor Vahlen in 1936. It is also the name of a movement closely associated with the journal whose aim was to promote "German mathematics" and eliminate "Jewish influence", similar to the Deutsche Physik movement...
, for which the Berlin mathematician Ludwig Bieberbach
Ludwig Bieberbach
Ludwig Georg Elias Moses Bieberbach was a German mathematician.-Biography:Born in Goddelau, near Darmstadt, he studied at Heidelberg and under Felix Klein at Göttingen, receiving his doctorate in 1910. His dissertation was titled On the theory of automorphic functions...
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
Prussian Academy of Sciences
The Prussian Academy of Sciences was an academy established in Berlin on 11 July 1700, four years after the Akademie der Künste or "Arts Academy", to which "Berlin Academy" may also refer.-Origins:...
in 1938.
It was in 1933 that Vahlen joined the Sturmabteilung
Sturmabteilung
The Sturmabteilung functioned as a paramilitary organization of the National Socialist German Workers' Party . It played a key role in Adolf Hitler's rise to power in the 1920s and 1930s...
(SA), and in 1936 he switched to the Schutzstaffel
Schutzstaffel
The Schutzstaffel |Sig runes]]) was a major paramilitary organization under Adolf Hitler and the Nazi Party. Built upon the Nazi ideology, the SS under Heinrich Himmler's command was responsible for many of the crimes against humanity during World War II...
(SS), in which he eventually held the rank of SS-Oberführer
Oberführer
Oberführer was an early paramilitary rank of the Nazi Party dating back to 1921. Translated as “Senior Leader”, an Oberführer was typically a Nazi Party member in charge of a group of paramilitary units in a particular geographical region...
.
Mathematics
Vahlen gained his doctorate with Beiträge zu einer additiven Zahlentheorie, and continued to specialise in number theoryNumber theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, but later turned to applied mathematics
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
.
Theodor Vahlen was an early proponent of geometric algebra
Geometric algebra
Geometric algebra , together with the associated Geometric calculus, provides a comprehensive alternative approach to the algebraic representation of classical, computational and relativistic geometry. GA now finds application in all of physics, in graphics and in robotics...
. His 1902 paper in Mathematische Annalen
Mathematische Annalen
Mathematische Annalen is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann...
recounts William Kingdon Clifford
William Kingdon Clifford
William Kingdon Clifford FRS was an English mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour, with interesting applications in contemporary mathematical physics...
's construction of his 2n dimensional algebra with n − 1 anti-commuting square roots of −1. Vahlen also recounts split-biquaternions and parabolic biquaternions
Dual quaternion
The set of dual quaternions is an algebra that can be used to represent spatial rigid body displacements. A dual quaternion is an ordered pair of quaternions  = and therefore is constructed from eight real parameters. Because rigid body displacements are defined by six parameters, dual...
originated by Clifford. But Vahlen cites Eduard Study
Eduard Study
Eduard Study was a German mathematician known for work on invariant theory of ternary forms and for the study of spherical trigonometry. He is also known for contributions to space geometry, hypercomplex numbers, and criticism of early physical chemistry.Study was born in Coburg in the Duchy of...
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 algebra
Clifford algebra
In mathematics, Clifford algebras are a type of associative algebra. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal...
s, his work contributed to the development of inversive ring geometry
Inversive ring geometry
In mathematics, inversive ring geometry is the extension of the concepts of projective line, homogeneous coordinates, projective transformations, and cross-ratio to the context of associative rings, concepts usually built upon rings that happen to be fields....
.
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.