Erhard Tornier

Erhard Tornier (born December 5, 1894 in Obernigk ; † 1982 ) was a German probability theorist who was best known for his role in the National Socialist influence on mathematics (see German mathematics ).

biography

Tornier studied mathematics and philosophy in Breslau, Berlin and Marburg and received his doctorate under Kurt Hensel at the University of Marburg in 1922 ( on the periodicity of g-adic, gamma-adic and pi-adic numbers and related questions ) and was in Kiel from 1929 as a colleague of Willy Feller , with whom he published and collaborated. He completed his habilitation in 1930 in Marburg and was then a private lecturer in Kiel, where in 1931 he asked the local professor Abraham Fraenkel for a position in order - as he put it in his letter - to learn from him. Fraenkel agreed so that the aspiring probability theorist Feller had a specialist colleague. Tornier also temporarily represented Fraenkel in Kiel when he taught in Jerusalem from 1929 to 1931. In 1932 Tornier joined the NSDAP . After the National Socialists came to power, he denounced Feller as a Jew and hoped in vain to succeed Fraenkel as professor in Kiel when he went to Jerusalem in 1933. Because of his political attitude, he was to be appointed director of the Mathematical Institute in Göttingen in 1934 until Helmut Hasse arrived. For a while he worked against the already decided appointment of Hasse. He was supported by the student body, u. a. Oswald Teichmüller , supported. After massive interventions by Helmut Hasse (who was a fellow student and colleague of Tornier in Marburg; they were apparently on friendly terms at the time. In his work Probability and Number Theory from 1930 he thanks Hasse for valuable information) at the responsible ministry, his appointment failed, instead Hasse was appointed as planned director of the institute. But Tornier also became director and temporarily held the chair of Edmund Landau, who had been pushed out of the university by the National Socialists . In 1934 he also arranged for the dismissal of Franz Rellich, who was critical of the regime .

Also in 1934, Tornier was proposed by Ludwig Bieberbach for the leadership of the DMV . According to Bieberbach, this should introduce the leader principle . Because it would not have been possible under the given circumstances to fundamentally contradict this demand, Helmut Hasse, Konrad Knopp and Oskar Perron agreed on Wilhelm Blaschke as the opposing candidate for Tornier. At the general meeting in Bad Pyrmont (at which Tornier appeared accompanied by an SA man in civilian clothes), Bieberbach's application to transition to the Führer principle with Tornier as the leader failed, instead the DMV went to the "moderate Führer principle" - a chairman elected for two years, who determined the members of the board of directors - with Blaschke as chairman, which, however, could not prevail because Bieberbach delayed the amendment to the statutes.

Tornier became head of the Institute for Mathematical Statistics in Göttingen in 1935, where an open power struggle with Hasse arose in the meantime, in continuation of Tornier's unsuccessful attempt to become leader of the DMV. Hasse threatened Theodor Vahlen with resignation. Tornier then officially left the University of Göttingen for health reasons in April 1936 and became a professor in Berlin in 1936. There he led an excessive life (one photo showed him with a turtle on a leash on a popular Berlin boulevard accompanied by a prostitute, which caused a scandal in the math faculty) and his marriage was divorced. In 1938 he sought his retirement because of a decline in intellectual abilities, which he was granted in 1939. The resignation was forced - there were proceedings against him because of over-indebtedness and seduction of a minor. An opinion from the head of the Psychiatric and Neurological Clinic at the University of Wroclaw confirmed that he had mental problems. Immediately after the annexation of Poland, Tornier moved to Krakow. In 1941, the NSDAP initiated a party expulsion process against him because he had not looked after the party since 1937 due to his nervous breakdown. At that time he was living in Warsaw and at his own request he became a teacher in the General Government (he was at a high school in Radom ). After the war he lived in Lübeck and later in Hamburg, where he dealt with the calculation of probability. He corresponded with Hilda Geiringer about the postponed probabilistic work of her husband Richard von Mises , which she was preparing for publication. Geiringer's tone, although she emigrated before the National Socialists herself, was friendly (in the publication of von Mises's posthumous works she made several references to significant contributions by Tornier on this subject) and she had the impression that Tornier had psychological problems .

plant

Tornier published several papers on measure theory and the foundations of probability theory in the 1930s . He worked on an axiomatization in the succession of Richard von Mises , an approach that was later pushed into the background by Andrei Kolmogorov's axiomatization .

Paul Halmos wrote about one of Tornier's works in the Mathematical Reviews that it would reproduce in its main part in great detail the theorems used for the standard constructions of the Jordan and Lebesgue measures, although the main difference to the usual procedure is actually only in the systematic use of the formula instead of existed. His book "Probability Theory and General Integration Theory", written in the 1930s, with its new axiomatics of probability theory, was published in the USA in 1944. After the war he published another book in 1952, "Theory of the Experimental Rules of the Calculus of Probabilities". In a review for the Mathematical Reviews , Jacob Wolfowitz noted that in Tornier's system of axioms, probabilities are only defined as finitely additive functions on sets and that Tornier's theory deals exclusively with finite probability spaces, where the calculated probabilities can be compared with relative frequencies in a sufficient number of experiments could check. ${\ displaystyle I (\ Sigma _ {i = 1} ^ {n} \ alpha _ {i})}$ ${\ displaystyle \ Sigma _ {i = 1} ^ {n} I (\ alpha _ {i})}$

Maistrow describes Tornier's attempt to mathematize von Mises' frequency theory as follows: A number of attempts were made to formalize frequency theory completely [...] Tornier refused the use of schemes which did not fit into the frequency interpretation. For this purpose, he constructed a cumbersome formal calculus and was forced to abandon the possibility of formulating and solving a number of elementary problems of probability theory, within the framework of his theory.

Fonts

Probability calculus and number theory. First communication , Journal for Pure and Applied Mathematics, Volume 161, 1930, p. 177
A new foundation of probability theory , Zeitschrift für Physik, Volume 63, 1930, pp. 697-705
Axioms of the Calculus of Probability , Journal für Reine und Angewandte Mathematik, Volume 163, 1930, pp. 45-64
with Willy Feller set theoretical investigations of properties of the number series , Mathematische Annalen, Volume 107, 1933, p. 188
with Willy Feller measurement and content theory of the Bairean null space , Mathematische Annalen, Volume 107, 1932, pp. 165-187
Fundamentals of Probability Theory , Acta Mathematica, Volume 60, 1933, pp. 239-380
Probability theory and general integration theory , Teubner 1936
To generate one test procedure from another by formal modification , Deutsche Mathematik, Volume 2, 1937, pp. 466-469, review by Erich Kamke
Theories of measure and content, in which the additivity of measures is only required in infinitely small ways , treatises of the Prussian Academy of Sciences, Math.-Naturwiss. Class 1941
with Hans Domizlaff theory of the experimental rules of the probability calculation , Kohlhammer 1952, review in Zentralblatt f. Math.

literature

Norbert Schappacher and Martin Kneser: Professional Association - Institute - State. In: Gerd Fischer u. a. (Ed.), A Century of Mathematics 1890–1990. Festschrift for the anniversary of the DMV, Vieweg 1990
Thomas Hochkirchen: Probability calculation in the field of tension between measure and frequency theory - life and work of the “German” mathematician Erhard Tornier (1894–1982). NTM Journal for the History of Science, Technology and Medicine, Volume 6, Issue 1 (1998), pp. 22-41.

Web links

Entry on Erhard Tornier in the Catalogus Professorum Halensis

Individual evidence

^ Mathematics Genealogy Project
^ Sanford Segal Mathematicians under the Nazis , Princeton University Press 2003, p. 149
^ Sanford Segal, p. 149.
↑ Sanford Segal, p. 150, he cites Fraenkel Lebenskreise 1967.
^ Reid Courant-Hilbert , Springer Verlag 1986, p. 385.
^ Reid Courant-Hilbert , Springer Verlag 1986, p. 393. Another affront. The SA man was finally asked to leave the meeting.
↑ Remmert, The German Mathematicians Association in the Third Reich, Communications DMV, 12-3, 2004, pp. 162f
↑ Sanford Segal, p. 156, he quotes Constance Reid Courant , Springer 1976 (in the edition Courant-Hilbert , Springer Verlag 1986, p. 402).
^ Sanford Segal, p. 156. He cites a letter from Wilhelm Süss to Hellmuth Kneser .
^ Sanford Segal, p. 157
^ Sanford Segal, p. 157
^ Sanford Segal, p. 150.
↑ Tornier's axiomatization approaches, those of Richard von Mises and Karl Dörge were presented, for example, by Erich Kamke in a review article in 1933, Kamke on newer foundations of the theory of probability ; Annual reports DMV, Volume 42, 1933, p. 14
↑ Tornier, Erhard; Domizlaff, Hans: Theory of the experimental rules of the probability calculation. W. Kohlhammer Verlag, Stuttgart, 1952. p. 108.
↑ The measure theory deals with lot of systems and content features that one can define it. The property of additivity, which is central to the modern concept of measure , was introduced by Émile Borel in 1909 and was initially viewed with some criticism. The Jordanian construction leads to only finitely additive content, the finite additivity (a weaker property than additivity) is a consequence of the definition of the content. Borel, on the other hand, postulates the additivity of measure and thus determines the measures of sets which are contained in an algebra that is complete under countable applications of certain set operations . Henry Lebesgue's definition of the integral in 1902, however, retained additivity. ${\ displaystyle \ sigma}$ ${\ displaystyle \ sigma}$ ${\ displaystyle \ sigma}$ ${\ displaystyle \ sigma}$ ${\ displaystyle \ sigma}$
↑ LE Maistrow: Theory of probability: a historical sketch

personal data
SURNAME	Tornier, Erhard
BRIEF DESCRIPTION	German probability theorist
DATE OF BIRTH	December 5, 1894
PLACE OF BIRTH	Obernigk
DATE OF DEATH	1982

[1] Mathematics Genealogy Project

[2] Sanford Segal Mathematicians under the Nazis , Princeton University Press 2003, p. 149

[3] Sanford Segal, p. 149.

[4] Sanford Segal, p. 150, he cites Fraenkel Lebenskreise 1967.

[5] Reid Courant-Hilbert , Springer Verlag 1986, p. 385.

[6] Reid Courant-Hilbert , Springer Verlag 1986, p. 393. Another affront. The SA man was finally asked to leave the meeting.

[7] Remmert, The German Mathematicians Association in the Third Reich, Communications DMV, 12-3, 2004, pp. 162f

[8] Sanford Segal, p. 156, he quotes Constance Reid Courant , Springer 1976 (in the edition Courant-Hilbert , Springer Verlag 1986, p. 402).

[9] Sanford Segal, p. 156. He cites a letter from Wilhelm Süss to Hellmuth Kneser .

[10] Sanford Segal, p. 157

[11] Sanford Segal, p. 157

[12] Sanford Segal, p. 150.

[13] Tornier's axiomatization approaches, those of Richard von Mises and Karl Dörge were presented, for example, by Erich Kamke in a review article in 1933, Kamke on newer foundations of the theory of probability ; Annual reports DMV, Volume 42, 1933, p. 14

[14] Tornier, Erhard; Domizlaff, Hans: Theory of the experimental rules of the probability calculation. W. Kohlhammer Verlag, Stuttgart, 1952. p. 108.

[15] The measure theory deals with lot of systems and content features that one can define it. The property of additivity, which is central to the modern concept of measure , was introduced by Émile Borel in 1909 and was initially viewed with some criticism. The Jordanian construction leads to only finitely additive content, the finite additivity (a weaker property than additivity) is a consequence of the definition of the content. Borel, on the other hand, postulates the additivity of measure and thus determines the measures of sets which are contained in an algebra that is complete under countable applications of certain set operations . Henry Lebesgue's definition of the integral in 1902, however, retained additivity. ${\ displaystyle \ sigma}$ ${\ displaystyle \ sigma}$ ${\ displaystyle \ sigma}$ ${\ displaystyle \ sigma}$ ${\ displaystyle \ sigma}$

[16] LE Maistrow: Theory of probability: a historical sketch