**Arnold Scholz** was a German mathematician who proved important results in number theory.

- In 1911 Scholz began his schooling at a primary school in Charlottenburg and later he moved to the Kaiserin Augusta Gymnasium, also in Charlottenburg, which had been founded in 1818 and named for Princess Augusta of Saxe-Weimar-Eisenach in 1876.
- While he was at the Gymnasium, Scholz was unsure whether to continue his studies in mathematics or in music.
- In 1923, while at the Kaiserin Augusta Gymnasium, Scholz was awarded his Abitur, giving him the right to study at university.
- Many German students of this time took courses at a number of different German universities but Scholz chose to spend only one semester away from Berlin and that was at the University of Vienna in the summer of 1927.
- By this time in his career, Scholz was undertaking research for his doctorate advised by Issai Schur and his research had taken him into areas to which Philipp Furtwängler had made substantial contributions.
- Scholz was looking at the inverse Galois group problem, namely whether a given finite group can be the Galois group of some extension of the rational numbers.
- The problem in general is still unsolved but Scholz was solving special cases.
- Even before going to Vienna, Scholz had read material produced by Helmut Hasse on class field theory.
- He wrote to Hasse on 22 April 1927, on the day before travelling to Vienna, suggesting ways that proofs of Hasse's results could be substantially simplified and, as a result, Scholz and Hasse wrote the joint paper Zur Klassenkörpertheorie auf Takagischer Grundlage Ⓣ(On class field theory based on Takagi) which was published in Mathematische Zeitschrift in 1928.
- It became Scholz's first paper.
- After his semester in Vienna, Scholz returned to Berlin in September 1927 and continued work on his thesis Über die Bildung algebraischer Zahlkörper mit auflösbarer Galoisscher Gruppe Ⓣ(On forming algebraic number fields with solvable Galois group).
- In October 1928 Scholz wrote to Hasse saying that he had constructed number fields with arbitrarily large class field towers.
- Scholz published this result in his paper Zwei Bemerkungen zum Klassenkörperturm Ⓣ(Two remarks on the class field tower) which appeared in Crelle's Journal in 1929.
- This paper consisting of his thesis material was one of four papers by Scholz published in 1929.
- In April 1929, after the award of his doctorate, Scholz was appointed as an assistant to Alfred Loewy at the University of Freiburg.
- Scholz habilitated at the University of Freiburg.
- However, he had been appointed to an honorary chair in Freiburg and so became an important colleague for Scholz.
- Scholz's interest in Zermelo's ideas is clear from the fact that he published Zermelos neue Theorie der Mengenbereiche Ⓣ(Zermelo's new theory of quantity ranges) in 1931.
- We mentioned above that Olga Taussky had met Scholz when he spent the summer of 1927 in Vienna.
- Another professor at Freiburg when Scholz began working there was Lothar Wilhelm Julius Heffter (1862-1962).
- In the summer of 1931 Gustav Doetsch was appointed to succeed Heffter and, at this time, Scholz changed from being Loewy's assistant to become an assistant to Gustav Doetsch.
- However, it was Zermelo with whom Scholz formed a close friendship and he tried hard to arrange a meeting between Zermelo and Kurt Gödel at the Deutsche Mathematiker-Vereinigung meeting held in Bad Elster in September 1931.
- Both Scholz and Zermelo worked in Freiburg.
- Scholz was eager to help Zermelo and thought a discussion with Gödel would achieve this.
- Scholz seemed to think that this was in fact the case, but he had not announced it and perhaps would never have done so.
- In the spring of 1932 Scholz, together with Zermelo, went on the "Hellas Tour" for teachers and students from German High Schools.
- At first it might look as if the Aryan Scholz would be unaffected by this but in fact this was far from the case and over the next few years Scholz's life was made extremely difficult because of the Nazi agenda.
- Within three months of the Nazis coming to power, Scholz was trying to get away from Freiburg.
- In the summer of 1933, Scholz visited Berlin and while there he talked with Erhard Schmidt about the possibility of transferring his habilitation to Berlin.
- Both Heffter and Doetsch were asked their opinion of Scholz's work by those deciding whether to award him a grant from the Emergency Association and they replied at the end of April and the beginning of May, rspectively.
- In 1934 Scholz was awarded the grant and, resigning as Doetsch's assistant, he continued to search for another position.
- Scholz has been told by Georg Feigl that Süss was a very nice person but he was not an algebraist.
- Meanwhile Doetsch had essentially eliminated higher algebra lectures from the Freiburg syllabus so Scholz now felt superfluous.
- Scholz next wrote to Hasse asking if he could transfer his habilitation to Göttingen.
- Hasse, however, told Scholz he had no chance of a position at Göttingen.
- Friedrich Karl Schmidt (1901-1977) suggested to Scholz that he might be able to get an appointment in Kiel.
- There can be no question about Scholz.
- In 1935 Scholz's grant from the Emergency Association ended and in August he made his first visit to Kiel.
- Scholz will not understand Nazism.
- In the summer of 1935 Scholz had applied for a position as an assistant to Friedrich Karl Schmidt at Jena.
- Scholz certainly considered trying to get a position abroad but he did not want to leave Germany and he was being advised to remain in Kiel.
- Scholz may also apply for one of these ...
- While in Kiel Scholz supervised the doctoral studies of Gunter Hannink.
- However, in May 1940 Scholz was conscripted into the army and sent as a radio operator to the East.
- At Flensburg, Scholz was a colleague of Ott-Heinrich Keller.
- However, this quickly became irrelevant since Scholz died on 1 February 1942 in Flensburg.
- Although Scholz published results of major importance in the top journals, his work seems not to have been influential except perhaps in as far as it influenced Hasse.
- The reason for the lack of influence may be that Scholz was one of those brilliant mathematicians who are so far ahead of their time that they fail to make an impact since contemporaries fail to understand the significance of their results.
- It seems, however, that few people except Hasse had any idea about the depth of Scholz's work on the norm theorem because his article is, to say the very least, very difficult to read.

Born 24 December 1904, Charlottenburg, Berlin, Germany. Died 1 February 1942, Flensburg, Germany.

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Origin Germany

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive