Beginning in the spring of 1906 she taught for about eighteen months as a teacher at the manor house of the Werdeck family near Cottbus. At the same time she took private mathematics instruction with Rudolf Tiemann so that she could take the final level school examinations. She could only sit these in Berlin, which she did at the Luisenstädtischen High School on 16 September 1907. Nugel then began her studies at Berlin University, attending lectures in mathematics, physics and German. It is worth looking for a moment at the mathematics department where Nugel was receiving her education.
Until he last years of the 19th century, Berlin had been the leading centre for mathematics in Germany, perhaps in the world, with Kummer, Weierstrass and Kronecker. However Schwarz had succeeded Weierstrass accepting a professorship in Berlin in 1892; Kronecker died in 1891 and was succeeded by Frobenius; and Kummer had retired and been replaced by Fuchs. Schwarz certainly seemed to give up mathematics after his appointment and it was left largely to Frobenius to try to maintain Berlin's leading status. Göttingen soon was recognised at the dynamic centre of German mathematics. The final sign that Göttingen had overtaken Berlin came in 1902 when Frobenius and Schwarz chose Hilbert to succeed to the Berlin chair which had become vacant on the death of Fuchs. Hilbert turned down the offer, preferring to remain at Göttingen. He became the first mathematician since Gauss to turn down a chair at Berlin, considered up to that time as the ultimate goal a mathematician could reach. The Berlin chair was then filled by Schottky who was a personal friend of Frobenius but, like Schwarz before him, he had moved to Berlin after his best days for mathematical research were behind him. Nugel attended lectures by Frobenius and Schur, who at the time was a dynamic young lecturer. She also attended lectures by Oskar Knobloch, Eugen Blasius, Arthur Wehnelt, and Heinrich Rubens.
After three terms of study in Berlin, Nugel moved to the University of Munich where she spent one term attending lectures by Ferdinand Lindemann and Aurel Voss. Then, beginning in the autumn of 1909, she began her doctoral studies at Halle. Her research supervisor was August Gutzmer, but she also gained considerable benefit by attending lectures by Cantor and Wangerin. She submitted her thesis Die Schraubenlinien. Eine monographische Darstellung to the Martin-Luther University of Halle-Wittenberg in 1912 and she was given oral examinations in mathematics, physics and philosophy over the two days 27-28 February. She was awarded the degree with distinction, graduating on 9 July 1912. In receiving a doctorate in mathematics, Nugel became one of the first German women to receive such a degree. Before her was Marie Gernet (awarded 1895 by Heidelberg), Annie Reineck (awarded 1907 by Bern) and Emmy Noether (awarded 1908 by Erlangen). Later in July Nugel passed the state examinations qualifying her to teach mathematics, physics and German in a Gymnasium.
Immediately after passing these examinations, Nugel was appointed as a teacher in the Augusta school on Cottbus. By this time she was engaged to be married to Louis Hahn who had been a research student studying for his doctorate in history at Halle at the same time as Nugel. They were married on 4 April 1914 and Nugel left her teaching post at Cottbus at this time and the newly married couple moved to Altena, Westphalia, where Louis Hahn had a job as an editor. On 1 March 1915 their first daughter Ingeborg was born and near the end of the year they moved from Altena to Emden. This was Louis Hahn's home town and there he took over as editor of a newspaper owned by his family.
Of course World War I had begun in August 1914 and Frieda Hahn had to make a contribution to the war effort despite having a young family. From the spring of 1916 she did war work at the Kaiser-Friedrich-Oberrealschule, but with her second child due she took a break from December 1916 until the spring of 1917. Her second child, Helmut was born on 2 March 1917 and she returned to her work very shortly after the birth. She continued with this war work until the end of 1918. She had two further children, Gerold born on 17 October 1920 and Waltraut born on 11 September 1922. With a young family Frieda Hahn could not take employment, but she was able to give private tuition in mathematics, physics and German in her home, which she did for ten years from 1918 to 1928 :-
All their children developed well under their care and showed particularly strong mathematical achievements. The daughters studied at the Lyzeum in Emden, the sons at the High School ... Apart from the tasks of educating she had to solve, and fitting in the private instruction which she gave, [Frieda] also supported the journalistic and historical work of her husband during the years of the Weimar Republic.However the 1920s were years of extreme difficulty in Germany with much political unrest. In January 1923 there was military occupation of the German industrial district in the Ruhr valley by France and Belgium. This triggered the beginning of hyperinflation and many businesses collapsed. One of these was the newspaper business of which Louis Hahn was both manager and editor. With no job, he worked at home, mostly doing unpaid work. It fell to Frieda Hahn to support the family and she returned to teaching. She taught for a few hours a week at the Kaiserin-Augusta-Viktoria school in Emden but in order to enter school teaching full time she had to take examinations again in Berlin. She took the examinations on 1 October 1928 and then took up full time teaching in Emden from 1 July 1930. As she had done earlier she taught mathematics, physics and German.
As World War II progressed conditions became increasingly difficult in Emden, particularly since it was the German seaport for Westphalia. The town came under increasing British and American bomb attacks and a decision was taken to move the Emden school to Bad Wildungen. Frieda Hahn had to leave her husband in Emden, which must have been a terrible experience for her knowing that the town was continually under attack. Indeed the school buildings in Emden were destroyed on 5 September 1944. However far worse was knowing that her two sons were in extreme danger, Helmut as a Captain in Russia and Gerold as a Lieutenant in Lorraine. In the summer of 1944 she received the word that she had feared; both of her sons were missing, presumed dead. There was only a few weeks between the two messages. Confirmation of the deaths was not made until 1961. Although Louis Hahn survived the war, he died in 1952 after a long illness. Frieda had retired from teaching in 1945 and cared for her husband through his illness.
Frieda Hahn continued to live in Emden, but after the death of her husband she lived with her daughter Ingeborg. Her younger daughter Waltraut was married and living in Bonn. In 1955 she moved to Bad Godesberg to support her younger daughter and there she helped to educate her three grandchildren. In 1962, fifty years after obtaining her doctorate, her thesis was deemed "mathematically historically particularly valuable" and she was honoured by the Martin-Luther University of Halle-Wittenberg. She also received honours from Bonn and from Cottbus.
There is one aspect of Frieda Hahn's life which we have not mentioned above. This is the articles she wrote arguing for women's rights, for better education for women, and argued from her own experiences on how the school education system might be improved. These essays include Die deutsche Hausfrau und der Krieg (1916), Frauenbewegung und Kinderemanzipation (1919), Die Frau in der Gemeindeverwaltung (1921), and Staat und Stadt Hamburg: Die dreijährige Grundschule vom Standpunkt der Mutter (1925).
Article by: J J O'Connor and E F Robertson