**Hans Reichardt**was born in Altenburg, a city in central Germany on the Pleisse River, about 40 km south of Leipzig. His father was a medical doctor. Hans attended the Humanistic Gymnasium in Altenburg where he learnt the three ancient languages of Latin, Greek and Hebrew. In 1925 he entered the University of Jena where he studied mathematics, physics and philosophy. He left Jena to spend one semester studying at the University of Königsberg in 1928, after which he went to Berlin where he was taught mathematics by Ludwig Bieberbach, Richard von Mises, Erhard Schmidt and Issai Schur. He also attended physics lectures in Berlin given by Albert Einstein, Max Planck and Max von Laue. From this outstanding collection of lecturers, it was Schur with his course of lectures on algebraic number theory which particularly attracted him. He remained in Berlin until the autumn of 1931 when he went to Hamburg intent on learning more about algebraic number theory. He spent one semester at the University of Hamburg attending lectures by Erich Hecke and Emil Artin. After this semester, he moved again, this time to the University of Marburg where he took courses on mathematics, physics and philosophy while undertaking research advised by Helmut Hasse. He was awarded his doctorate in 1932 for his thesis

*Arithmetische Theorie der kubischen Körper als Radikalkörper*Ⓣ.

On 30 January 1933 Hitler came to power and on 7 April 1933 the Civil Service Law provided the means of removing Jewish teachers from the universities. This did not affect Reichardt directly but it had a major affect on the lecturers in the universities in which he obtained posts. He joined the NSDAP (commonly known in English as the Nazi Party) in 1933. Three of his papers on algebraic number theory appeared in 1933, namely* Die Anzahl der durch 4 teilbaren Invarianten der Klassengruppe eines beliebigen quadratischen Zahlkörpers* Ⓣ; *Zur Struktur der absoluten Idealklassengruppe im quadratischen Zahlkörper* Ⓣ; and a paper based on his thesis *Arithmetische Theorie der kubischen Körper als Radikalkörper* Ⓣ. In 1934 he was appointed to the University of Frankfurt, becoming Carl Ludwig Siegel's assistant. The Civil Service Law did not affect Siegel who was an Aryan (to use the terminology of the time which Siegel hated) and, at this stage it did not affect some other teachers at Frankfurt, namely Paul Epstein, Ernst Hellinger or Max Dehn who, although Jewish, fell under a clause which exempted non-Aryans who had fought for Germany in World War I. Otto Szasz, however, had been dismissed from his post and had emigrated to the United States. Although Siegel was not affected by the Civil Service Law, he hated the Nazi regime and this was the beginning of a very unhappy time for him.

Reichardt's post was only for a one year and, in 1935, he moved to Jena where he was appointed as Friedrich Karl Schmidt's assistant. Schmidt had held a temporary post in Göttingen in 1933 and, in the same year succeeded Richard Courant as editor of Springer-Verlag's famous "Yellow Series" of mathematical monographs when Courant was dismissed because he was Jewish. Schmidt was a Roman Catholic, and not Jewish, but he was quickly out of favour with the Nazis when he refused to remove Richard Courant's name from the title page of the Springer series. He also maintained contacts with his Jewish colleagues which displeased the Nazis. In October 1934 he had been called to Jena as ordinary professor of mathematics and director of the mathematical institute. One year later, Reichardt was appointed as his assistant. Reichardt spent two years in this position during which time he published four further papers* Die Diskriminante einer normalen einfachen Algebra* Ⓣ; *Der Primdivisorsatz für algebraische Funktionenkörper über einem Konstantenkörper* Ⓣ; *Über Normalkörper mit Quaternionengruppe* Ⓣ; and *Eine Bemerkung zur vorstehenden Arbeit von F K Schmidt* Ⓣ.

In 1937 Reichardt moved again, this time going to the University of Leipzig where he worked under Bartel van der Waerden who had been appointed professor of mathematics there in 1931. Although working in Germany, van der Waerden refused to give up his Dutch citizenship and this was making his life very difficult around the time Reichardt became his assistant in 1937. Reichardt worked mainly on two particular areas of algebraic number theory, namely on the inverse problem of Galois theory and on the rational points on an elliptic curve. In March 1939, he submitted his habilitation thesis *Über die Diophantische Gleichung* *ax*^{4} + *bx*^{2}*y*^{2} + *cy*^{4} = *ez*^{2} Ⓣ to the Philosophy Faculty of the University of Leipzig and became a docent at Leipzig in 1940. However, by this time World War II had begun with the Germany invasion of Poland in September 1939. During the war Reichardt kept his position on the staff at the University of Leipzig but did war work for the navy and, from 1943, worked in Berlin for Telefunken AG, one of the major producers of electrical and communications equipment. Telefunken played an important part in Germany's war effort, supplying radio transmitters and radar equipment to help defend the country from the Allied bombing attacks.

After the war, from 1946 to 1952 Reichardt was in the Soviet Union, where he worked on problems of missile technology on the island of Gorodomlja in Lake Seliger in the Valdai Hills which is the source of the river Volga. There had been a biological research station on the island of Gorodomlja since 1928 but it was only in 1946 that a research and development facility for space rockets was established there. Reichardt was not the only German working at the research facility, for several German rocket engineers, such as Helmut Gröttrup who had been Wernher von Braun's assistant during his period developing German rockets during World War II, lived and worked there. Reichardt returned to Germany from the Soviet Union in 1952 when he was appointed extraordinary professor at the Humboldt University in Berlin. In 1954 he became a full professor with a chair which he held until he retired and became professor emeritus in 1973. At the Humboldt University he supervised the doctorates of many students, including Helmut Boseck, Gunter Schwarze, Rolf Sulanke, Helmut Koch, Manfred Peschel, Herbert Frank, Thomas Friedrich, Ernst-Wilhelm Zink, and Andreas Schierwagen. All the students we have named have become university lecturers supervising their own doctoral students. In 1959, in addition to his university chair, Reichardt was appointed as Director of the Institute of Pure Mathematics of the Berlin Academy of Sciences where he also headed the number theory research group. In the 1960s Reichardt was a founding organiser of the Mathematical Olympiad Competitions in the German Democratic Republic.

Reichardt's mathematical interests turned towards differential geometry and later towards the history of mathematics. One of his first publications on the history of mathematics was *Gauss-Gedenkband, herausgegeben anlässlich das 100 Todestages am 23 Februar 1955* Ⓣ (1957) in commemoration of the 100^{th} anniversary of Carl Friedrich Gauss's death. Also in 1957 he published the book *Vorlesungen über Vektor- und Tensorrechnung* Ⓣ. In 1960, in collaboration with Wilhelm Blaschke, he published *Einführung in die Differentialgeometrie* Ⓣ. Reichardt continued his deep interest in Gauss and his contributions, publishing *Gauss und die nicht-euklidische Geometrie* Ⓣ in 1976. Ivor Grattan-Guinness writes in a review:-

Nine years later, in 1985, Reichardt publishedThis short book, written as a contribution to Gauss celebrations in1977, covers rather more ground than its title suggests, for it starts with the Greek tradition and wends its way through some eighteenth-century figures and Gauss and then on to Riemann and Hilbert. This is in itself reasonable since Gauss is renowned for his failure to make his insights public. The account is straightforward, and has judicious extracts quoted from Gauss's correspondence and the writings of others. Students may find it an adequate introduction, and draw educational benefit from the models of(pseudo-)Euclidean geometry given in the last chapter. But those seeking deeper historical information about this history, especially the philosophical aspects which are so prominent in it, will do better among the recent literature to read I Toth's works.

*Gauss und die Anfänge der nicht-euklidischen Geometrie*Ⓣ. This book contains a reprint of Reichardt's 1976 book

*Gauss und die nicht-euklidische Geometrie*Ⓣ but to this had been added reprints of papers on non-euclidean geometry by Janos Bolyai, Nikolai Ivanovich Lobachevsky and Felix Klein. He also contributed articles on Gauss to various encyclopaedias, for example the 1974 edition of

*Encyclopaedia Britannica*.

We should mention another aspect of Reichardt's contributions, namely his work with the Heinrich-Hertz-Gymnasium in Berlin. The high school was named after the physicist Heinrich Hertz in 1961 but the school only received its mathematical emphasis in 1965 through the efforts of Reichardt and his colleague at the Humboldt University in Berlin, Heinrich Grell (1903-1974). Grell had been a doctoral student of Emmy Noether and had worked at the University of Jena and the University of Halle. However, he had lost his teaching licence in 1935 after being accused of acts of homosexuality. After undertaking war work, he was reinstated and appointed as a professor at the Humboldt University in 1948 where he was joined by Reichardt four years later. He was also a colleague of Reichardt's in the German Academy of Sciences where the two worked closely. Reichardt and Grell were the driving force behind the movement of the Heinrich-Hertz-Gymnasium towards being a specialist mathematics school and, by 1969 when it moved to new buildings, all classes in the school were mathematically oriented. The school quickly gained an outstanding reputation throughout the whole country.

Reichardt, who became professor emeritus in 1973, received many honours for his contributions. He was elected a corresponding member of the Berlin Academy of Sciences in 1962 and, in the same year, elected a member of the German Academy of Scientists Leopoldina. In 1964 he became a full member of the Berlin Academy of Sciences. In 1961 and again in 1964 he received the National Award for Science and Technology of the German Democratic Republic.

**Article by:** *J J O'Connor* and *E F Robertson*

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