# Alexander Dinghas

### Born: 9 February 1908 in Smyrna (now Izmir), Turkey

Died: 19 April 1974 in Berlin, Germany

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**Alexander Dinghas**'s father was a primary school teacher. Alexander attended primary school in Smyrna and began his secondary schooling there. In 1922 his parents moved from Smyrna to Athens and Alexander moved with the family to complete the last three years of his secondary schooling there. In 1925 he entered the Athens Technical University where he studied engineering, graduating in 1930 with a diploma in electrical and mechanical engineering. He married Fanny Grafiadou in 1931.

In 1931 Dinghas began his studies at Berlin. His original intention was to study physics and he began taking courses in both physics and mathematics, as well as some philosophy courses. The three professors of mathematics were Schmidt, Schur and Bieberbach. However, many other talented mathematicians and theoretical physicists were also at Berlin and influenced Dinghas. In particular Schrödinger, von Mises, von Laue, von Neumann, Richard Rado, Bernhard Neumann and Wielandt. It was the teaching of Schmidt in particular which convinced Dinghas that mathematics rather than physics was the subject for him to pursue.

Right from the time he began his studies in 1931, Dinghas became interested in Nevanlinna theory. He attended lectures on the topic given by Schmidt and it was these lectures which Schmidt gave "with almost religious enthusiasm" which turned Dinghas from an engineer/physicist into a mathematician. He studied for his doctorate under Schmidt and it was awarded in 1936. Two years later he submitted his habilitation thesis and obtained the right to lecture in a university.

However, as a non-German his career during the Nazi years was extremely difficult. Despite the award of his habilitation he did not receive a permanent teaching post although he did manage to continue teaching throughout. However, after the end of World War II he became professor at the reopened Humbolt University in 1947. From 1949 until his death he was a professor at the Free University of Berlin and director of the Mathematical Institute there.

His work is in many areas of mathematics including differential equations, functions of a complex variable, functions of several complex variables, measure theory and differential geometry. His most important work was in function theory, in particular Nevanlinna theory and the growth of subharmonic functions.

Dinghas produced a series of papers on isoperimetric problems in spaces of constant curvature. His work here was much influenced by Schmidt who also produced important results which Dinghas used in his work.

The article [5] contains a bibliography of 121 papers by Dinghas, and in addition lists three books and five historical or general articles. Although Dinghas had a wonderful feel for mathematics, he frequently waved his hands somewhat when he gave a proof. His papers were [5]:-

His three books are... not always easy to read and on occasion proofs were only sketched or contained serious gaps. However, the gaps have largely been filled in and the vision of the basic ideas will secure a permanent niche for their author in the theory of functions.

*Vorlesungen über Funktionentheorie*(1961),

*Minkowskische Summen und Integrale. Superadditive Mengenfunktionale. Isoperimetrische Ungleichungen*(1961), and

*Einführung in die Cauchy-Weierstrass'sche Funktionentheorie*(1968). The first of these is described by a reviewer:-

The treatise is in four parts. The final part containing chapters on the maximum principle and the distribution of values, geometric function theory and conformal mapping, and Nevanlinna theory.This treatise presents an amazing amount of function theory in its modest400pages. The presentation is concise and clear. Also each of the nine chapters ends with a section... which presents various interesting topics, frequently in quite abbreviated form. Examples are the formula of Plana-Abel-Cauchy, the theorem of Julia-Wolff-Caratheodory, and the theory of Nevanlinna and of Hallstrom. Each chapter contains a useful section on the history and literature of the chapter's topics. This book will clearly prove valuable as a reference or as a text for any student who already knows a modest amount of elementary function theory.

His 1968 book is described as follows:-

Hayman writes of Dinghas's personality in [5]:-This little paperback book contains in107pages the core material and usual preliminaries of the standard first course in analytic functions of a complex variable. Definitions and theorems are stated precisely in modern terminology, but the underlying attitude is basically traditional and perhaps somewhat innocent topologically. ... Some topics treated which are not always found in the older short elementary texts are the homotopy concept for closed curves, cluster sets of meromorphic functions, removable compact sets of singularities, the monodromy theorem, and the Mittag-Leffler partial fraction expansion of a meromorphic function.

Dinghas received many honours for his work. In particular he was elected to membership of the Heidelberg Academy, the Finnish Academy and the Norwegian Academy.Dinghas was a complex personality and a German professor of the old school. On the one hand he expected and was awarded the respect due to his position, and his students and colleagues were somewhat in awe of him. ... However this was only one side of his nature. he was extremely hospitable and generous and had a puckish sense of humour. ... He felt profound sympathy for those less fortunate. On one occasion he saw a man in a restaurant looking rather forlorn and with a single cup of coffee. Dinghas felt the man's hunger and got the waiter to send him food and drink which Dinghas paid for. On another occasion he felt sorry for a newspaper seller and bought every one of his papers. he always supported students against the teaching staff when he felt they had a good case.

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

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