**Alfred Tauber**studied at the University of Vienna, beginning his course in 1884. Although his main interests were in mathematics, he studied a wide range of topics including physics, philosophy and political economy. He undertook research for his doctorate being advised by Gustav von Escherich but he was also strongly influenced by Emil Weyr. He presented his doctoral thesis

*Über einige Sätze der Gruppentheorie*Ⓣ to the University of Vienna in 1888 and was awarded the degree. Tauber's intention was to publish his thesis but in fact this never happened. He continued to study at Vienna working towards his habilitation. In 1891 he completed his dissertation

*Über den Zusammenhang des rellen und imaginären Teiles einer Potenzreihe*Ⓣ. This was published as a 40 page paper in

*Monatsh. Math. Phys*. in the same year and Tauber began to lecture in Vienna as a privatdozent.

He lectured in Vienna on the theory of series, trigonometric series, and potential theory. He published papers such as *Über die Neumann'sche Methode des arithmetischen Mittels* Ⓣ (1894), *Über das Poisson'sche und das demselben conjugierte Integral* Ⓣ (1895), *Über die Newton'sche Näherungsmethode* Ⓣ (1895), and *Druckfehlerberichtigung: über das Poisson'sche und das demselben conjugierte Integral* Ⓣ (1895). In 1895 he began to lecture on the mathematics of insurance. This was a topic which was of little interest to Tauber, yet he was still a privatdozent so needed to earn money and his lectures on the mathematics of insurance gave him a monthly salary. He was able to supplement his income still further in 1899 by giving lectures on the mathematics of insurance at the Technical University of Vienna. He was appointed as an Honorardozent at the Technical University in 1901. Tauber's main income, however, came from his position as Head of Mathematics at the Phönix Insurance Company in Vienna.

Tauber's lack of success in being given a professorial position was certainly not due to any lack of mathematical ability, for he continued to publish a series of high quality papers. For example *Über das specielle Zweitheilungsproblem der hyperelliptischen Functionen* Ⓣ (1896), *Über das Potential einer Doppelbelegung* Ⓣ (1897), *Ein Satz aus der Theorie der unendlichen Reihen* Ⓣ (1897), *Über die Weierstrass'sche Function* Ⓣ (1897), *Über einige Sätze der Potentialtheorie* Ⓣ (1898). Only in 1908 did Tauber get a position as assistant lecturer at the University of Vienna, and at this stage he resigned at head of mathematics at the Phönix Insurance Company, although he remained as an advisor to the company over the next four years. For more on Tauber's work for the Phönix Insurance Company, see [4].

Tauber's research was on function theory and potential theory. He obtained important results on divergent series and the name 'Tauberian Theorems' was coined by Hardy and Littlewood. This all came out of his work on Abel's limit theorem which dated back to 1826. The conditions which Tauber gave to allow him to prove the converse of Abel's limit theorem on power series are now known as 'Tauberian conditions' and appeared in *Ein Satz aus der Theorie der unendlichen Reihen* Ⓣ (1897). This is by far his most significant piece of work. Further major results in this area were obtained by Norbert Wiener. Of lesser importance is Tauber's work on differential equations and the gamma function, but let us give the title of one of his papers on this latter topic, namely *über die unvollständigen Gammafunktionen* (1906).

Although, as we pointed out above, Tauber did not enjoy working on the mathematics of insurance, nevertheless he did produce important contributions to the area. In particular his papers *Über die Hypothekenversicherung* Ⓣ (1897) and *Gutachten für die sechste internationale Tagung der Versicherungswissenschaften* Ⓣ (1909) contain his formulation of the Tisiko equation.

The date of his death is unknown. He was sent by the Nazis to Theresienstadt concentration camp on June 28 1942. Just after Tauber arrived the entire non-Jewish population of 3,700 of Theresienstadt was evacuated and he was one of 53,000 inhabitants of the camp.

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

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