# Otto Szász

### Born: 11 December 1884 in Hungary

Died: 19 December 1952 in Cincinnati, Ohio, USA

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**Otto Szász**studied at the University of Budapest but he went from there to Göttingen, Munich and Paris where he greatly broadened his education. He received his doctorate in 1911 from the University of Budapest and was appointed onto the staff there as a privatdozent. From 1914 he lectured in Frankfurt, first as a privatdozent and then later as a professor, being a colleague of Bieberbach for 6 years.

In 1933 the Nazis came to power in Germany and Szász was forced out of his chair at Frankfurt. It was a period of extraordinary hardship for many mathematicians in Germany, Poland, Hungary and countries around them. Many mathematicians, like Szász, lost their positions. Others suffered far greater hardships; some were sent to concentration camps, many were murdered. However, there was a positive side effect which changed the course of mathematical research in the United States, for many of these top quality European mathematicians went there and, to the country's credit, it did an exceptional job in accepting them and helping them to find positions.

Szász, like many others, left Germany and emigrated to the United States in 1933. His initial position was at the Massachusetts Institute of Technology. His next post was at Brown University and then, in 1936, he was appointed to the Faculty of the University of Cincinnati where he spent the rest of his career. He did make a research visit spending a year at the Institute of Numerical Analysis at the University of California in Los Angeles but he seemed content to devote the rest of his life to teaching, research, and his students in Cincinnati [1]:-

Szász's main work was in real analysis, particularly Fourier series. In fact his most notable research was done before he emigrated to the United States, but this was not too surprising since he was in his fiftieth year when he emigrated. His most important contributions are probably between 1915 and 1930 when he made a series of remarkable contributions to a number of different areas.His steady preoccupation with mathematics, his erudition and broad knowledge of classical and contemporary literature and his perseverance in dealing with open problems of a number of varied fields have secured a firm place for him in the mathematical life of Hungary, Germany and of the United States.

Some of his earliest work was on continued fractions in which he studied certain convergence questions. Perron, influenced by Pringsheim at Munich, had published an important work on continued fractions

*Die Lehre von den Kettenbrüchen*Ⓣ in 1913. Szász generalised some of Perron's results and also, in 1915, published a paper proving one of Perron's conjectures. A few years before Szász began his mathematical researches, Sergei Bernstein had made major contributions to the theory of approximation. Bernstein stated a problem concerning the completeness of a certain set of powers on an interval and, although Szász did not solve this problem, he did make contributions which were themselves important in the development of the theory of approximations.

Other work by Szász made major contributions to questions posed by Landau on the maximum modulus of the partial sums of a power series. He also studied problems on power series related to work of Frigyes Riesz. In fact Szász worked on problems associated with both Riesz brothers, and he gave a very simple proof a theorem by Marcel Riesz on rational functions with given bounds on the unit circle. Some of Szász's contributions to Fourier series related to results proved by Bernstein, Hardy, Littlewood and Fejér.

All these results were achieved before 1933 and many of the mathematicians we have mentioned, such as Perron, Pringsheim, Edmund Landau, and Fejér were all Szász's personal friends. His major contribution during the years from 1915 to 1930 was recognised by the Hungarian Mathematical and Physical Society in 1939 when they awarded him their Julius König prize.

We must not give the impression, however, that Szász did not make any research contributions after emigrating to the United States. His work in this later period was mainly on [1]:-

The following tribute to Szász is made by Szegő in [1]:-... Tauberian theorems, various methods of summability, Gibbs phenomenon, etc.

His students and friends will always warmly remember him as a man of gentle, unassuming and quiet personality. His life and energy were dedicated to the promotion of simple and beautiful problems of mathematics, in particular of the classical analysis. His nearly one hundred and thirty mathematical papers remain a living document of his efforts.

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

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