# Stanisław Saks

### Quick Info

Kalisz, Russian Empire (now Poland)

Warsaw, Poland

**Stanisław Saks**was a Polish mathematician who worked in topology, set theory and functional analysis. He was one of the frequenters of the

*Scottish Café*.

### Biography

**Stanisław Saks**was born into a Jewish family, his parents being Philip Saks and Ann Labedz Saks. Stanisław was born in Kalisz in west-central Poland, not in Warsaw as stated in [1], but he did attend secondary school in Warsaw. He entered the University of Warsaw in November 1915. In fact this was a very special occasion for education in Warsaw and we should look at a little Polish history to explain just why this was so special.

Poland had been partitioned in 1772 with the south called Galicia and under Austrian control while Russia controlled much of the rest of the country, in particular the Warsaw region. In a policy implemented between 1869 and 1874, all secondary schooling had to be conducted in the Russian language. The University of Warsaw was closed by the Russian administration in 1869 and from then until World War I there were no Polish language universities.

In August 1915 the Russian forces, which had held Poland for many years, withdrew from Warsaw. Germany and Austria-Hungary took control of most of the country and a German governor general was installed in Warsaw. One of the first moves after the Russian withdrawal was the refounding of the University of Warsaw and it began operating as a Polish university in November 1915. Saks entered the newly refounded university on this occasion of great rejoicing for all patriotic Poles. Kuratowski tells us in [3] that:-

... in a short time [Saks] shone as one of the most talented students of mathematics. Mathematical analysis, and especially those of its branches which used modern methods of set theory and topology, became his main field of interest.At the Paris Peace Conference in 1919 Poland demanded the return of the former Prussian sector of Upper Silesia from Germany. There had already been an uprising against the Germans in December 1918 in Poznań. The Treaty of Versailles was signed in the summer of 1919 and it gave Poland part, but not all, of the Prussian sector. There were three insurrections in Upper Silesia as the Polish population rebelled against the German administration. Saks participated in the insurrections and was awarded the Cross of Valour for his patriotic actions.

Saks continued to study mathematics for his doctorate, which was supervised by Mazurkiewicz, at the University of Warsaw. As well as his supervisor he was greatly influenced by Sierpiński who was appointed to the university in 1919 and began to work closely with Mazurkiewicz, Saks' supervisor. In 1920 Mazurkiewicz and Sierpiński became editors of

*Fundamenta Mathematicae*and Polish mathematics was flourishing. Certainly, therefore it was an exciting period during which Saks embarked on a research career and he was awarded his doctorate in 1922 for the thesis

*A contribution to the theory of surfaces and plane domains*.

Even before the doctorate was awarded, Saks began teaching at Warsaw Technical University and from 1926 he also lectured at the University of Warsaw. The following year, from 7 to 10 September, he attended the First Polish Mathematical Congress held at Lvov as part of the Warsaw contingent and lectured to the conference. Steinhaus recalls a contribution Saks made around the same time (see for example [2]):-

In 1927, a collaboration [between Steinhaus and] Banach resulted in a paper "Sur le principe de la condensation des singularités" Ⓣ published in Fundamenta Mathematicae 9. ... Stanisław Saks helped edit the paper and later deepened the result by introducing in its proof the notion of category. This helped make the paper an important contribution to the Polish success between the two wars in the area of functional operations ....Banach and Saks collaborated on a joint paper

*Sur la convergence forte dans le champ Lp*Ⓣ. Published in 1930 [2]:-

... the paper addressed the problem of summability in abstract spaces. This gave birth to a class of spaces that are still actively studied and that are now called spaces with the Banach-Saks property.Saks continued to teach at both Warsaw institutions until 1939. However, he did spend a year, namely academic year 1931-32, in the United States on a visit financed through a Rockefeller scholarship. He spent most of his time in the United States at Brown University.

Zygmund had become a colleague and friend of Saks early in his career. He was appointed to Warsaw Technical University shortly after Saks began to lecture there, and the two began to collaborate on mathematical projects. One of the works for which Saks is most famous is their joint book

*Analytic functions*which appeared in 1938 as volume eight in the

*Mathematical Monographs*series. This book received a prize from the Polish Academy of Sciences in the year it was published. This was not Saks' first monograph, however, for he had already published an important volume in the

*Mathematical Monographs*series. This earlier volume, the volume two in the series published in 1933, was his famous work

*Theory of the integral*. This monograph was based on lecture courses Saks had given at the University of Warsaw. Hawkins, in [1], writes:-

In this highly original work Saks systematically developed the theory of integration and differentiation from the standpoint of countably additive set functions.In 1937 an English translation of

*Theory of the integral*was published with Banach's article

*The Lebesgue integral in abstract spaces*as an appendix.

We have already mentioned Mazurkiewicz, Sierpiński, and Zygmund as major influences on Saks. We should mention, in addition, that he was also influenced by Luzin's work. Saks' contributions, including the important texts mentioned above [1]:-

... involved the theory of real functions, such as problems on the differentiability of functions and the properties of Denjoy-Perron integrals.Kuratowski in [3] describes of Saks as a teacher:-

Stanisław Saks was a brilliant lecturer, universally respected and very popular with his colleagues and students.When war broke out in 1939 Saks joined the Polish army and retreated with them to Lvov which was by that time under Russian control. There he worked with Banach in the Soviet held town for two years, being appointed a professor at Lvov University which had been renamed the Ivan Franko University by the Russians. At this time he taught in the Department with Banach at its head. In Lvov, Saks joined the community of mathematicians working and drinking in the Scottish Café. He contributed problems to the

*Scottish Book*, the famous book in which the mathematicians working in the Café entered unsolved problems. One problem on subharmonic functions was entered into the

*Book*by Saks on 8 February 1940 with the promise of a kilo of bacon to the first person to solve it!

You can see a picture of the Scottish Café at THIS LINK.

In June 1941 the German army entered Lvov and a systematic extermination of Jews began. Saks returned to Warsaw where he was arrested, put in prison and killed by the Gestapo (allegedly while attempting to escape from prison).

### References (show)

- T Hawkins, Biography in
*Dictionary of Scientific Biography*(New York 1970-1990). See THIS LINK. - R Kaluza,
*The life of Stefan Banach*(Boston, 1996). - H Steinhaus,
*Reminiscences*(Polish) (Cracow, 1970). - P Wojtaszczyk, The Work of Saks in Functional Analysis,
*The Mathematical Intelligencer***9**(1) (1987), 41-43. - P Wojtaszczyk, Bibliography of Stanislaw Saks (Polish),
*Wiadomosci matematyczne*(2)**24**(1982), 158-160. - P Wojtaszczyk, The papers of S Saks in functional analysis (Polish),
*Wiadom. Mat.***24**(2) (1982), 156-158. - A Zygmund, Stanislaw Saks 1897-1942,
*The Mathematical Intelligencer***9**(1) (1987), 36-41. - A Zygmund, Stanislaw Saks (1897-1942) (Polish),
*Wiadomosci matematyczne*(2)**24**(1982), 145-156.

### Additional Resources (show)

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Written by J J O'Connor and E F Robertson

Last Update February 2000

Last Update February 2000