# 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

**Stanislaw Saks**was born into a Jewish family, his parents being the clerk Filip Salomon Saks (born in Kalisz on 4 May 1872) and Anna Emma Labez Bosak (born 1870). Filip and Anna had been married in 1890 and they had two sons, Stanislaw Saks, the subject of this biography, and Wincenty Saks (born in Kalisz on 26 May 1904).

Stanislaw was born in Kalisz in west-central Poland, not in Warsaw as stated in [1]. He began his education in 1905 at a primary school in Kalisz, then after two years his parents moved to Warsaw and, in 1907, he continued his education at the Michal Kreczmar junior high school in Warsaw. To understand why this school was so important in his upbringing, 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 state 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.

School education was difficult in Russian controlled Poland at this time. Beginning in autumn of 1904 there were school strikes as pupils and their parents protested against school teaching being in Russian and pupils being even forbidden to speak Polish in school. When school strikes occurred, the Russian authorities reacted by closing the school. It appears that the Russian authorities were happy to close schools and keep illiteracy in Poland as high as possible. The Jan Kreczmar high school, a private secondary school, was founded in 1907 by Jan Kreczmar. The Russians allowed private Polish schools, but their number was limited and they were subject to frequent inspections. The school taught in Polish and was run by teachers affiliated to the Society of Polish Culture who created a patriotic atmosphere and made the pupils sensitive to social problems. Many students of this school later played a large role in the socialist movement in the country. After the death of Jan Kreczmar, his brother Michal ran the school and it became known as the Michal Kreczmar High School. Saks completed his studies at this school and received his high school diploma in 1915.

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. He was taught algebra in his first year of studies by Samuel Dickstein.

Kazimierz 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.In addition to Dickstein, two of Saks' first teachers at the University of Warsaw were Zygmunt Janiszewski and Stefan Mazurkiewicz who both began teaching there when the university reopened in November 1915. One of Saks' fellow students was Kazimierz Kuratowski who wrote [3]:-

As early as 1917 [Janiszewski and Mazurkiewicz] were conducting a topology seminar, presumably the first in that new, exuberantly developing field. The meeting of that seminar, taken up to a large extent with sometimes quite vehement discussions between Janiszewski and Mazurkiewicz, were a real intellectual treat for the participants.The ZNMS (Union of Independent Socialist Youth) was founded in 1917 by university students in Cracow, Warsaw and Lwów. It both supported the economic interests of students and undertook educational work. Saks was one of the founders of the Union. Saks became an editor of its paper "Independent Voice". Later he became a member of the Polish Socialist Party (PPS) and wrote articles for

*Robotnik*, the newspaper of the PPS, under the pseudonym "Zygfryd".

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 Poznan. 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 took a break from his studies in 1919-21 serving in the Polish Army and participating in a plebiscite campaign in Upper Silesia which yielded mixed results. He participated in the insurrections; he was a member of the PPS Combat Organisation [Organizacja Bojows] in the Third Silesian Uprising which began in May 1921. He was awarded the Cross of Valour for his patriotic actions.

In 1921 Saks' first mathematics paper,

*Sur l'équivalence de deux théorèmes de la théorie des ensembles*Ⓣ, was published in the second volume of

*Fundamenta Mathematicae.*He begins the paper as follows:-

In a note "Un théorèm sur les ensembles fermés" Ⓣ (1918) M Sierpinski shows without the aid of Zermelo's axiom a generalisation of Cantor's Durchschnittssatz. We propose showing that the said theorem of Sierpinski is equivalent to Borel's theorem and that this equivalence is valid in more general "spaces".Saks continued to study mathematics for his doctorate, returning to the University of Warsaw on 21 November 1921. His thesis advisor was Mazurkiewicz but, as well as his supervisor, he was greatly influenced by Sierpinski who was appointed to the university in 1919 and began to work closely with Mazurkiewicz. In 1920 Mazurkiewicz and Sierpinski had 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 on 26 October 1922, Cum Laude Maxima, for the thesis

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

Saks' second paper was written in collaboration with Aleksander Rajchman (1890-1940). Like Saks, Rajchman was born in the Polish part of the Russian Empire into a Jewish family. After being educated in Paris, he returned to Poland in 1919 as an assistant at the University of Warsaw. After the award of a doctorate from Lwów with Hugo Steinhaus as his advisor he was appointed to the University of Warsaw in 1922. We note at this point that Rajchman died in the Sachsenhausen concentration camp in the summer of 1940. The Saks-Rajchman joint paper was

*Sur la dérivabilité des fonctions monotones*Ⓣ (1923). They write:-

The point of this note is to give a simple elementary proof of a theorem of M Lebesgue, according to which any monotonic function is almost everywhere derivable, and to the theorem of M Fubini, according to which a convergent series of non-decreasing functions can be almost everywhere differentiated term by term.In 1924 Saks published a number of papers:

*Sur les nombres dérivés des fonctions*Ⓣ;

*Sur un théorème de M Lusin*Ⓣ;

*Sur l'homéomorphie des variétés deux dimensions*Ⓣ; (with Antoni Zygmund)

*Sur les faisceaux des tangentes à une courbe*Ⓣ; and

*Sur l'homéomorphie des variétés à deux dimensions*Ⓣ. They were all published in

*Fundamenta Mathematicae.*The last of these papers consisted of material from his thesis. He writes:-

This Memoir comprises the first part, slightly modified, of my thesis presented in the month of May 1922 to the University of Warsaw to obtain the degree of doctor of philosophy.He gives the following acknowledgements in this paper:-

Before finishing it, allow me here to address my affectionate thanks to MM Mazurkiewicz and Sierpinski, the professors at the University of Warsaw who were kind enough to guide the beginnings of this work, and MM Knaster and Kuratowski whose help was so precious for the writing of this Memoir. It is to M Kuratowski, who was kind enough to take an interest in this work, that I owe a special gratitude for the simplifications that he was able to bring to several of my statements as well as for the bibliographical information from which I took great advantage.Even before the doctorate was awarded, Saks began teaching at Warsaw Technical University and from 1926 he also lectured at the University of Warsaw after he habilitated there on 22 October 1926. The following year, from 7 to 10 September, he attended the First Polish Mathematical Congress held at Lwów as part of the Warsaw contingent and lectured to the conference. Steinhaus recalls a contribution Saks made around the same time (see for example [4]):-

In 1927, a collaboration [between Steinhaus and] Banach resulted in a paper "Sur le principe de la condensation des singularités" Ⓣ published in 'Fundamenta Mathematicae'. ... Stanislaw 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 ....Saks married the school teacher Zofia Karolina Korzeniowski (11 September 1902, Warsaw - 3 June 1992, Warsaw). Zofia was the daughter of Mieczyslaw Maksymilian Korzeniowski (1870-1908) and Maria Aniela Fiszer (1872-1938). Stanislaw and Zofia Saks had one son, Marek Saks.

Banach and Saks collaborated on a joint paper

*Sur la convergence forte dans le champ*$L^{p}$ Ⓣ. 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 sailed from Hamburg, Germany, on the ship President Roosevelt, arriving in New York on 11 September 1931. He spent most of his time in the United States at Brown University where he worked with Jacob David Tamarkin. The work they did together led to their joint paper

*On a Theorem of Hahn-Steinhaus*which was published in the

*Annals of Mathematics*in 1933.

Antoni 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 Polish in 1930 and in French 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

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

*The Lebesgue integral in abstract spaces*as an appendix. It is quite remarkable that this work should still [in 2020] be in print as a Dover Hardback edition of 2012 and as a paperback Franklin Classics Trade Press of 2018.

For Prefaces to these two books by Saks, see THIS LINK.

For some extracts of reviews of various editions of these books, see THIS LINK.

We have already mentioned Mazurkiewicz, Sierpinski, 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:-

Stanislaw Saks was a brilliant lecturer, universally respected and very popular with his colleagues and students.Zygmund also writes about Saks as a teacher in [20]:-

Saks was an extremely talented lecturer. The precision, clarity and elegance of his style were very attractive and attracted listeners, to which should be added his personal kindness when organising the work and scientific cooperation of students.Three times Saks was put forward as a candidate for a mathematics chair. Despite the support of most leading Polish mathematicians the proposal of the Faculty Council of Mathematics and Natural Sciences of the Stefan Batory University of Vilnius was not approved by the Ministry of the Ministry of Agriculture and Rural Development in 1932 because of lack of funds for the founding a new chair. The application to the Faculty Council of Mathematics and Natural Sciences of the University of Warsaw in 1936 ran into difficulties due to the growing anti-Semitism and, to avoid further unpleasantness, Saks withdrew the application himself. The next proposal of the Faculty Council of Mathematics and Natural Sciences of the Stefan Batory University of Vilnius in 1939 failed because of the outbreak of war before a decision had been reached.

When war broke out in 1939 Saks joined the Polish army and retreated with them to Lwów which was by that time under Russian control. There he worked with Banach in the Soviet held town for two years, being appointed an extraordinary professor at Lwów 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 Lwów, 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 more about the Scottish Café at THIS LINK.

Hugo Steinhaus writes about these times in [4]:-

Although our Soviet "guests" needed a lot of coaching before they acquired some manners - such as removing their caps at appropriate times - it must be admitted that they got the university machine up and running. They made Banach Dean of the Division of Mathematics and Natural Sciences, and thanks to his belief that cooperation was optimal in our situation, he managed to get Saks and Knaster appointed professors - not an easy thing to do since the Soviets seemed to have an innate dislike of people from Warsaw. The heads of the departments in the Division were Banach, Schauder, Zarzycki, Mazur and I, while the extraordinary professors - that is, without departments under them - were Saks, Knaster, Chwistek, Jacob, Auerbach, and Orlicz. Our docents were Eidelheit, Szpilrajn [Marczewski], and Wojdyslawaki. This represented a powerful collection of mathematicians, and in normal times such a team would have achieved a great deal. Of course, the Polish Mathematical Society was no more, but the mathematicians of the division continued the scientific meetings informally. We also managed to bring out Volume IX of 'Studia Mathematica', with the slight modification that each paper now had to include a Ukrainian summary. Following Lavrentiev's visit, a number of us - Banach, Zarycki, Schauder, Mazur, Saks and I - became corresponding members of the Kiev Academy of Sciences, a smart move, in particular since it entitled each of us to a payment of a few hundred rubles a month, which, supplemented with our university salaries, enabled us to live tolerably well.In June 1941 the German army entered Lwów 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).

Zygmund writes in the Preface to the English edition of

*Analytic functions*(1952):-

Stanislaw Saks was a man of moral as well as physical courage, of rare intelligence and wit. To his colleagues and pupils he was an inspiration not only as a mathematician but as a human being. In the period between the two world wars he exerted great influence upon a whole generation of Polish mathematicians in Warsaw and Lwów. In November 1942, at the age of 45, Saks died in a Warsaw prison, victim of a policy of extermination.Zygmund also writes in [20]:-

Saks left a son Marek and a wife Zofia née Korzeniowski. He also left the memory of not only an outstanding scholar, but also an extremely noble man. For those who knew him closely, he will always be a beautiful memory.

### 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). - K Kuratowski,
*Half a century of Polish mathematics*: remembrances and reflections (Regamon Press, Oxford, 1980). - H Steinhaus,
*Reminiscences*(Polish) (Cracow, 1970). - A S Besicovitch, Review: Théorie de l'Intégrale, by Stanislaw Saks,
*The Mathematical Gazette***19**(232) (1935), 57-58. - Biography of Stanislaw Saks,
*fundacia matematyków wroclawskich*.

http://www.fmw.uni.wroc.pl/nagrody-stypendium-saksa/życiorys-saksa/życiorys-stanislawa-saksa - T Grebski, Stanislaw Saks,
*The Mathteacher*.

http://www.tomaszgrebski.pl/viewpage.php?page_id=285 - M Heins, Review: Analytic functions (1952), by S Saks and A Zygmund,
*Bull. Amer. Math. Soc.***60**(5) (1954), 495-497. - B Jessen, Review: Theory of the Integral (2nd revised edition), by Stanislaw Saks,
*Matematisk Tidsskrift. B, tematisk tidsskrift. B*(1938), 65-67. - Z Pawlikowska-Brozek, Stanislaw Saks 1897-12-30 - 1942-11-23,
*Internetowy Polski Slownik Biograficzny*.

https://www.ipsb.nina.gov.pl/a/biografia/stanislaw-saks - J D Tamarkin, Review: Théorie de l'Intégrale, by Stanislaw Saks,
*Bull. Amer. Math. Soc.***40**(1) (1934), 16-18. - J D Tamarkin, Review: Theory of the Integral (2nd revised edition), by Stanislaw Saks,
*Bull. Amer. Math. Soc.***44**(9.1) (1938), 615-616. - J Todd, Review: Theory of the Integral (2nd revised edition), by Stanislaw Saks,
*The Mathematical Gazette***22**(248) (1938), 84-85. - 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),
*Wiadomosci matematyczne*(2)**24**(1982), 156-158. - E M Wright, Review: Analytic functions (2nd edition), by S Saks and A Zygmund,
*The Mathematical Gazette***54**(388) (1970), 187-188. - E C Zeeman, Review: Analytic functions (1952), by S Saks and A Zygmund,
*The Mathematical Gazette***39**(327) (1955), 79-80. - 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.

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Written by J J O'Connor and E F Robertson

Last Update July 2020

Last Update July 2020