# Roman Sikorski

### Born: 11 July 1920 in Mszczonów, Poland

Died: 12 September 1983 in Warsaw, Poland

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**Roman Sikorski**'s parents were Ignacy Sikorski (born about 1885 in Osuchów), who was a potter, and Józefa Wasilewska (born about 1891 in Mszczonów). Ignacy and Józefa were married in Mszczonów, a small town in central Poland, in 1910. After elementary schooling in Mszczonów, Roman attended the Adam Skwarczynski Gymnasium in the nearby town of Zyrardów. While studying at this Gymnasium, he was one of the editors of the school magazine "Young blades". Physics and mathematics were his favourite subjects at the Gymnasium so it was a natural choice that he enrolled to study physics at the University of Warsaw.

Sikorski began his university studies in 1937 and, of course, his physics course involved taking various mathematics options. He soon found that he was more enthusiastic about mathematics than physics so he changed to make this his major topic. After two years of study at university, things changed very dramatically with the outbreak of World War II.

On 1 September 1939 German troops entered Poland and the German Luftwaffe began bombing all strategically important sites. By 4 September they were within 60 km of Warsaw which they encircled with two pincer movements coming from the north and south, one to the east of Warsaw the other to the west. On 22 September, Russian troops entered Poland occupying Lwów and on 27 September Warsaw surrendered. The Germans and Russians had agreed to partition Poland between them and this now came about. Warsaw was occupied by the Germans who closed the University of Warsaw. The university buildings became a military barracks. In fact the Germans closed all higher education establishments in Poland for their idea was that they would make use of Poles to carry out their menial tasks so there was no need to educate them.

With the university closed, Sikorski left Warsaw and returned to his home in Mszczonów. Although education was now banned in Poland, and punishable by death, many risked their lives to educate young people in secret. With help from others and working on his own, Sikorski continued to study at what he would later jokingly call the "University of Mszczonów." On 17 January 1945 Warsaw was liberated by Russian troops but at this stage, with the city and university largely destroyed, it was unclear whether the city and its university would be rebuilt. However staff and students who had survived the war began returning to the university and Sikorski was among them. During 1945 he married Krystyna Bobinskich (born 1917); they had one son Krzysztof Lech Sikorski (born 1946), who went on to study engineering and became a construction engineer. The University of Warsaw reopened in December 1945 with 4000 students attending lectures in a campus which was basically little more than a ruin. Sikorski at this stage was both a student but also an assistant, helping to teach other students.

In 1946 Sikorski obtained the only scholarship available in Poland to fund study abroad, and he went to Zürich where he spent eight months. Returning to Warsaw, he now worked with Andrzej Mostowski who had taken up the position of acting professor in September 1946. Sikorski was awarded his Master's degree in 1947 and, advised by Mostowski, he undertook research for his doctorate. He submitted his doctoral thesis in 1949, defended his thesis

*On extension of homomorphisms*on 4 July of that year, and was awarded a doctorate in natural and mathematical sciences. A paper from his thesis was published in the 1948 volume of the

*Annales de la Société Polonaise de Mathematique*(which did not appear in print until 1949). He had already been appointed as an assistant professor in 1948, which gave him the right to teach and direct students' scientific work.

From 1947 Sikorski began publishing papers in English and French. The following eight papers appeared in 1947 and 1948:

*On the Cartesian product of metric spaces*(1947);

*Sur les corps de Boole topologiques*Ⓣ (1948);

*Sur la convergence des suites d'homomorphies*Ⓣ (1948); (with Edward Marczewski)

*Measures in non-separable metric spaces*(1948);

*On a generalization of theorems of Banach and Cantor-Bernstein*(1948);

*On the representation of Boolean algebras as fields of sets*(1948);

*Remarks on a problem of Banach*(1948);

*A theorem on extension of homomorphisms*(1948); and

*On an ordered algebraic field*(1948).

In 1949 Sikorski became a research worker in the Institute of Mathematical Sciences in Warsaw, which was the first part of the Polish Academy of Sciences to be established. The Institute of Mathematical Sciences began operating in November 1948 so was a very new institution when Sikorski began working there. Its director was Kazimierz Kuratowski. The Polish Academy of Sciences was founded in 1952 and incorporated the Institute of Mathematical Sciences. In addition to his position in the Institute, on 11 October 1950 he was appointed as an assistant professor in the Warsaw University of Technology becoming, at 30 years of age, the youngest professor in Poland. He was promoted in 1951 and headed the Department of Mathematics in the Faculty of Chemistry at the Warsaw University of Technology where he taught analysis and applications of mathematics. Two years later, in 1952, he was appointed extraordinary professor in the Department of Mathematical Analysis of the University of Warsaw. In 1955 he submitted five papers to the Institute of Mathematical Sciences of the Polish Academy of Sciences for the equivalent of a D.Sc. degree. His submission was examined by Edward Marczewski, Stanisław Mazur and Władysław Orlicz. He became a full professor at the University of Warsaw in 1957 when he was appointed to the Chair of Real Functions. There he taught a range of different topics including the foundations of mathematics, algebra, calculus, differential geometry and topology. In 1962 Sikorski was elected to the Polish Academy of Sciences as a corresponding member and then in 1969 as a full member. He served as a member of its Committee of Mathematical Sciences, being the Committee chairman from 1969 to 1971. From 1956 to 1977 he was director of Academy's Institute of Mathematical Sciences.

In addition to his impressive research record, Sikorski played an extremely important role in Polish mathematics through his tremendous support for the Polish Mathematical Society. This Society had been founded after World War I but, being unable to operate during World War II, it had to be reestablished in 1945. Kazimierz Kuratowski was president of the Society from 1945 to 1953. Sikorski was an active member in the second half of the 1940s and became Secretary of the Society in 1951. He held this position until 1955, then in 1957 he became Vice-President. He continued in the role of Vice-President until 1965 when he was elected President of the Society, a role he held until 1977. In this year he was forced to give up all his mathematical activities due to ill health but the Polish Mathematical Society recognised his enormous contribution by awarding his honorary membership of the Polish Mathematical Society at this time. At the Ninth Congress of Polish Mathematicians held in Kraków in 1969, Sikorski gave the

*Address presented September 3, 1969 at the inauguration of the Jubilee of the Polish Mathematical Society*(Polish) which was published in 1971. This address contained an account of the rebirth and development of the Polish Mathematical Society since 1945.

The Polish Mathematical Society was only one of several different ways that Sikorski made a major contribution to the development of mathematics in Poland. Another was the editorial work he undertook serving on the editorial boards of a number of journals such as "Fundamenta Mathematicae", "Studia Mathematica", "Colloquium Mathematicum" and "Mathematical Monographs".

There are many mathematical concepts which are named for Sikorski. Let us mention a few: Sikorski spaces, the Rasiowa-Sikorski lemma (Helena Rasiowa worked with Sikorski and this lemma is contained in their joint work as are the other concepts named for these two mathematicians), Hopf-Sikorski algebras, the Loomis-Sikorski theorem (the theorem was discovered by both the American mathematician Lynn Harold Loomis (1915-1994) and Sikorski at the same time but independently), the Loomis-Sikorski representation, Sikorski CW-complexes, the Rasiowa-Sikorski deduction system, Sikorski differential spaces, and Sikorski's trace formula. We have found over 60 papers (as of November 2016) which have titles containing one of these concepts. There are (as of November 2016) 519 papers in MathSciNet with "Sikorski" in the review text. Many relate to his work on Boolean algebras or his work on first order logic. However, there are also many that refer to his work on differential spaces or on Banach spaces.

A number of books by Sikorski have made important contributions to the teaching of mathematics in Poland and others have been research monographs which have been translated into several languages (including English) and have played an important role. His most important monograph is

*Boolean Algebras*which was first published in 1960 with a second edition four years later. R S Pierce, reviewing the first edition writes:-

The same reviewer had even stronger praise for the second edition:-There has long been a need for a book on the mathematical theory of Boolean algebras at the graduate or research level. The author's book fills this need in spectacular fashion.

Other reviews of Sikorski'sThe new edition of the author's distinguished book brings the story of Boolean algebras pretty much up to date. In doing this, it retains all of the virtues of the original work. This monograph is amazingly complete. Everything that the research worker needs to know about Boolean algebras can be found between its covers. Still more remarkable is the fact that the book could serve very well to introduce a serious student to a wide range of topics in set theory, topology, measure theory, logic, and, of course, the theory of Boolean algebras.

*Boolean Algebras*are given at THIS LINK.

Among Sikorski's other books we mention

*Real functions*(2 volumes) (Polish) (1958, 1959);

*Differential and integral calculus: Functions of several variables*(Polish) (1967) which was translated in English as

*Advanced Calculus. Functions of Several Variables*(1969); and

*Introduction to differential geometry*(Polish) (1972). Note that these books ran to several editions, for example the fourth edition of

*Differential and integral calculus*(Polish) appeared in 1977 and the fifth edition in 1980. For extracts from reviews of these books see THIS LINK.

There is one other book which Sikorski wrote jointly with Helena Rasiowa which deserves a special mention. This book,

*The Mathematics of Metamathematics*(1963), is a very interesting and somewhat unusual work. Melvin Fitting gives the following assessment of this book:-

For extracts from two other reviews of this book see THIS LINK.It was a strange book. On the one hand, it was painfully exhaustive and thorough in the presentation of material. Page after page enumerated detailed results almost in the form of a catalogue, dry and utilitarian. On the other hand, the ideas were of a sort I had never come across before, and I was enchanted. This way of using algebra, producing known results in classical logic, then applying similar techniques to non-classical logics to get new results it all seemed like magic. Profound results fell out so effortlessly, it seemed. How could one read this book and remain unaffected?

Sikorski made many trips to give lectures abroad. Countries he lectured in include Switzerland (1956), USSR (1956), USA (1958, 1961, 1966, 1970), Argentina (1958) and Canada (1967). On the first of these trips to the USA, Sikorski was a member of the Institute for Advanced Study at Princeton from September 1958 to December 1958.

Bogdan Mis writes (see [15]):-

Sikorski received many awards for his outstanding contributions. He received the Stefan Mazurkiewicz Award of the Polish Mathematical Society in 1950 and various State prizes such as Officer of the Cross of Merit (1968) and Commander of the Cross of Merit (1974). He also received the Order of Poland Reborn.One of the wittiest and most charming people I have known in my life - in addition to being a world-class mathematician - Professor Roman Sikorski, was known by several generations of mathematicians under the deservedly frivolous nickname "Ersik" ...

After an extremely active life, Sikorski had several years of suffering before his death in September 1983. He was buried in the Powazki cemetery in the Wola district of west Warsaw. We note that several eminent mathematicians are also buried in this cemetery including Stefan Mazurkiewicz and Wacław Sierpiński.

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

**List of References** (17 books/articles)

**Mathematicians born in the same country**

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