# Stefan Mazurkiewicz

### Quick Info

Warsaw, Russian Empire (now Poland)

Grodzisk, Mazowiecki (near Warsaw), Poland

**Stefan Mazurkiewicz**was a Polish mathematician who worked in mathematical analysis, topology, and probability.

### Biography

**Stefan Mazurkiewicz**'s father was a barrister in Warsaw. Stefan attended secondary school in Warsaw, graduating in 1907. Mazurkiewicz decided not to remain in Warsaw for his university education, taking what was a typical route for Poles at this time. We shall give some background to the political situation in Poland to explain why this was so.

The first thing to note is that when Mazurkiewicz graduated from secondary school in 1907, Poland did not formally exist. Poland had been partitioned in 1772 and the south was called Galicia and under Austrian control. Russia controlled much of the rest of the country and in the years prior to Mazurkiewicz's birth there had been strong moves by Russia to make "Vistula Land", as it was called, be dominated by Russian culture. In a policy implemented between 1869 and 1874, all secondary schooling was in the Russian language. Warsaw only had a Russian language university after the University of Warsaw was closed by the Russian administration in 1869. Galicia, although under Austrian control, retained Polish culture and was often where Poles from "Vistula Land" went for their education. Indeed Mazurkiewicz first went to Kraków, in Galicia but, again following the pattern of students of the time to spend sessions at a number of different universities, he went next to Munich, then to the renowned mathematical research centre at Göttingen.

Mazurkiewicz returned to Galicia for his doctorate, which was supervised by Sierpiński on space filling curves at the University of Lvov. His doctorate was awarded in 1913, but World War I began the following year and it was to bring major changes in Poland and to Mazurkiewicz's life. 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. At this point Mazurkiewicz became a professor at this reborn University of Warsaw and he would remain on the staff of the university for the rest of his life.

Kuratowski attended seminars given by Mazurkiewicz in Warsaw before the end of the war. He writes in [2]:-

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 role that Mazurkiewicz played in the creation of the Polish School of Mathematics was an important one. Kuratowski writes in [2]:-

... Stefan Mazurkiewicz was the central figure among professors of mathematics, especially in the early years of the university's existence. A brilliant lecturer, a very active research worker, he had a great influence on young people and encouraged them to do research of their own in modern fields of mathematics ...His main work was in topology and the theory of probability. His notion of dimension of a compact set preceded that of Menger and Urysohn by seven years. Mazurkiewicz applied topological methods to the theory of functions, obtaining powerful results. His theory gave particularly strong results when applied to the Euclidean plane, giving deep knowledge of its topological structure.

Many of the ideas introduced by Mazurkiewicz were studied independently by Hahn. They independently proved that [1]:-

... every continuous function that transforms a compact linear set into a plane set with interior points takes the same value in at least three points.Other results by Mazurkiewicz gave information about the topological structure of curves. He proved strong results on continuous functions containing Sierpiński's curve and wrote several papers on functional spaces.

The style employed by Mazurkiewicz, both in research and teaching, is described by Kuratowski in [2]:-

Mazurkiewicz's passion was solving problems and raising new and often very profound ones. This unusually creative scholar's almost sportsmanlike attitude towards mathematics was in some sense manifested in the way he lectured and prepared his results for publication: Mazurkiewicz used no notes while lecturing, and his lectures were not always completely elaborated but they were greatly admired by his audience for their ingenuity and deep intelligence. Very often, however, his publications were not sufficiently polished and presented only a draft of an argument and therefore were not easily understandable; but as a rule they contained new ideas and fascinated the reader by their author's inventive powers and the wealth of his methods.Mazurkiewicz held many important positions in the University of Warsaw as it flourished between the two wars. He was elected vice-rector of the University and he was Dean of the Faculty of Mathematical and Natural Sciences for nine years. He was also president of the Polish Mathematical Society in 1933-35 and he continued the tradition established in Lvov of meetings in coffee houses.

After Janiszewski died in 1920, Mazurkiewicz and Sierpiński took over the editorship of the journal

*Fundamenta Mathematicae*which Janiszewski had set up. In [6] Tamarkin wrote:-

Under masterful guidance of its editors, S Mazurkiewicz and W Sierpinski, Fundamenta Mathematicae immediately developed into a unique periodical which attracted international recognition and cooperation, and whose history became the history of development of the modern theory of functions and point sets.Throughout his career Mazurkiewicz was interested in the theory of probability. He proved the strong law of large numbers in 1922, a result which was proved independently by Cantelli. He also considered axiom systems for probability theory, publishing different versions in the years 1933 and 1934.

After the German invasion of Poland in 1939 life there became extremely difficult. There was a strategy by the Nazi invaders to put an end to the intellectual life of Poland and to achieve this they sent many academics to concentration camps and murdered others. It was during this period of occupation that Mazurkiewicz wrote a treatise on probability including his own results on the topic.

Near the end of the war, Warsaw became the centre for Polish resistance. In 1944 the people, knowing that Soviet forces were nearing the city, rose up against the German garrison which by this time was severely depleted. However, German reinforcements were sent and the Polish resistance was defeated. Hitler ordered the destruction of the city in retaliation for the uprising. The Germans systematically destroyed the buildings using explosives on some and setting fire to others. Around 175,000 of the population of Warsaw died as a result of the uprising. Mazurkiewicz escaped with his life, but the manuscript of his treatise on probability was destroyed as the buildings burned.

At this time Mazurkiewicz was greatly weakened as a result of the difficult life he had led in Warsaw and also through an illness from which he now suffered. However, he attempted to rewrite his treatise on probability which had been burnt in the destruction. Although he only managed to recreate part of the work it was completed eleven years after his death and published as number 32 in the

*Mathematical Monographs*series.

Despite being gravely ill, Mazurkiewicz thought only of the recreation of Polish mathematics as the war drew to a close, being filled with the same enthusiasm which he had displayed at the end of World War I. On 25 February 1945 he submitted a report to the Ministry of Education on the recovery route that mathematics should take. He argued strongly for the creation of a Mathematical Institute along the lines of Kuratowski's report made before the start of the war.

Already moves were under way to re-establish the University of Warsaw and the Technical University. Mazurkiewicz took part in these meetings despite his failing health. Desperately ill he was taken to a hospital at Grodzisk Mazowiecki on the outskirts of Warsaw where he died during an operation for a gastric ulcer.

### References (show)

- B Knaster, Biography in
*Dictionary of Scientific Biography*(New York 1970-1990). See THIS LINK. - K Kuratowski,
*Half a century of Polish mathematics*(Warsaw, 1973). - S Mazurkiewicz,
*Travaux de topologie et ses applications*(Warsaw, 1969). - B Koszela, The contribution of Józef Marcinkiewicz, Stefan Mazurkiewicz and Hugo Steinhaus in developing Polish mathematics: A biographical sketch (Polish),
*Mathematics at the turn of the twentieth century*(Katowice, 1992), 104-110. - K Kuratowski, Stefan Mazurkiewicz et son oeuvre scientifique,
*Fundamenta mathematicae***34**(1947), 316-331. - J D Tamarkin, 25 volumes of Fundamenta Mathematicae,
*Bull. Amer. Math. Soc.***42**(1936), 300.

### Additional Resources (show)

Other websites about Stefan Mazurkiewicz:

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Written by J J O'Connor and E F Robertson

Last Update February 2000

Last Update February 2000