Background
Stefan Mazurkiewicz was born on September 25, 1888, in Warsaw, Russian Empire (now Mazowieckie, Poland) to the family of a barrister Jan Mazurkiewicz and Michalina Piotrowska. His brother Wladyslaw was a diplomat.
1915
Poland
Portrait Photo of Stefan Mazurkiewicz around 1915.
1935
Poland
Stefan Mazurkiewicz around 1935.
rynek Kleparski 18, 31-150 Kraków, Poland
Mazurkiewicz passed his maturity test in 1906 at the 4th Cracow Gymnasium.
Gołębia 24, 31-007 Kraków, Poland
Mazurkiewicz started his studies in mathematics at the Faculty of Philosophy at the Jagiellonian University in Cracow.
Geschwister-Scholl-Platz 1, 80539 München, Germany
Mazurkiewicz continued his studies at the Ludwig Maximilian University of Munich.
Wilhelmsplatz 1, 37073 Göttingen, Germany
Mazurkiewicz continued his studies at the Georg-August University of Göttingen.
Universytetska St, 1, Lviv, L'vivs'ka oblast, Ukraine, 79000
Mazurkiewicz was awarded a Doctor of Philosophy in 1913 from the University of Lvov for his thesis, done under Wacław Sierpiński, on curves filling the square (“O krzywych wypelniajacych kwadrat”).
Stefan Mazurkiewicz was a member of the Polish Academy of Sciences and Letters.
Stefan Mazurkiewicz was a member of the Polish Mathematical Society, which elected him its president for the years 1933-1935.
Stefan Mazurkiewicz was a member of the Warsaw Scientific Society, which elected him its secretary-general in 1935.
Stefan Mazurkiewicz was born on September 25, 1888, in Warsaw, Russian Empire (now Mazowieckie, Poland) to the family of a barrister Jan Mazurkiewicz and Michalina Piotrowska. His brother Wladyslaw was a diplomat.
Mazurkiewicz received his secondary education at the Gymnasium in Warsaw in 1897-1906. He passed his maturity test in 1906 at the 4th Cracow Gymnasium. The same year he started his studies in mathematics at the Faculty of Philosophy at the Jagiellonian University in Cracow. He continued his studies at the universities of Munich, Göttingen, and Lvov, and was awarded a Doctor of Philosophy in 1913 from the University of Lvov for his thesis, done under Wacław Sierpiński, on curves filling the square (“O krzywych wypelniajacych kwadrat”).
Mazurkiewicz's 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 the reborn University of Warsaw and he would remain on the staff of the university for the rest of his life. He was several times elected dean of the Faculty of Mathematical and Natural Sciences and, in 1937, protector of the University of Warsaw.
Mazurkiewicz's book on the theory of probability was written in Warsaw during the German occupation of Poland. The manuscript was destroyed in 1944 when the Germans burned and destroyed Warsaw before their retreat; it was partly rewritten by Mazurkiewicz and published in Polish eleven years after his death.
Mazurkiewicz’s scientific activity was in two principal areas: topology with its applications to the theory of functions, and the theory of probability. The topology seminar given by him and Janiszewski, beginning in 1916, was probably the world’s first in this discipline. He exerted a great influence on the scientific work of his students and collaborators by the range of the ideas and problems in which he was interested, by the inventive spirit with which he treated them, and by the diversity of the methods that he applied to them.
In a series of later publications, Mazurkiewicz contributed considerably to the development of topology by means of solutions to several fundamental problems posed by Sierpiński, Karl Menger, Paul Alexandroff, Pavel Uryson, and others, through which he singularly deepened our knowledge, especially of the topological structure of the Euclidean plane. In solving the problem published by Sierpiński (in Fundamenta mathematicae, 2), he constructed on the plane a closed connected set which is the sum of a denumerable infinity of disjoint closed sets (1924) and which, in addition, has the property that all these summands except one are connected; at the same time he showed (independently of R. L. Moore) that on the plane the connectedness of all the summands in question is impossible, although, according to a result of Sierpiński’s, it ought to be possible in space. Mazurkiewicz also solved, affirmatively, Alexandroff’s problem (1935) on the existence of an indecomposable continuum (that is, one which is the sum of not fewer than 280 subcontinua different from itself) in every continuum of more than one dimension; that of Menger (1929) on the existence, for every positive integer n, of weakly n-dimensional sets; and that of Uryson (1927) on the existence, for every integer n>1, of separable complete n-dimensional spaces devoid of connected subsets containing more than one point. He also showed (1929) that if R is a region in n-dimensional Euclidean space and E is a set of n-2 dimensions, then the difference R-E is always connected and is even a semicontinuum.
Mazurkiewicz also contributed important results concerning the topological structure of curves, in particular concerning that of indecomposable continua, as well as an ingenious demonstration, by use of the Baire category method, that the family of hereditarily indecomposable continua of the plane, and therefore that the continua of less paradoxical structure occur in it only exceptionally (1930).
By applying the same method to the problems of the theory of functions, Mazurkiewicz showed (1931) that the set of periodic continuous functions f, for which the integral diverges everywhere, is of the second Baire category in the space of all continuous real functions, and that the same is true with the set of continuous functions which are nowhere differentiable. In addition, he provided the quite remarkable result that the set of continuous functions transforming the segment of the straight line into plane sets which contains Sierpiński’s universal plane curve (universality here designating the presence of homeomorphic images of every plane curve) is also of the second Baire category. Among Mazurkiewiez’ other results on functions are those concerning functional spaces and the sets in those spaces that are called projective (1936, 1937), as well as those regarding the set of singular points of an analytic function and the classical theorems of Eugène Roché, Julius Pál and Michael Fekete.
Mazurkiewicz supported the candidacy of the Polonized archduke Karol Stefan Habsburg-Lotaryński for the throne of the Polish Kingdom under the auspices of Austro-Hungary and Germany.
As early as 1913 Mazurkiewicz gave to topology an ingenious characterization of the continuous images of the segment of the straight line, known today as locally connected continua. He based it on the notions of the oscillation of a continuum at a point and on that of relative distance; the latter concept, which he introduced, was shown to be valuable for other purposes. This characterization, therefore, differs from those established at about the same time by Hans Hahn and by Sierpiéski, which were based on other ideas. It is also this characterization that is linked with the Mazurkiewicz-Moore theorem on the arcwise connectedness of continua.
Mazurkiewicz’ theorems, according to which every continuous function that transforms a compact linear set into a plane set with interior points takes the same value in at least three distinct points (a theorem established independently by Hahn), while every compact plane set that is devoid of interior-point is a binary continuous image, enabled him to define the notion of dimension of compact sets as follows: the dimension of such a set C is at most n when n is the smallest whole number for which there exists a continuous function transforming onto C a nondense compact linear set and taking the same value in at most n + 1 distinct points of this set. This definition preceded by more than seven years that of Karl Menger and Pavel Uryson, to which it is equivalent for compact sets.
In the theory of probability, Mazurkiewicz formulated and demonstrated, in a work published in Polish (1922), the strong law of large numbers (independently of Francesco Cantelli); established several axiom systems of this theory (1933, 1934); and constructed a universal separable space of random variables by suitably enlarging that of the random variables of the game of heads or tails to a complete space (1935). These results and many others were included and developed in his book on the theory of probability.
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.
Stefan Mazurkiewicz was a member of the Polish Academy of Sciences and Letters; of the Warsaw Scientific Society, which elected him its secretary-general in 1935; of the Polish Mathematical Society, which elected him its president for the years 1933-1935; and member of the editorial boards of Fundamenta mathematicae and the Monografie matematyozne from their beginnings.
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.
Quotes from others about the person
"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." - Kazimierz Kuratowski, Polish mathematician and a pupil of Mazurkiewicz
Stefan Mazurkiewicz was married to Kazimiera Badior with whom he had a son who died during the Warsaw Uprising. The divorced. His second wife was Maria Brzozowska.