Kazimierz Zarankiewicz

Quick Info

2 May 1902
Częstochowa, Russian Empire (now Poland)
5 September 1959
London, England

Kazimierz Zarankiewicz was a Polish mathematician who worked in topology.


Kazimierz Zarankiewicz was born and brought up in Czestochowa in south-central Poland. He attended secondary school in Bedzin, which is near Czestochowa, and for much of his time at school Poland was going through the difficult events of World War I.

When we say that Zarankiewicz was brought up in Poland, this must be seen in relation to the political circumstances of the time. Poland had been partitioned in 1772 with the south, which was called Galicia, under Austrian control and Russia in control of much of the rest of the country. This situation, which was the position throughout the early years of Zarankiewicz's life, lasted until the outbreak of World War I in 1914. At this time Russia tried to win Polish support, particularly in Galicia, by promising the Poles autonomy. By the end of 1914 Russian forces controlled almost all of Galicia.

However, the Central Powers (Germany and Austria- Hungary) recaptured Galicia and large parts of Congress Poland which had been under Russian control. A German governor general was installed in Warsaw and a new Kingdom of Poland was declared on 5 November 1916. The University of Warsaw, which had been a Russian language university for many years, became Polish again in November 1915 following the withdrawal of the Russian forces from Warsaw in August 1915.

Zarankiewicz completed his secondary school education and entered the University of Warsaw in 1919. From the time its reopening the university had rapidly become a leading world centre for topology. Janiszewski and Mazurkiewicz were conducting a topology seminar there from 1917 onwards, Sierpiński arrived in 1918, and in 1919, the year Zarankiewicz arrived, Kuratowski had just graduated and was beginning his doctoral studies. Saks was also studying for his doctorate at this time.

With such a concentration on topology, and the excitement of those studying this new discipline in their newly freed country, it is not surprising that this was the area which attracted Zarankiewicz. He wrote his doctoral dissertation on cut points in connected sets and, in 1923, he was awarded a Ph.D. Although his thesis was published, this did not happen until 1927.

Zarankiewicz was appointed to Warsaw University as an assistant in 1924 and continued with his research on topological properties of the plane for his habilitation thesis. On acceptance of this thesis in 1929 Zarankiewicz was appointed as a dozent at the University of Warsaw. During the year 1930-31 he visited Vienna where he worked with Menger, and he also visited Berlin where he worked with von Mises, Bergman and others.

On his return to Warsaw, Zarankiewicz taught both at the Polytechnic and at the Agricultural College. There was no position for him at the university at this time so he was not able to teach his specialist research topics, but rather he had to teach mechanics, and statistics. However, he taught a course on conformal mappings, one of his current research interests, for a semester at Tomsk in 1936. After he returned to Warsaw from Tomsk he substituted for the professor at Warsaw Polytechnic in 1937. He was put forward for a professorship himself in 1939 but the events of that year, namely the start of World War II, brought normal life to an end and his professorship would have to be put on hold to be considered again only at the end of the war.

Zarankiewicz risked his life during the war teaching in the underground university which had been set up by the Poles in German occupied Warsaw to try to keep the intellectual life going. Kuratowski writes in [2]:-
Almost all our professors of mathematics lectured at these clandestine universities, and quite a few of the students then are now professors or docent themselves. Due to that underground organisation, and in spite of extremely difficult conditions, scientific work and teaching continued, though on a considerably smaller scale of course. The importance of clandestine education consisted among others in keeping up the spirit of resistance, as well as optimism and confidence in the future, which was so necessary in the conditions of occupation. The conditions of a scientist's life at that time were truly tragic. Most painful were the human losses.
Zarankiewicz paid dearly for teaching in the underground university for in 1944 he was sent to a labour camp in Germany. He survived this experience and returned to Warsaw at the end of the war in 1945. He resumed his teaching duties in 1946 at Warsaw Polytechnic. The long delayed decision to promote him to professor at Warsaw Polytechnic eventually took effect and, in 1948, he became a full professor. Also in 1948 he went to the United States for several months and taught at a number of universities including Harvard.

Zarankiewicz did important work in topology and graph theory. He also wrote on complex functions and number theory. His work on triangular numbers inspired Sierpiński to further work on this topic while Zarankiewicz also worked jointly with Kuratowski on topology. Another of his favourite research topics was complex function theory and, in this topic, he proved results which [1]:-
... played an important role in the development of the theory of the kernel and its generalisations to several variables, notably to pseudo-conformal transformations in space of more than three dimensions.
Zarankiewicz made several other important contributions to mathematics. From 1949 until 1957 he coached the Polish Olympiad team of school pupils. He served as president of the Warsaw section of the Polish Mathematical Society from 1948 till 1951. His death in London in 1959 came during the Tenth Congress of the International Astronautical Federation of which he was the President.

References (show)

  1. B Knaster, Biography in Dictionary of Scientific Biography (New York 1970-1990). See THIS LINK.
  2. K Kuratowski, Half a century of Polish mathematics (Warsaw, 1973).
  3. S Bergman R Duda, B Knaster, J Mycielski and A Schinzel, Kazimierz Zarankiewicz (Polish), Wiadom. Mat. (2) 9 (1966/1967), 175-185
  4. S Bergman R Duda, B Knaster, J Mycielski and A Schinzel, Kazimierz Zarankiewicz (2. V. 1902-5. IX. 1959), Colloq. Math. 12 (1964), 277-288.

Additional Resources (show)

Other websites about Kazimierz Zarankiewicz:

  1. Dictionary of Scientific Biography
  2. MathSciNet Author profile
  3. zbMATH entry

Written by J J O'Connor and E F Robertson
Last Update May 2000