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Kazimierz Zarankiewicz (2 May 1902 – 5 September 1959) was a Polish
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
and Professor at the
Warsaw University of Technology The Warsaw University of Technology () is one of the leading institutes of technology in Poland and one of the largest in Central Europe. It employs 2,453 teaching faculty, with 357 professors (including 145 titular professors). The student body ...
who was interested primarily in
topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
and
graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...
.


Biography

Zarankiewicz was born in
Częstochowa Częstochowa ( , ) is a city in southern Poland on the Warta with 214,342 inhabitants, making it the thirteenth-largest city in Poland. It is situated in the Silesian Voivodeship. However, Częstochowa is historically part of Lesser Poland, not Si ...
, to father Stanisław and mother Józefa (''née'' Borowska). He studied at the
University of Warsaw The University of Warsaw (, ) is a public university, public research university in Warsaw, Poland. Established on November 19, 1816, it is the largest institution of higher learning in the country, offering 37 different fields of study as well ...
, together with Zygmunt Janiszewski,
Stefan Mazurkiewicz Stefan Mazurkiewicz (25 September 1888 – 19 June 1945) was a Polish mathematician who worked in mathematical analysis, topology, and probability. He was a student of Wacław Sierpiński and a member of the Polish Academy of Learning (''PAU''). ...
,
Wacław Sierpiński Wacław Franciszek Sierpiński (; 14 March 1882 – 21 October 1969) was a Polish mathematician. He was known for contributions to set theory (research on the axiom of choice and the continuum hypothesis), number theory, theory of functions ...
,
Kazimierz Kuratowski Kazimierz Kuratowski (; 2 February 1896 – 18 June 1980) was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics. He worked as a professor at the University of Warsaw and at the Ma ...
, and
Stanisław Saks Stanisław Saks (30 December 1897 – 23 November 1942) was a Polish mathematician and university tutor, a member of the Lwów School of Mathematics, known primarily for his membership in the Scottish Café circle, an extensive monograph on the t ...
. During
World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
, Zarankiewicz took part in illegal teaching, forbidden by the German authorities, and was eventually sent to a
concentration camp A concentration camp is a prison or other facility used for the internment of political prisoners or politically targeted demographics, such as members of national or ethnic minority groups, on the grounds of national security, or for exploitati ...
. He survived and became a teacher at
Warsaw University of Technology The Warsaw University of Technology () is one of the leading institutes of technology in Poland and one of the largest in Central Europe. It employs 2,453 teaching faculty, with 357 professors (including 145 titular professors). The student body ...
(Polish: ''Politechnika Warszawska''). He visited universities in
Tomsk Tomsk (, ) is a types of inhabited localities in Russia, city and the administrative center of Tomsk Oblast in Russia, on the Tom (river), Tom River. Population: Founded in 1604, Tomsk is one of the oldest cities in Siberia. It has six univers ...
,
Harvard Harvard University is a private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher lear ...
,
London London is the Capital city, capital and List of urban areas in the United Kingdom, largest city of both England and the United Kingdom, with a population of in . London metropolitan area, Its wider metropolitan area is the largest in Wester ...
, and
Vienna Vienna ( ; ; ) is the capital city, capital, List of largest cities in Austria, most populous city, and one of Federal states of Austria, nine federal states of Austria. It is Austria's primate city, with just over two million inhabitants. ...
. He served as president of the
Warsaw Warsaw, officially the Capital City of Warsaw, is the capital and List of cities and towns in Poland, largest city of Poland. The metropolis stands on the Vistula, River Vistula in east-central Poland. Its population is officially estimated at ...
section of the
Polish Mathematical Society The Polish Mathematical Society () is the main professional society of Polish mathematicians and represents Polish mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU). History The society was ...
and the
International Astronautical Federation The International Astronautical Federation (IAF) is an international space advocacy organization based in Paris, and founded in 1951 as a non-governmental organization to establish a dialogue between scientists around the world and to lay t ...
. He died in
London London is the Capital city, capital and List of urban areas in the United Kingdom, largest city of both England and the United Kingdom, with a population of in . London metropolitan area, Its wider metropolitan area is the largest in Wester ...
, England.


Research contributions

Zarankiewicz wrote works on cut-points in
connected space In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union (set theory), union of two or more disjoint set, disjoint Empty set, non-empty open (topology), open subsets. Conne ...
s, on conformal mappings, on complex functions and
number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
, and
triangular number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...
s. The Zarankiewicz problem is named after Zarankiewicz. This problem asks, for a given size of (0,1)-matrix, how many matrix entries must be set equal to 1 in order to guarantee that the matrix contains at least one ''a'' × ''b''
submatrix In mathematics, a matrix (: matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object. ...
is made up only of 1's. An equivalent formulation in
extremal graph theory Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory. In essence, extremal graph theory studies how global properties of a graph influence loca ...
asks for the maximum number of edges in a
bipartite graph In the mathematics, mathematical field of graph theory, a bipartite graph (or bigraph) is a Graph (discrete mathematics), graph whose vertex (graph theory), vertices can be divided into two disjoint sets, disjoint and Independent set (graph theo ...
with no complete bipartite subgraph ''K''''a'',''b''. The Zarankiewicz crossing number conjecture in the mathematical field of
graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...
is also named after Zarankiewicz. The
conjecture In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), ha ...
states that the crossing number of a
complete bipartite graph In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first set is connected to every vertex of the second set..Electronic edition page 17. Graph theory ...
K_ equals :\text(K_) = \left\lfloor\frac\right\rfloor\left\lfloor \frac\right\rfloor\left\lfloor \frac\right\rfloor\left\lfloor \frac\right\rfloor.\ Zarankiewicz proved that this formula is an upper bound for the actual crossing number. The problem of determining the number \text(K_) was suggested by Paul Turán and became known as Turán's brick factory problem.


See also

*
List of Polish mathematicians A list of notable Poland, Polish mathematicians: References

{{DEFAULTSORT:Polish mathematicians Polish mathematicians, Lists of Polish people by occupation, Mathematicians Lists of mathematicians by nationality, Polish ...


References


External links

* {{DEFAULTSORT:Zarankiewicz, Kazimierz 20th-century Polish mathematicians Topologists University of Warsaw alumni Academic staff of the Warsaw University of Technology Nazi concentration camp survivors People from Częstochowa 1902 births 1959 deaths