display | more...

Kazimierz Kuratowski (1896-1980) was a famous Polish mathematician who helped rebuild Polish mathematics after the destruction of academia in Poland after World War II. He also helped break new ground in graph theory by establishing an important theorem in 1930 that bears his name.

Kuratowski was born in Warsaw, Poland, in 1896, the son of a famous Warsaw lawyer. He went on to a top secondary school in Glasgow, Scotland in 1913 but after the outbreak of World War I in 1914, he was called home. He enrolled in Warsaw University in 1915 and was an active member of the Polish patriotic student movement there.

Kuratowski's passion was mathematics, though, and he published his first paper in 1919 and received his Ph. D. in 1921 and continued postgraduate work there until 1927. During those years, he was an active member of the group known as the Warsaw School of Mathematics, who collaborated heavily in founding and advancing the areas of set theory and topology. In 1927, he was appointed as a professor at Lwow Polytechnical University, where he would stay for seven years. During his stay at Lwow, he became interested in graph theory and spent much of his time there characterizing planar graphs.

In 1930, while at Lwow, he established a vital theorem in the study of planar graphs, which states that a graph is nonplanar if and only if it contains a subgraph homeomorphic to K(3,3) or K(5). This single theorem provided an easy way to demonstrate whether a graph was planar or nonplanar, which made it much easier to study complex graphs.

In 1934 he returned to Warsaw University as a full professor. He was quite active in teaching and researching there until 1939, when the onset of World War II and the resultant persecution of educated Poles forced him into hiding.

Kuratowski took on an assumed name and helped to found a clandestine version of Warsaw University. Kuratowski risked his life teaching at this underground establishment until 1945, when Poland was liberated. Unfortunately, the entire educational system of Poland had been utterly destroyed during the war and had to be entirely rebuilt.

After the war, Kuratowski helped revive Polish mathematics, serving as director of the Polish National Mathematics Institute starting in 1949, holding the position until 1968. In addition to his teaching and public service, Kuratowski also published roughly 180 papers, as well as three mathematical texts that were widely used. Kuratowski retired in 1971 and passed away in 1980, leaving a legacy of mathematics in his wake.

Besides his famed theorem, Kuratowski contributed quite a bit in many other ways to the study of mathematics, especially in the areas of set theory and topology. He introduced the idea of using the notion of a limit point to give closure axioms to define a topological space, a major advancement in how topology is approached. In 1922, he used Boolean algebra to characterise the topology of an abstract space independently of the notion of points, the mathematics of which are used today when computers quickly construct topological maps. His work in set theory introduced the idea of considering a function as a set of ordered pairs. He also dabbled in other areas that sometimes overlapped his own, as heconsidered the topology of the continuum, the theory of connectivity, dimension theory, and answered measure theory questions. He also contributed to the study of compactness and metric spaces, and was the author of Topologie, a major work in the study of metric spaces.