- Witold Hurewicz
:"Not to be confused with"
Witold Hurewicz (
June 29 1904- September 6 1956) was a Polish mathematician.
Early life and education
He was born to a Jewish family in
Łódź, Russian Empire(now Poland).
His father was an industrialist. Hurewicz attended school in a Russian controlled Poland but with
World War Ibeginning before he had begun secondary school, major changes occurred in Poland. In August 1915 the Russian forces which had held Poland for many years withdrew. Germanyand Austria-Hungarytook control of most of the country and the University of Warsawwas refounded and it began operating as a Polish university. Rapidly, a strong school of mathematics grew up in the University of Warsaw, with topologyone of the main topics. Although Hurewicz knew intimately the topology that was being studied in Poland he chose to go to Viennato continue his studies.
He studied under
Hans Hahnand Karl Mengerin Vienna, receiving a Ph.D.in 1926. Hurewicz was awarded a Rockefeller scholarshipwhich allowed him to spend the year 1927-28 in Amsterdam. He was assistant to Brouwerin Amsterdam from 1928 to 1936. He was given study leave for a year which he decided to spend in the United States. He visited the Institute for Advanced Studyin Princeton, New Jerseyand then decided to remain in the United States and not return to his position in Amsterdam. Given the impending war in Europethis was clearly a wise decision.
Hurewicz worked first at the
University of North Carolina at Chapel Hillbut during World War IIhe contributed to the war effort with research on applied mathematics. In particular, the work he did on servomechanismsat that time was classified because of its military importance. From 1945 until his death he worked at the Massachusetts Institute of Technology.
Hurewicz's early work was on
set theoryand topology. The " Dictionary of Scientific Biography" describes it as: "...a remarkable result of this first period  is his topological embeddingof separable metric spacesinto compact spacesof the same (finite) dimension.*"
In the field of general topology his contributions are centred around
dimension theory. He wrote an important text with Henry Wallman, " Dimension Theory", published in 1941. A reviewer writes that the book "...is truly a classic. It presents the theory of dimension for separable metric spaces with what seems to be an impossible mixture of depth, clarity, precision, succinctness, and comprehensiveness."
Hurewicz is best remembered for two remarkable contributions to mathematics, his discovery of the
higher homotopy groupsin 1935-36, and his discovery of exact sequencesin 1941. His work led to homological algebra. It was during Hurewicz's time as Brouwer's assistant in Amsterdam that he did the work on the higher homotopy groups; "...the idea was not new, but until Hurewicz nobody had pursued it as it should have been. Investigators did not expect much new information from groups, which were obviously commutative..."
Hurewicz had a second textbook published, but this was not until 1958 after his death. "Lectures on
ordinary differential equations" is an introduction to ordinary differential equations which again reflects the clarity of his thinking and the quality of his writing.
He died during an outing at the
International Symposium on Algebraic Topologyin Uxmal, Mexicoafter tripping and falling off the top of a Mayan ziggurat. In the " Dictionary of Scientific Biography" it is suggested that he was "...a paragon of absentmindedness, a failing that probably led to his death."
Solomon Lefschetz" [http://projecteuclid.org/euclid.bams/1183521492 Witold Hurewicz, In memoriam] " Bull. Amer. Math. Soc. 63, (1957), 77-82.
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