Career
Hurewicz worked first at the University of North Carolina at Chapel Hill but during World War II he contributed to the war effort with research on applied mathematics. In particular, the work he did on servomechanisms at 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 theory and topology. The Dictionary of Scientific Biography describes it as: "...a remarkable result of this first period is his topological embedding of separable metric spaces into compact spaces of 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 groups in 1935-36, his discovery of the long exact homotopy sequence for fibrations in 1941, and the Hurewicz theorem connecting homotopy and homology groups. 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 after participating in the International Symposium on Algebraic Topology at the National Autonomous University of Mexico in Mexico City. He tripped and fell off the top of a Mayan step pyramid during an outing in Uxmal, Mexico. In the Dictionary of Scientific Biography it is suggested that he was "...a paragon of absentmindedness, a failing that probably led to his death."
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