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{{Short description|Polish Mathematician (1904–1956)}}
[[pl:Witold Hurewicz]]▼
{{Redirect|Hurewicz|people with similar names|J. C. Hurewitz|and|Hurwitz}}
{{more citations needed|date=September 2019}}
'''Witold Hurewicz''' ([[June 29]] [[1904]] - [[September 6]] [[1956]]) was a [[Poland|Polish]] mathematician. He was born in [[Lodz]] and died in [[Uxmal]], [[Mexico]].▼
{{infobox scientist
|birth_date={{birth date|1904|06|29}}
|birth_place=[[Łódź]], [[Poland]]
|death_date={{death date and age|1956|07|06|1904|06|29}}
|death_place=[[Uxmal]], [[Mexico]]
|field=[[Mathematics]]
|known_for=[[Hurewicz theorem]]<br>[[Hurewicz space]]
|thesis_title=Über eine Verallgemeinerung des Borelschen Theorems
|thesis_url=
|thesis_year=1926
|doctoral_advisor=[[Hans Hahn (mathematician)|Hans Hahn]]<br>[[Karl Menger]]
|doctoral_students=[[Felix Browder]]<br>[[Allen Shields]]<br>[[Yael Dowker]]<br>[[James Dugundji]]<br>[[Barrett O'Neill]]
|alma_mater=[[University of Vienna]]
|workplaces=[[Princeton University]]<br>[[Radcliffe College]]<br>[[Massachusetts Institute of Technology]]
}}
▲'''Witold Hurewicz''' (
==Early life and education==
Witold Hurewicz was born in [[Łódź]], at the time one of the main Polish industrial hubs with economy focused on the textile industry. His father Mieczysław Hurewicz was an industrialist born in [[Wilno]], which until 1939 was mainly populated by Poles and Jews.<ref>[https://books.google.com/books?id=6EICfJrepKQC&pg=PR45 Samuel Eilenberg, Witold Hurewicz (personal reminiscences)]</ref> His mother Katarzyna Finkelsztain hailed from [[Biała Cerkiew]], a town that belonged to the [[Crown of the Kingdom of Poland|Kingdom of Poland]] until the [[Second Partition of Poland]] (1793) when it was taken by [[Russia]].
Hurewicz attended school in a German-controlled Poland but with [[World War I]] beginning before he had begun [[secondary school]], major changes occurred in Poland. In August 1915 the Russian forces that had held Poland for many years withdrew. [[Germany]] and [[Austria-Hungary]] took control of most of the country and the [[University of Warsaw]] was refounded and it began operating as a Polish university. Rapidly, a [[Warsaw School (mathematics)|strong school of mathematics]] grew up in the University of Warsaw, with [[topology]] one of the main topics. Although Hurewicz knew intimately the topology that was being studied in Poland he chose to go to [[Vienna]] to continue his studies.
See also: [[Zygmunt Janiszewski]]▼
He studied under [[Hans Hahn (mathematician)|Hans Hahn]] and [[Karl Menger]] in [[Vienna]], receiving a [[PhD]] in 1926. Hurewicz was awarded a [[Rockefeller Foundation|Rockefeller scholarship]], which allowed him to spend the year 1927–28 in [[Amsterdam]]. He was assistant to [[L. E. J. Brouwer]] in 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 Study]] in [[Princeton, New Jersey]] and then decided to remain in the United States and not return to his position in Amsterdam.
== External links ==▼
==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]]'' states:
[[Category:Mathematicians]]▼
"...a remarkable result of this first period [1930] is his [[topological embedding]] of [[separable space|separable]] [[metric spaces]] into [[compact spaces]] of the same ([[finite set|finite]]) [[dimension]].*"
In the field of [[general topology]] his contributions are centred on [[dimension theory]]. He wrote an important text with [[Henry Wallman]], ''Dimension Theory'', published in 1941.<ref>{{cite journal|author=Smith, P. A.|author-link=Paul A. Smith|title=Review: ''Dimension Theory'', by W. Hurewicz and H. Wallman|journal=[[Bull. Amer. Math. Soc.]]|year=1942|volume=48|issue=9, Part 1|pages=641–642|url=http://www.ams.org/journals/bull/1942-48-09/S0002-9904-1942-07723-8/|doi=10.1090/S0002-9904-1942-07723-8|doi-access=free}}</ref> 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 three remarkable contributions to mathematics: his discovery of the [[higher homotopy groups]] in 1935–36, his discovery of the [[Homotopy long exact sequence#Long exact sequence of a fibration|long exact homotopy sequence]] for [[fibration]]s in 1941, and the [[Hurewicz theorem]] connecting homotopy and [[Homology (mathematics)|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 [[Group (mathematics)|groups]], which were obviously [[commutative]]..."
In the late 1940s, he was the doctoral advisor of [[Yael Dowker]].
Hurewicz had a second textbook published, but this was not until 1958 after his death. ''Lectures on [[ordinary differential equations]]''<ref>{{cite journal|author=Coddington, Earl A.|title=Review: ''Lectures on ordinary differential equations'', by W. Hurewicz|journal=Bull. Amer. Math. Soc.|year=1959|volume=65|issue=1|pages=25–26|url=http://www.ams.org/journals/bull/1959-65-01/S0002-9904-1959-10266-4/|doi=10.1090/s0002-9904-1959-10266-4|doi-access=free}}</ref> is an introduction to ordinary differential equations that again reflects the clarity of his thinking and the quality of his writing.
He died after participating in the International Symposium on Algebraic Topology <ref>{{cite web |last1=Hurewicz |first1=Witold |title=Symposium Internacional de Topologia Algebraica |url=https://www.google.com/search?q=International+Symposium+on+Algebraic+Topology#ip=1 |website=University of Edinburgh |access-date=February 25, 2024}}</ref> at the [[National Autonomous University of Mexico]] in [[Mexico City]]. He tripped and fell off the top of a [[Maya civilization|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."
==See also==
==References==
{{reflist}}
* {{MacTutor Biography|id=Hurewicz}}
* {{MathGenealogy|id=5856}}
* {{cite journal | last1 = Lefschetz | first1 = Solomon | author-link = Solomon Lefschetz | year = 1957 | title = Witold Hurewicz, In memoriam | url = http://projecteuclid.org/euclid.bams/1183521492 | journal = Bull. Amer. Math. Soc. | volume = 63 | issue = 2 | pages = 77–82 | doi=10.1090/s0002-9904-1957-10101-3| doi-access = free }}
* [[Krystyna Kuperberg]] (ed.): ''[http://www.ams.org/bookstore?fn=20&arg1=geotopo&ikey=CWORKS-4 Collected Works of Witold Hurewicz]'', 1995, {{ISBN|0-8218-0011-6}}
* {{DNB-Portal|11945291X}}
{{Authority control}}
{{DEFAULTSORT:Hurewicz, Witold}}
[[Category:1956 deaths]]
[[Category:20th-century Polish mathematicians]]
[[Category:Accidental deaths from falls]]
[[Category:Accidental deaths in Mexico]]
[[Category:American people of Polish-Jewish descent]]
[[Category:Polish expatriates in the United States]]
[[Category:Academic staff of the University of Amsterdam]]
[[Category:University of Vienna alumni]]
[[Category:Massachusetts Institute of Technology faculty]]
[[Category:Institute for Advanced Study faculty]]
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