Witold Hurewicz (June 29, 1904 – September 6, 1956) 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, structure, space, models, and change.
History
On ...
.
Early life and education
Witold Hurewicz was born in
Łódź
Łódź, also rendered in English as Lodz, is a city in central Poland and a former industrial centre. It is the capital of Łódź Voivodeship, and is located approximately south-west of Warsaw. The city's coat of arms is an example of canti ...
, 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
Vilnius ( , ; see also #Etymology and other names, other names) is the capital and List of cities in Lithuania#Cities, largest city of Lithuania, with a population of 592,389 (according to the state register) or 625,107 (according to the munic ...
, which until 1939 was mainly populated by Poles and Jews. His mother was Katarzyna Finkelsztain who hailed from
Biała Cerkiew
Bila Tserkva ( uk, Бі́ла Це́рква ; ) is a city in the center of Ukraine, the largest city in Kyiv Oblast (after Kyiv, which is the administrative center, but not part of the oblast), and part of the Right Bank. It serves as the admi ...
Russia
Russia (, , ), or the Russian Federation, is a List of transcontinental countries, transcontinental country spanning Eastern Europe and North Asia, Northern Asia. It is the List of countries and dependencies by area, largest country in the ...
.
Hurewicz attended school in a German-controlled Poland but with
World War I
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
beginning before he had begun
secondary school
A secondary school describes an institution that provides secondary education and also usually includes the building where this takes place. Some secondary schools provide both '' secondary education, lower secondary education'' (ages 11 to 14) ...
, major changes occurred in Poland. In August 1915 the Russian forces that had held Poland for many years withdrew.
Germany
Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...
and
Austria-Hungary
Austria-Hungary, often referred to as the Austro-Hungarian Empire,, the Dual Monarchy, or Austria, was a constitutional monarchy and great power in Central Europe between 1867 and 1918. It was formed with the Austro-Hungarian Compromise of ...
took control of most of the country and the
University of Warsaw
The University of Warsaw ( pl, Uniwersytet Warszawski, la, Universitas Varsoviensis) is a public university in Warsaw, Poland. Established in 1816, it is the largest institution of higher learning in the country offering 37 different fields of ...
was refounded and it began operating as a Polish university. Rapidly, a strong school of mathematics grew up in the University of Warsaw, with
topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...
one of the main topics. Although Hurewicz knew intimately the topology that was being studied in Poland he chose to go to
Vienna
en, Viennese
, iso_code = AT-9
, registration_plate = W
, postal_code_type = Postal code
, postal_code =
, timezone = CET
, utc_offset = +1
, timezone_DST ...
Vienna
en, Viennese
, iso_code = AT-9
, registration_plate = W
, postal_code_type = Postal code
, postal_code =
, timezone = CET
, utc_offset = +1
, timezone_DST ...
, receiving a
PhD PHD or PhD may refer to:
* Doctor of Philosophy (PhD), an academic qualification
Entertainment
* '' PhD: Phantasy Degree'', a Korean comic series
* ''Piled Higher and Deeper'', a web comic
* Ph.D. (band), a 1980s British group
** Ph.D. (Ph.D. albu ...
in 1926. Hurewicz was awarded a
Rockefeller scholarship Rockefeller is a German surname, originally given to people from the village of Rockenfeld near Neuwied in the Rhineland and commonly referring to subjects associated with the Rockefeller family. It may refer to:
People with the name Rockefeller fa ...
, which allowed him to spend the year 1927–28 in
Amsterdam
Amsterdam ( , , , lit. ''The Dam on the River Amstel'') is the Capital of the Netherlands, capital and Municipalities of the Netherlands, most populous city of the Netherlands, with The Hague being the seat of government. It has a population ...
. He was assistant to
L. E. J. Brouwer
Luitzen Egbertus Jan Brouwer (; ; 27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, who worked in topology, set theory, measure theory and compl ...
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
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...
in
Princeton, New Jersey
Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...
and then decided to remain in the United States and not return to his position in Amsterdam.
Career
Hurewicz worked first at the
University of North Carolina at Chapel Hill
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States ...
but during
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
he contributed to the war effort with research on
applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical s ...
. In particular, the work he did on
servomechanisms
In control engineering a servomechanism, usually shortened to servo, is an automatic device that uses error-sensing negative feedback to correct the action of a mechanism. On displacement-controlled applications, it usually includes a built-in ...
at that time was classified because of its military importance. From 1945 until his death he worked at the
Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...
.
Hurewicz's early work was on
set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...
and
topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...
930
Year 930 ( CMXXX) was a common year starting on Friday (link will display the full calendar) of the Julian calendar.
Events
By place
Europe
* 17 June (traditional date) – The Althing, the parliament of Iceland, is established at ...
compact spaces
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space by making precise the idea of a space having no "punctures" or "missing endpoints", ...
dimension
In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...
.*"
In the field of general topology his contributions are centred on
dimension theory
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...
Dimension Theory
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...
'', 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 three remarkable contributions to mathematics: his discovery of the
higher homotopy groups
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, denoted \pi_1(X), which records information about loops in a space. Intuitively, homotop ...
in 1935–36, his discovery of the
long exact homotopy sequence
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, denoted \pi_1(X), which records information about loops in a space. Intuitively, homotop ...
for fibrations in 1941, and the
Hurewicz theorem
In mathematics, the Hurewicz theorem is a basic result of algebraic topology, connecting homotopy theory with homology theory via a map known as the Hurewicz homomorphism. The theorem is named after Witold Hurewicz, and generalizes earlier results ...
connecting homotopy and homology groups. His work led to
homological algebra
Homological algebra is the branch of mathematics that studies homology (mathematics), homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precurs ...
. 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
A group is a number of persons or things that are located, gathered, or classed together.
Groups of people
* Cultural group, a group whose members share the same cultural identity
* Ethnic group, a group whose members share the same ethnic iden ...
, which were obviously commutative..."
In the late 1940s, he was the doctoral advisor of
Yael Dowker
Yael Naim Dowker (1919–2016) was an English mathematician, prominent especially due to her work in the fields of measure theory, ergodic theory and topological dynamics.
Biography
Yael Naim (later Dowker) was born in Tel Aviv. She left for t ...
.
Hurewicz had a second textbook published, but this was not until 1958 after his death. ''Lectures on
ordinary differential equations
In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast w ...
'' 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
International is an adjective (also used as a noun) meaning "between nations".
International may also refer to:
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* International (Kevin Michael album), ''International'' (Kevin Michael album), 2011
* International (New Order album), ' ...
at the
National Autonomous University of Mexico
The National Autonomous University of Mexico ( es, Universidad Nacional Autónoma de México, UNAM) is a public research university in Mexico. It is consistently ranked as one of the best universities in Latin America, where it's also the bigges ...
in
Mexico City
Mexico City ( es, link=no, Ciudad de México, ; abbr.: CDMX; Nahuatl: ''Altepetl Mexico'') is the capital and largest city of Mexico, and the most populous city in North America. One of the world's alpha cities, it is located in the Valley o ...
. He tripped and fell off the top of a
Mayan
Mayan most commonly refers to:
* Maya peoples, various indigenous peoples of Mesoamerica and northern Central America
* Maya civilization, pre-Columbian culture of Mesoamerica and northern Central America
* Mayan languages, language family spoken ...
Uxmal
Uxmal (Yucatec Maya: ''Óoxmáal'' ) is an ancient Maya city of the classical period located in present-day Mexico. It is considered one of the most important archaeological sites of Maya culture, along with Palenque, Chichen Itza and Calakmul i ...
,
Mexico
Mexico (Spanish: México), officially the United Mexican States, is a country in the southern portion of North America. It is bordered to the north by the United States; to the south and west by the Pacific Ocean; to the southeast by Guatema ...
. In the '' Dictionary of Scientific Biography'' it is suggested that he was "...a paragon of absentmindedness, a failing that probably led to his death."
Hurewicz theorem
In mathematics, the Hurewicz theorem is a basic result of algebraic topology, connecting homotopy theory with homology theory via a map known as the Hurewicz homomorphism. The theorem is named after Witold Hurewicz, and generalizes earlier results ...
*
Hurewicz space In mathematics, a Hurewicz space is a topological space that satisfies a certain basic selection principle that generalizes σ-compactness. A Hurewicz space is a space in which for every sequence of open covers \mathcal_1, \mathcal_2, \ldots of the ...