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 cant ...
, 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, a town that belonged to the
Kingdom of Poland
The Kingdom of Poland ( pl, Królestwo Polskie; Latin: ''Regnum Poloniae'') was a state in Central Europe. It may refer to:
Historical political entities
* Kingdom of Poland, a kingdom existing from 1025 to 1031
* Kingdom of Poland, a kingdom exi ...
until the
Second Partition of Poland
The 1793 Second Partition of Poland was the second of three partitions (or partial annexations) that ended the existence of the Polish–Lithuanian Commonwealth by 1795. The second partition occurred in the aftermath of the Polish–Russian W ...
(1793) when it was taken by
Russia
Russia (, , ), or the Russian Federation, is a transcontinental country spanning Eastern Europe and Northern Asia. It is the largest country in the world, with its internationally recognised territory covering , and encompassing one-eig ...
.
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, 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 o ...
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 words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
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
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, postal_code =
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, utc_offset = +1
, timezone_DST ...
to continue his studies.
He studied under Hans Hahn and
Karl Menger
Karl Menger (January 13, 1902 – October 5, 1985) was an Austrian-American mathematician, the son of the economist Carl Menger. In mathematics, Menger studied the theory of algebras and the dimension theory of low- regularity ("rough") curves ...
in
Vienna
en, Viennese
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, registration_plate = W
, postal_code_type = Postal code
, postal_code =
, timezone = CET
, utc_offset = +1
, timezone_DST ...
, receiving a PhD in 1926. Hurewicz was awarded a Rockefeller scholarship, which allowed him to spend the year 1927–28 in
Amsterdam
Amsterdam ( , , , lit. ''The Dam on the River Amstel'') is the capital and most populous city of the Netherlands, with The Hague being the seat of government. It has a population of 907,976 within the city proper, 1,558,755 in the urban ar ...
. 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 schola ...
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 opposing ...
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 mathemati ...
. 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
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 words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
. The ''
Dictionary of Scientific Biography
The ''Dictionary of Scientific Biography'' is a scholarly reference work that was published from 1970 through 1980 by publisher Charles Scribner's Sons, with main editor the science historian Charles Gillispie, from Princeton University. It consi ...
'' states:
"...a remarkable result of this first period 930is his
topological embedding
In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.
When some object X is said to be embedded in another object Y, the embedding is giv ...
metric spaces
In mathematics, a metric space is a set together with a notion of ''distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general settin ...
finite
Finite is the opposite of infinite. It may refer to:
* Finite number (disambiguation)
* Finite set, a set whose cardinality (number of elements) is some natural number
* Finite verb, a verb form that has a subject, usually being inflected or marke ...
)
dimension
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 coor ...
.*"
In the field of
general topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometri ...
his contributions are centred on dimension theory. He wrote an important text with
Henry Wallman
Henry "Hank" Wallman (1915Biography of 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 three 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
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. 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 ide ...
, which were obviously
commutative
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name of ...
..."
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 ...
Mexico City
Mexico City ( es, link=no, Ciudad de México, ; abbr.: CDMX; Nahuatl: ''Altepetl Mexico'') is the capital city, capital and primate city, largest city of Mexico, and the List of North American cities by population, most populous city in North Amer ...
. 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 ...
step pyramid
A step pyramid or stepped pyramid is an architectural structure that uses flat platforms, or steps, receding from the ground up, to achieve a completed shape similar to a geometric pyramid. Step pyramids are structures which characterized several ...
during an outing in
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 ...
,
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
The ''Dictionary of Scientific Biography'' is a scholarly reference work that was published from 1970 through 1980 by publisher Charles Scribner's Sons, with main editor the science historian Charles Gillispie, from Princeton University. It consi ...
'' it is suggested that he was "...a paragon of absentmindedness, a failing that probably led to his death."
See also
*
Zygmunt Janiszewski
Zygmunt Janiszewski (12 July 1888 – 3 January 1920) was a Polish mathematician.
Early life and education
He was born to mother Julia Szulc-Chojnicka and father, Czeslaw Janiszewski who was a graduate of the University of Warsaw and served as t ...
*
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 ...