Witold Hurewicz
Encyclopedia
Witold Hurewicz was a Polish
mathematician
.
(now Poland
).
His father was an industrialist. Hurewicz attended school in a Russian 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 which 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 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.
He studied under Hans Hahn
and Karl Menger
in Vienna
, receiving a Ph.D.
in 1926. Hurewicz was awarded a Rockefeller scholarship
which allowed him to spend the year 1927-28 in Amsterdam
. He was assistant to 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.
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 [1930] 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, and his discovery of exact sequences in 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 Topology in Uxmal
, Mexico
after tripping and falling off the top of a Mayan
step pyramid
. In the Dictionary of Scientific Biography
it is suggested that he was "...a paragon of absentmindedness, a failing that probably led to his death."
Poland
Poland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
Early life and education
Witold Hurewicz was born to a Jewish family in Łódź, Russian EmpireRussian Empire
The Russian Empire was a state that existed from 1721 until the Russian Revolution of 1917. It was the successor to the Tsardom of Russia and the predecessor of the Soviet Union...
(now Poland
Poland
Poland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...
).
His father was an industrialist. Hurewicz attended school in a Russian controlled Poland but with World War I
World War I
World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...
beginning before he had begun secondary school
Secondary school
Secondary school is a term used to describe an educational institution where the final stage of schooling, known as secondary education and usually compulsory up to a specified age, takes place...
, major changes occurred in Poland. In August 1915 the Russian forces which had held Poland for many years withdrew. Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
and Austria-Hungary
Austria-Hungary
Austria-Hungary , more formally known as the Kingdoms and Lands Represented in the Imperial Council and the Lands of the Holy Hungarian Crown of Saint Stephen, was a constitutional monarchic union between the crowns of the Austrian Empire and the Kingdom of Hungary in...
took control of most of the country and the University of Warsaw
University of Warsaw
The University of Warsaw is the largest university in Poland and one of the most prestigious, ranked as best Polish university in 2010 and 2011...
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
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
one of the main topics. Although Hurewicz knew intimately the topology that was being studied in Poland he chose to go to Vienna
Vienna
Vienna is the capital and largest city of the Republic of Austria and one of the nine states of Austria. Vienna is Austria's primary city, with a population of about 1.723 million , and is by far the largest city in Austria, as well as its cultural, economic, and political centre...
to continue his studies.
He studied under Hans Hahn
Hans Hahn
Hans Hahn was an Austrian mathematician who made contributions to functional analysis, topology, set theory, the calculus of variations, real analysis, and order theory.-Biography:...
and Karl Menger
Karl Menger
Karl Menger was a mathematician. He was the son of the famous economist Carl Menger. He is credited with Menger's theorem. He worked on mathematics of algebras, algebra of geometries, curve and dimension theory, etc...
in Vienna
Vienna
Vienna is the capital and largest city of the Republic of Austria and one of the nine states of Austria. Vienna is Austria's primary city, with a population of about 1.723 million , and is by far the largest city in Austria, as well as its cultural, economic, and political centre...
, receiving a Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in 1926. Hurewicz was awarded a Rockefeller scholarship
Rockefeller Foundation
The Rockefeller Foundation is a prominent philanthropic organization and private foundation based at 420 Fifth Avenue, New York City. The preeminent institution established by the six-generation Rockefeller family, it was founded by John D. Rockefeller , along with his son John D. Rockefeller, Jr...
which allowed him to spend the year 1927-28 in Amsterdam
Amsterdam
Amsterdam is the largest city and the capital of the Netherlands. The current position of Amsterdam as capital city of the Kingdom of the Netherlands is governed by the constitution of August 24, 1815 and its successors. Amsterdam has a population of 783,364 within city limits, an urban population...
. He was assistant to Brouwer
Brouwer
Brouwer is a Dutch and Flemish surname. The word brouwer means 'beer brewer'.- Brouwer :* Adriaen Brouwer , Flemish painter* Andries Brouwer, Dutch mathematician and computer programmer...
in Amsterdam from 1928 to 1936. He was given study leave for a year which he decided to spend in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
. He visited the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton, New Jersey
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
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 HillUniversity of North Carolina at Chapel Hill
The University of North Carolina at Chapel Hill is a public research university located in Chapel Hill, North Carolina, United States...
but during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
he contributed to the war effort with research on applied mathematics
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
. 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
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
.
Hurewicz's early work was on set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
and topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
. The Dictionary of Scientific Biography
Dictionary of Scientific Biography
The Dictionary of Scientific Biography is a scholarly reference work that was published from 1970 through 1980. It is supplemented by the New Dictionary of Scientific Biography and an electronic version that includes both publications....
describes it as:
"...a remarkable result of this first period [1930] is his topological embedding of separable metric spaces into compact spaces of the same (finite) dimension
Dimension
In physics and mathematics, the dimension of a 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 because only one coordinate is needed to specify a point on it...
.*"
In the field of general topology his contributions are centred around dimension theory
Dimension theory
In mathematics, dimension theory is a branch of general topology dealing with dimensional invariants of topological spaces.-See also:*Lebesgue covering dimension*Inductive dimensions *Dimension...
. He wrote an important text with Henry Wallman
Henry Wallman
Henry Wallman was an American mathematician, known for his work in lattice theory, dimension theory, topology, and electronic circuit design.A native of Brooklyn and a 1933 graduate of Brooklyn College, Wallman received his Ph.D...
, Dimension Theory
Dimension theory
In mathematics, dimension theory is a branch of general topology dealing with dimensional invariants of topological spaces.-See also:*Lebesgue covering dimension*Inductive dimensions *Dimension...
, 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, and his discovery of exact sequences in 1941. His work led to homological algebra
Homological algebra
Homological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology and abstract algebra at the end of the 19th century, chiefly by Henri Poincaré and...
. 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
Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity...
, 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 Topology in Uxmal
Uxmal
Uxmal was dominant from 875 to 900 CE. The site appears to have been the capital of a regional state in the Puuc region from 850-950 CE. The Maya dynasty expanded their dominion over their neighbors. This prominence didn't last long...
, Mexico
Mexico
The United Mexican States , commonly known as Mexico , is a federal constitutional republic in North America. It is bordered on the north by the United States; on the south and west by the Pacific Ocean; on the southeast by Guatemala, Belize, and the Caribbean Sea; and on the east by the Gulf of...
after tripping and falling off the top of a Mayan
Maya civilization
The Maya is a Mesoamerican civilization, noted for the only known fully developed written language of the pre-Columbian Americas, as well as for its art, architecture, and mathematical and astronomical systems. Initially established during the Pre-Classic period The Maya is a Mesoamerican...
step pyramid
Step pyramid
Step pyramids are structures which characterized several cultures throughout history, in several locations throughout the world. These pyramids typically are large and made of several layers of stone...
. In the Dictionary of Scientific Biography
Dictionary of Scientific Biography
The Dictionary of Scientific Biography is a scholarly reference work that was published from 1970 through 1980. It is supplemented by the New Dictionary of Scientific Biography and an electronic version that includes both publications....
it is suggested that he was "...a paragon of absentmindedness, a failing that probably led to his death."
External links
- Solomon LefschetzSolomon LefschetzSolomon Lefschetz was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.-Life:...
Witold Hurewicz, In memoriam Bull. Amer. Math. Soc. 63, (1957), 77-82.