Witold Hurewicz (June 29, 1904 - September 6, 1956) was a Polish mathematician. He was born in Lodz, Russian Empire (now Poland), and died during a conference on algebraic topology in Uxmal, Mexico after tripping and falling off the top of a Mayan ziggurat. June 29 is the 180th day of the year (181st in leap years) in the Gregorian Calendar, with 185 days remaining. ... 1904 is a leap year starting on a Friday (link will take you to calendar). ... September 6 is the 249th day of the year (250th in leap years). ... 1956 (MCMLVI) was a leap year starting on Sunday of the Gregorian calendar. ... . Łódź (pronunciation: ) is the second-largest city (population 776,297 in 2004) of Poland, located in the centre of the country. ... Imperial Russia is the term used to cover the period of Russian history from the expansion of Russia under Peter the Great, through the expansion of the Russian Empire from the Baltic to the Pacific Ocean, to the deposal of Nicholas II of Russia, the last tsar, at the start... Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. ... Uxmal is a large Pre-Columbian ruined city of the Maya civilization in the state of Yucatán, Mexico. ... Bold textItalic textThe adjective Mayan refers to a people of what is now parts of Mexico and Central America, their culture, language, and history. ... Dur-Untash, or Choqa zanbil, built in 13th century BC by Untash Napirisha, is one of the worlds best preserved ziggurats. ...

Witold Hurewicz's father was an industrialist. Witold 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. World War I was primarily a European conflict with many facets: immense human sacrifice, stalemate trench warfare, and the use of new, devastating weapons - tanks, aircraft, machine guns, and poison gas World War I, also known as the First World War, the Great War, the War of the Nations and... Secondary school may refer to Secondary school in the United Kingdom, is the general term for the schools for children between the ages of eleven and eighteen in most areas (a few areas have schools for 13-18 year olds instead, and these are called upper schools). ... Austria-Hungary, also known as the Dual monarchy (or: the k. ... Warsaw University (Polish Uniwersytet Warszawski) - the biggest and one of the most prestigious universities in Poland. ... Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants. ... Vienna (German: Wien [viːn]; Hungarian: Bécs, Czech: Vídeň, Slovak: Viedeň, Romany Vidnya; Serbian: Beč) is the capital of Austria, and also one of Austrias nine states (Land Wien). ...

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 and then decided to remain in the United States and not return to his position in Amsterdam. Given the impending war in Europe this was clearly a wise decision. Hans Hahn (1879 - 1934) was an Austrian mathematician who made many contributions to functional analysis, topology, set theory, the calculus of variations, real analysis, and order theory. ... This article is about the mathematician. ... Doctor of Philosophy (Ph. ... Amsterdam Location Country The Netherlands Province North Holland Population 739,295 (1 January 2005) Coordinates 4°54E - 52°22N Website www. ... Brouwer is the last name of different people. ... Fuld Hall The Institute for Advanced Study is a private institution in Princeton Township, New Jersey, designed to foster pure cutting-edge research by scientists in a variety of fields without the complications of teaching or funding, or the agendas of sponsorship. ... Princeton is the name of several places in the United States of America: Princeton, Florida Princeton, Illinois Princeton, Indiana Princeton, Iowa Princeton, Kansas Princeton, Kentucky Princeton, Louisiana Princeton, Maine Princeton, Massachusetts Princeton, Minnesota Princeton, Missouri Princeton, New Jersey Princeton, North Carolina Princeton, South Carolina Princeton, Texas Princeton, West Virginia Princeton... Europe forms the westernmost part of Eurasia. ...

Hurewicz worked first at the University of North Carolina 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 died falling off a ziggurat during a conference outing at the International Symposium on Algebraic Topology in 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." The University of North Carolina, often called the University of North Carolina System to avoid confusion, is a federation of all sixteen public universities in North Carolina. ... World War II was a truly global conflict with many facets: immense human suffering, fierce indoctrinations, and the use of new, extremely devastating weapons such as the atom bomb. ... Applied mathematics is a branch of mathematics that concerns itself with the application of mathematical knowledge to other domains. ... The Massachusetts Institute of Technology, or MIT, is a research and educational institution located in the city of Cambridge, Massachusetts, USA. MIT is a widely renowned leader in science and technology, as well as in many other fields, including engineering systems, management, economics, linguistics, political science, and philosophy. ... Dur-Untash, or Choqa zanbil, built in 13th century BC by Untash Napirisha, is one of the worlds best preserved ziggurats. ...

Hurewicz's early work was on set theory and topology. Again from the Dictionary of Scientific Biography, "...a remarkable result of this first period [1930] is his topological embedding of separable metric spaces into compact spaces of the same (finite) dimension." Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants. ... In mathematics, an embedding (or imbedding) is one instance of some mathematical object contained within another instance, such as a group that is a subgroup. ... Separable can refer to: Separable space in topology Separable sigma algebra in measure theory Separable differential equations This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ... In mathematics, a metric space is a set (or space) where a distance between points is defined. ... In mathematics, a compact space is a space that resembles a closed and bounded subset of Euclidean space Rn in that it is small in a certain sense and contains all its limit points. The modern general definition calls a topological space compact if every open cover of it has... In mathematics, a set is called finite if and only if there is a bijection between the set and some set of the form {1, 2, ..., n} where is a natural number. ... In common usage, the dimensions (from Latin measured out) of an object are the parameters or measurements required to define its shape and size, that is, usually, its height, width, and length. ...

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..." In mathematics, especially in homological algebra and other applications of Abelian category theory, as well as in group theory, an exact sequence is a (finite or infinite) sequence of objects and morphisms between them such that the image of one morphism equals the kernel of the next. ... Homological algebra is the branch of mathematics which studies the methods of homology and cohomology in a general setting. ... The term group can refer to several concepts: In music, a group is another term for band or other musical ensemble. ... In mathematics, especially abstract algebra, a binary operation * on a set S is commutative if x * y = y * x for all x and y in S. Otherwise * is noncommutative. ...

Hurewicz had a second textbook published, but this was not until 1958 after his death. "Lectures on ordinary differential equations" is a beautiful introduction to ordinary differential equations which again reflects the clarity of his thinking and the quality of his writing. In mathematics, a differential equation is an equation that describes a prescribed relationship between a set of unknowns which are to be regarded as an unknown function and its (ordinary or partial) derivatives. ...

Article by: J J O'Connor and E F Robertson

See also: Zygmunt Janiszewski Zygmunt Janiszewski (b. ...

External links

• Biography at the MacTutor archive