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Samuel Eilenberg (September 30, 1913—January 30, 1998) was a Polish
Poland

Poland , officially the Republic of Poland , is a country in Central Europe. Poland is 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 Enclave and exclave, to the north....
 and American
United States

The United States of America is a Federal government constitutional republic comprising U.S. state and a federal district. The country is situated mostly in central North America, where its Contiguous United States and Washington, D.C., the Capital districts and territories, lie between the Pacific Ocean and Atlantic Oceans, Borders of the U...
 mathematician
Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
 of Jewish descent
Jew

A Jew is a member of the Jewish people, an ethnoreligious group that traces its ancestry to the Israelites or Hebrews of the Ancient Near East....
. He was born in Warsaw
Warsaw

Warsaw is the Capital and World's largest cities of Poland. It is located on the Vistula River roughly from both the Baltic Sea coast and the Carpathian Mountains....
, Russian Empire
Russian Empire

File:Russian Emperor Flag.jpgFile:Romanov Flag.svgThe Russian Empire was a state that existed from 1721 until the Russian Revolution of 1917....
 (now in Poland
Poland

Poland , officially the Republic of Poland , is a country in Central Europe. Poland is 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 Enclave and exclave, to the north....
) and died in New York City
New York City

The City of New York is the List of United States cities by population in the United States, while the New York metropolitan area ranks among the List of urban areas by population....
, USA
United States

The United States of America is a Federal government constitutional republic comprising U.S. state and a federal district. The country is situated mostly in central North America, where its Contiguous United States and Washington, D.C., the Capital districts and territories, lie between the Pacific Ocean and Atlantic Oceans, Borders of the U...
, where he had spent much of his career as a professor at Columbia University
Columbia University

Columbia University in the City of New York , is a private university in the United States and a member of the Ivy League. Columbia's main campus lies in the Morningside Heights, Manhattan neighborhood in the borough of Manhattan, in New York City....
.

He earned his Ph.D.
Ph.D.

Ph.D. or PHD may stand for:* Doctor of Philosophy, an academic degree* Ph.D. , a 1980s British group* Piled Higher and Deeper, a web comic strip...
 from Warsaw University in 1936. His thesis advisor was Karol Borsuk
Karol Borsuk

Karol Borsuk was a Poland mathematician.His main interest was topology.Borsuk introduced the theory of absolute retracts and absolute neighborhood retracts , and the cohomotopy groups, later called Borsuk-Spanier cohomotopy groups....
. His main interest was algebraic topology
Algebraic topology

Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant that classification theorem topological spaces up to homeomorphism....
. He worked on the axiomatic treatment of homology theory
Homology theory

In mathematics, homology theory is the axiomatic study of the intuitive geometric idea of homology of cycles on topological spaces. It can be broadly defined as the study of Homology theories on topological spaces....
 with Norman Steenrod
Norman Steenrod

Norman Earl Steenrod was a preeminent topologist who most widely known for his contributions to the field of Algebraic Topology....
 (whose names the Eilenberg-Steenrod axioms
Eilenberg-Steenrod axioms

In mathematics, specifically in algebraic topology, the Eilenberg-Steenrod axioms are properties that homology theory of topological spaces have in common....
 bear), and on 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 Poincar? and David Hilbert....
 with Saunders Mac Lane
Saunders Mac Lane

Saunders Mac Lane was an United States mathematician who cofounded category theory with Samuel Eilenberg....
.






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Samuel Eilenberg (September 30, 1913—January 30, 1998) was a Polish
Poland

Poland , officially the Republic of Poland , is a country in Central Europe. Poland is 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 Enclave and exclave, to the north....
 and American
United States

The United States of America is a Federal government constitutional republic comprising U.S. state and a federal district. The country is situated mostly in central North America, where its Contiguous United States and Washington, D.C., the Capital districts and territories, lie between the Pacific Ocean and Atlantic Oceans, Borders of the U...
 mathematician
Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
 of Jewish descent
Jew

A Jew is a member of the Jewish people, an ethnoreligious group that traces its ancestry to the Israelites or Hebrews of the Ancient Near East....
. He was born in Warsaw
Warsaw

Warsaw is the Capital and World's largest cities of Poland. It is located on the Vistula River roughly from both the Baltic Sea coast and the Carpathian Mountains....
, Russian Empire
Russian Empire

File:Russian Emperor Flag.jpgFile:Romanov Flag.svgThe Russian Empire was a state that existed from 1721 until the Russian Revolution of 1917....
 (now in Poland
Poland

Poland , officially the Republic of Poland , is a country in Central Europe. Poland is 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 Enclave and exclave, to the north....
) and died in New York City
New York City

The City of New York is the List of United States cities by population in the United States, while the New York metropolitan area ranks among the List of urban areas by population....
, USA
United States

The United States of America is a Federal government constitutional republic comprising U.S. state and a federal district. The country is situated mostly in central North America, where its Contiguous United States and Washington, D.C., the Capital districts and territories, lie between the Pacific Ocean and Atlantic Oceans, Borders of the U...
, where he had spent much of his career as a professor at Columbia University
Columbia University

Columbia University in the City of New York , is a private university in the United States and a member of the Ivy League. Columbia's main campus lies in the Morningside Heights, Manhattan neighborhood in the borough of Manhattan, in New York City....
.

He earned his Ph.D.
Ph.D.

Ph.D. or PHD may stand for:* Doctor of Philosophy, an academic degree* Ph.D. , a 1980s British group* Piled Higher and Deeper, a web comic strip...
 from Warsaw University in 1936. His thesis advisor was Karol Borsuk
Karol Borsuk

Karol Borsuk was a Poland mathematician.His main interest was topology.Borsuk introduced the theory of absolute retracts and absolute neighborhood retracts , and the cohomotopy groups, later called Borsuk-Spanier cohomotopy groups....
. His main interest was algebraic topology
Algebraic topology

Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant that classification theorem topological spaces up to homeomorphism....
. He worked on the axiomatic treatment of homology theory
Homology theory

In mathematics, homology theory is the axiomatic study of the intuitive geometric idea of homology of cycles on topological spaces. It can be broadly defined as the study of Homology theories on topological spaces....
 with Norman Steenrod
Norman Steenrod

Norman Earl Steenrod was a preeminent topologist who most widely known for his contributions to the field of Algebraic Topology....
 (whose names the Eilenberg-Steenrod axioms
Eilenberg-Steenrod axioms

In mathematics, specifically in algebraic topology, the Eilenberg-Steenrod axioms are properties that homology theory of topological spaces have in common....
 bear), and on 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 Poincar? and David Hilbert....
 with Saunders Mac Lane
Saunders Mac Lane

Saunders Mac Lane was an United States mathematician who cofounded category theory with Samuel Eilenberg....
. In the process, Eilenberg and Mac Lane created category theory
Category theory

In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from set s and function s to objects linked in diagrams by morphisms or arrows....
.

Eilenberg took part in the Bourbaki
Nicolas Bourbaki

Nicolas Bourbaki is the collective pseudonym under which a group of 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935....
 group meetings, and, with Henri Cartan
Henri Cartan

Henri Paul Cartan was a son of ?lie Cartan, and was, as his father was, a distinguished and influential France mathematician....
, wrote the 1956 book Homological Algebra, which became a classic.

Later in life he worked mainly in pure category theory
Category theory

In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from set s and function s to objects linked in diagrams by morphisms or arrows....
, being one of the founders of the field. The Eilenberg swindle (or telescope) is a construction applying the telescoping cancellation idea to projective module
Projective module

In mathematics, particularly in abstract algebra and homological algebra, the concept of projective module over a ring R is a more flexible generalisation of the idea of a free module ....
s.

Eilenberg also wrote an important book on automata theory
Automata theory

In theoretical computer science, automata theory is the study of abstract machines and problems which they are able to solve. Automata theory is closely related to formal language theory as the automata are often classified by the class of formal languages they are able to recognize....
. The X-machine
X-machine

The 'X-machine' is a theoretical model of computation introduced by Samuel Eilenberg in 1974.S. Eilenberg Automata, Languages and Machines, Vol....
, a form of automaton, was introduced by Eilenberg in 1974.

Selected publications

  • Samuel Eilenberg, Automata, Languages and Machines. ISBN 0-12-234001-9
  • Samuel Eilenberg & Tudor Ganea, , Annals of Mathematics, 2nd Ser., 65 (1957), no. 3, 517 – 518.
  • Samuel Eilenberg & Saunders Mac Lane, "Relations between homology and homotopy groups of spaces", Annals of Mathematics
    Annals of Mathematics

    The Annals of Mathematics , abbreviated as Ann. of Math. and often just called Annals, is a bimonthly mathematics research journal published by Princeton University and the Institute for Advanced Study....
     46 (1945), 480–509.
  • Samuel Eilenberg & Saunders Mac Lane, "Relations between homology and homotopy groups of spaces. II", Annals of Mathematics 51 (1950), 514–533.
  • Samuel Eilenberg & Norman E. Steenrod, Axiomatic approach to homology theory, Proc. Nat. Acad. Sci. U. S. A. 31, (1945). 117--120.
  • Samuel Eilenberg & Norman E. Steenrod, Foundations of algebraic topology, Princeton University Press
    Princeton University Press

    The Princeton University Press is an independent Academic publishing with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large....
    , Princeton, New Jersey, 1952. xv+328 pp.


See also

  • Stefan Banach
    Stefan Banach

    Stefan Banach was a Polish mathematician who worked in Second Polish Republic and in Soviet Ukraine.A self-taught mathematics Child prodigy, Banach was the founder of modern functional analysis and a founder of the Lw?w School of Mathematics....
  • Stanislaw Ulam
  • Eilenberg-Ganea conjecture
    Eilenberg-Ganea conjecture

    The Eilenberg-Ganea conjecture is a claim in algebraic topology. It was formulated by Samuel Eilenberg and Tudor Ganea in 1957, in a short, but influential paper....
  • Eilenberg-MacLane space
    Eilenberg-MacLane space

    In mathematics, an Eilenberg-MacLane space is a special kind of topological space that can be regarded as a building block for homotopy theory. These spaces are important in many contexts in algebraic topology, including stage-by-stage constructions of spaces, computations of homotopy groups of spheres, and definition of cohomology operations...
  • Eilenberg-Moore spectral sequence
    Eilenberg-Moore spectral sequence

    In mathematics, in the field of algebraic topology, the Eilenberg-Moore spectral sequence addresses the calculation of the homology groups of a pullback over a fibration....


External links

  • - from the National Academies Press
    National Academies Press

    National Academies Press was created by the United States National Academies, to publish the reports issued by the United States National Academy of Sciences,...
    , by Hyman Bass
    Hyman Bass

    Hyman Bass is an American mathematician, known for work in algebra. From 1959-1998 he was Professor in the Mathematics Department at Columbia University, where he is now professor emeritus....
    , Henri Cartan
    Henri Cartan

    Henri Paul Cartan was a son of ?lie Cartan, and was, as his father was, a distinguished and influential France mathematician....
    , Peter Freyd, Alex Heller and Saunders Mac Lane
    Saunders Mac Lane

    Saunders Mac Lane was an United States mathematician who cofounded category theory with Samuel Eilenberg....
    .