Samuel Eilenberg
Encyclopedia
Samuel Eilenberg was a Polish
and American
mathematician
of Jewish descent. He was born in Warsaw
, Russian Empire
(now in Poland
) and died in New York City
, USA
, where he had spent much of his career as a professor at Columbia University
.
He earned his Ph.D.
from University of Warsaw
in 1936. His thesis advisor was Karol Borsuk
. His main interest was algebraic topology
. He worked on the axiomatic treatment of homology theory
with Norman Steenrod
(whose names the Eilenberg–Steenrod axioms bear), and on homological algebra
with Saunders Mac Lane
. In the process, Eilenberg and Mac Lane created category theory
.
Eilenberg was a member of the Bourbaki
and with Henri Cartan
, wrote the 1956 book Homological Algebra, which became a classic.
Later in life he worked mainly in pure category theory, being one of the founders of the field. The Eilenberg swindle (or telescope) is a construction applying the telescoping cancellation idea to projective module
s.
Eilenberg also wrote an important book on automata theory
. The X-machine
, a form of automaton, was introduced by Eilenberg in 1974.
Eilenberg was also a prominent collector of Asian art. His collection mainly consisted of small sculptures and other artifacts from India, Indonesia, Pakistan, Nepal, Thailand, Cambodia, Sri Lanka and Central Asia. In 1991-1992, the Metropolitan Museum of Art in New York staged an exhibition from more than 400 items that Eilenberg had donated to the museum, entitled The Lotus Transcendent: Indian and Southeast Asian Art From the Samuel Eilenberg Collection".
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...
and American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
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....
of Jewish descent. He was born in Warsaw
Warsaw
Warsaw is the capital and largest city of Poland. It is located on the Vistula River, roughly from the Baltic Sea and from the Carpathian Mountains. Its population in 2010 was estimated at 1,716,855 residents with a greater metropolitan area of 2,631,902 residents, making Warsaw the 10th most...
, Russian Empire
Russian 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 in 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...
) and died in New York City
New York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
, USA
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
, 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, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
.
He earned his 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...
from 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...
in 1936. His thesis advisor was Karol Borsuk
Karol Borsuk
Karol Borsuk was a Polish 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. He also founded the so called Shape theory...
. 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 invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.Although algebraic topology...
. 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.-The general idea:...
with Norman Steenrod
Norman Steenrod
Norman Earl Steenrod was a preeminent mathematician most widely known for his contributions to the field of algebraic topology.-Life:...
(whose names the Eilenberg–Steenrod axioms 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 Poincaré and...
with Saunders Mac Lane
Saunders Mac Lane
Saunders Mac Lane was an American mathematician who cofounded category theory with Samuel Eilenberg.-Career:...
. In the process, Eilenberg and Mac Lane created category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
.
Eilenberg was a member of 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. With the goal of founding all of mathematics on set theory, the group strove for rigour and generality...
and with Henri Cartan
Henri Cartan
Henri Paul Cartan was a French mathematician with substantial contributions in algebraic topology. He was the son of the French mathematician Élie Cartan.-Life:...
, wrote the 1956 book Homological Algebra, which became a classic.
Later in life he worked mainly in pure category theory, 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 the computational problems that can be solved using these machines. These abstract machines are called automata...
. 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.
Eilenberg was also a prominent collector of Asian art. His collection mainly consisted of small sculptures and other artifacts from India, Indonesia, Pakistan, Nepal, Thailand, Cambodia, Sri Lanka and Central Asia. In 1991-1992, the Metropolitan Museum of Art in New York staged an exhibition from more than 400 items that Eilenberg had donated to the museum, entitled The Lotus Transcendent: Indian and Southeast Asian Art From the Samuel Eilenberg Collection".
Selected publications
- Samuel Eilenberg, Automata, Languages and Machines. ISBN 0-12-234001-9.
- Samuel Eilenberg & Tudor Ganea, On the Lusternik-Schnirelmann category of abstract groups, 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 MathematicsAnnals of MathematicsThe Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study. It ranks amongst the most prestigious mathematics journals in the world by criteria such as impact factor.-History:The journal began as The Analyst in 1874 and was...
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 PressPrinceton University Press-Further reading:* "". Artforum International, 2005.-External links:* * * * *...
, Princeton, New Jersey, 1952. xv+328 pp.
See also
- Stefan BanachStefan BanachStefan Banach was a Polish mathematician who worked in interwar Poland and in Soviet Ukraine. He is generally considered to have been one of the 20th century's most important and influential mathematicians....
- Stanisław Ulam
- Eilenberg–Ganea conjecture
- Eilenberg–MacLane space
- Eilenberg-Montgomery fixed point theorem
- Eilenberg–Moore spectral sequence
External links
- Eilenberg's biography − from the National Academies PressNational Academies PressNational Academies Press was created by the United States National Academies, to publish the reports issued by the National Academy of Sciences, the National Academy of Engineering, the Institute of Medicine, and the National Research Council. It publishes nearly 200 books a year on a wide range...
, by Hyman BassHyman BassHyman Bass is an American mathematician, known for work in algebra and in mathematics education. From 1959-1998 he was Professor in the Mathematics Department at Columbia University, where he is now professor emeritus...
, Henri CartanHenri CartanHenri Paul Cartan was a French mathematician with substantial contributions in algebraic topology. He was the son of the French mathematician Élie Cartan.-Life:...
, Peter Freyd, Alex Heller and Saunders Mac LaneSaunders Mac LaneSaunders Mac Lane was an American mathematician who cofounded category theory with Samuel Eilenberg.-Career:...
.