Samuel Eilenberg

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Samuel Eilenberg
Samuel Eilenberg (1970)
Born(1913-09-30)September 30, 1913
DiedJanuary 30, 1998(1998-01-30) (aged 84)
New York City, United States
CitizenshipRussian, Polish, American
Alma materUniversity of Warsaw
Known forAcyclic model
Category theory
Weak dimension
Projective module
Shuffle algebra
Simplicial set
Standard complex
Eilenberg's obstruction theory
Eilenberg swindle
Eilenberg–Ganea conjecture
Eilenberg–Ganea theorem
Eilenberg–MacLane space
Eilenberg–Moore spectral sequence
Eilenberg–Niven theorem
Eilenberg–Steenrod axioms
Eilenberg–Zilber theorem
Cartan–Eilenberg resolution
Chevalley–Eilenberg complex
AwardsWolf Prize (1986)
Leroy P. Steele Prize (1987)
Scientific career
InstitutionsColumbia University
Thesis On the Topological Applications of Maps onto a Circle  (1936)
Doctoral advisorsKazimierz Kuratowski
Karol Borsuk
Doctoral studentsJonathan Beck
David Buchsbaum
Martin Golumbic
Daniel Kan
William Lawvere
Ramaiyengar Sridharan
Myles Tierney

Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish-American mathematician who co-founded category theory (with Saunders Mac Lane) and homological algebra.

Early life and education[edit]

He was born in Warsaw, Kingdom of Poland to a Jewish family. He spent much of his career as a professor at Columbia University.

He earned his Ph.D. from University of Warsaw in 1936, with thesis On the Topological Applications of Maps onto a Circle; his thesis advisors were Kazimierz Kuratowski and Karol Borsuk.[1] He died in New York City in January 1998.


Eilenberg's main body of work was in algebraic topology. He worked on the axiomatic treatment of homology theory with Norman Steenrod (and the Eilenberg–Steenrod axioms are named for the pair), and on homological algebra with Saunders Mac Lane. In the process, Eilenberg and Mac Lane created category theory.

Eilenberg was a member of Bourbaki and, with Henri Cartan, wrote the 1956 book Homological Algebra.[2]

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 modules.

Eilenberg contributed to automata theory and algebraic automata theory. In particular, he introduced a model of computation called X-machine and a new prime decomposition algorithm for finite state machines in the vein of Krohn–Rhodes theory.

Art collection[edit]

Eilenberg was also a prominent collector of Asian art. His collection mainly consisted of small sculptures and other artifacts from India, Indonesia, 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.[3] In reciprocity, the Metropolitan Museum of Art donated substantially to the endowment of the Samuel Eilenberg Visiting Professorship in Mathematics at Columbia University.[4]

Selected publications[edit]

Saunders Mac Lane and Eilenberg at a conference in July 1992
  • Eilenberg, Samuel (1974). Automata, Languages and Machines, Volume A. ISBN 0-12-234001-9.
  • Eilenberg, Samuel (1976). Automata, Languages and Machines, Volume B. Academic Press. ISBN 0-12-234002-7.
  • Eilenberg, Samuel; Ganea, Tudor (1957). "On the Lusternik-Schnirelmann category of abstract groups". Annals of Mathematics. 2nd Series. 65 (3): 517–518. doi:10.2307/1970062. JSTOR 1970062. MR 0085510.
  • Eilenberg, Samuel; Mac Lane, Saunders (1945). "Relations between homology and homotopy groups of spaces". Annals of Mathematics. 46 (3): 480–509. doi:10.2307/1969165. JSTOR 1969165.
  • Eilenberg, Samuel; Mac Lane, Saunders (1950). "Relations between homology and homotopy groups of spaces. II". Annals of Mathematics. 51 (3): 514–533. doi:10.2307/1969365. JSTOR 1969365.
  • Eilenberg, Samuel; Moore, John C. (1962), "Limits and spectral sequences", Topology, 1 (1): 1–23, doi:10.1016/0040-9383(62)90093-9, ISSN 0040-9383
  • Eilenberg, Samuel; Niven, Ivan (1944). "The "fundamental theorem of algebra" for quaternions". Bulletin of the American Mathematical Society. 50 (4): 246–248. doi:10.1090/s0002-9904-1944-08125-1. MR 0009588.
  • Eilenberg, Samuel; Steenrod, Norman E. (1945). "Axiomatic approach to homology theory". Proceedings of the National Academy of Sciences of the United States of America. 31 (4): 117–120. Bibcode:1945PNAS...31..117E. doi:10.1073/pnas.31.4.117. PMC 1078770. PMID 16578143.
  • Eilenberg, Samuel; Steenrod, Norman E. (1952). Foundations of algebraic topology. Princeton, New Jersey: Princeton University Press. MR 0050886.[5]

See also[edit]


External links[edit]