Samuel Eilenberg (1970)
September 30, 1913|
Warsaw, Poland, Russian Empire
|Died||January 30, 1998
New York City, United States
|Alma mater||University of Warsaw|
|Doctoral advisor||Kazimierz Kuratowski
|Doctoral students||Jonathan Beck
|Known for||Eilenberg–Steenrod axioms
|Notable awards||Wolf Prize (1986)
Leroy P. Steele Prize (1987)
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.
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.
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".
- Samuel Eilenberg (1974), Automata, Languages and Machines, Volume A. ISBN 0-12-234001-9.
- Samuel Eilenberg (1976), Automata, Languages and Machines, Volume B. ISBN 0-12-234002-7.
- Samuel Eilenberg & Tudor Ganea (1957), On the Lusternik-Schnirelmann category of abstract groups, Annals of Mathematics, 2nd Ser., 65, no. 3, 517 – 518. MR0085510
- Eilenberg, Samuel; Mac Lane, Saunders (1945). "Relations between homology and homotopy groups of spaces". Annals of Mathematics. 46: 480–509. doi:10.2307/1969165.
- Eilenberg, Samuel; Mac Lane, Saunders (1950). "Relations between homology and homotopy groups of spaces. II". Annals of Mathematics. 51: 514–533. doi:10.2307/1969365.
- Eilenberg, Samuel; Moore, John C. (1962), "Limits and spectral sequences", Topology, 1 (1): 1–23, ISSN 0040-9383, doi:10.1016/0040-9383(62)90093-9
- Eilenberg, Samuel; Niven, Ivan (1944). "The "fundamental theorem of algebra" for quaternions". Bull. Amer. Math. Soc. 50 (4): 246–248. MR 0009588. doi:10.1090/s0002-9904-1944-08125-1.
- Eilenberg, Samuel; Steenrod, Norman E. (1945). "Axiomatic approach to homology theory". Proc. Natl. Acad. Sci. U.S.A. 31 (4): 117–120. PMC . PMID 16578143. doi:10.1073/pnas.31.4.117.
- Samuel Eilenberg & Norman E. Steenrod (1952), Foundations of algebraic topology, Princeton University Press, Princeton, New Jersey. xv+328 pp.
- Stefan Banach
- Stanislaw Ulam
- Eilenberg–Ganea conjecture
- Eilenberg–Ganea theorem
- Eilenberg–MacLane space
- Eilenberg–Montgomery fixed point theorem
- Eilenberg–Moore spectral sequence
- Mac Lane, Saunders (1956). "Review: Homological algebra, by Henri Cartan and Samuel Eilenberg". Bull. Amer. Math. Soc. 62 (6): 615–624. doi:10.1090/S0002-9904-1956-10082-7.
- Pace, Eric (February 3, 1998), "Samuel Eilenberg, 84, Dies; Mathematician at Columbia", The New York Times
- Spanier, E. H. (1958). "Review: Foundations of Algebraic Topology, by S. Eilenberg and N. Steenrod". Bull. Amer. Math. Soc. 64 (4): 190–192. doi:10.1090/s0002-9904-1958-10204-9.
- Samuel Eilenberg at the Mathematics Genealogy Project
- O'Connor, John J.; Robertson, Edmund F., "Samuel Eilenberg", MacTutor History of Mathematics archive, University of St Andrews.
- Eilenberg's biography − from the National Academies Press, by Hyman Bass, Henri Cartan, Peter Freyd, Alex Heller and Saunders Mac Lane.