# Samuel Eilenberg

Samuel Eilenberg | |
---|---|

Samuel Eilenberg (1970) | |

Born |
Warsaw, Poland, Russian Empire | September 30, 1913

Died |
January 30, 1998 84) New York City, United States | (aged

Citizenship | American |

Nationality | Polish, American |

Fields | Mathematics |

Institutions | Columbia University |

Alma mater | University of Warsaw |

Doctoral advisor |
Kazimierz Kuratowski Karol Borsuk |

Doctoral students |
Jonathan Beck David Buchsbaum Kuo-Tsai Chen Martin Golumbic Alex Heller Daniel Kan William Lawvere Ramaiyengar Sridharan |

Known for |
Eilenberg–Steenrod axioms Eilenberg swindle |

Notable awards |
Wolf Prize (1986) Leroy P. Steele Prize (1987) |

**Samuel Eilenberg** (September 30, 1913 – January 30, 1998) was a Polish-born American mathematician.

## Biography

He was born in Warsaw, Kingdom of Poland to a Jewish family and died in New York City, United States, 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 Bourbaki and with Henri Cartan, wrote the 1956 book *Homological Algebra*,^{[1]} 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 modules.

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, 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". ^{[2]}*

## Selected publications

- Samuel Eilenberg (1974),
*Automata, Languages and Machines*. ISBN 0-12-234001-9. - Samuel Eilenberg & Tudor Ganea (1957),
*On the Lusternik-Schnirelmann category of abstract groups*,*Annals of Mathematics*, 2nd Ser.,**65**, no. 3, 517 – 518. MR 0085510 - 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, doi:10.1016/0040-9383(62)90093-9, ISSN 0040-9383 - Eilenberg, Samuel; Niven, Ivan (1944). "The "fundamental theorem of algebra" for quaternions".
*Bull. Amer. Math. Soc.***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".
*Proc. Natl. Acad. Sci. U.S.A.***31**(4): 117–120. doi:10.1073/pnas.31.4.117. PMC 1078770. PMID 16578143. - Samuel Eilenberg & Norman E. Steenrod (1952),
*Foundations of algebraic topology*, Princeton University Press, Princeton, New Jersey. xv+328 pp.^{[3]}

## See also

- Stefan Banach
- Stanislaw Ulam
- Eilenberg–Ganea conjecture
- Eilenberg–Ganea theorem
- Eilenberg–MacLane space
- Eilenberg–Montgomery fixed point theorem
- Eilenberg–Moore spectral sequence

## Footnotes

- ↑ 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.

## External links

- 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.