Samuel Eilenberg

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.{{MathGenealogy |id=7643}} 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. As a result of this work, Eilenberg and Mac Lane developed the field of category theory, for which they are now best known.

Eilenberg was a member of Bourbaki and, with Henri Cartan, wrote the 1956 book Homological Algebra.{{cite journal|last=Mac Lane|first= Saunders|author-link=Saunders Mac Lane|title=Review: Homological algebra, by Henri Cartan and Samuel Eilenberg|journal=Bulletin of the American Mathematical Society |year=1956|volume=62|issue=6|pages=615–624|url=http://www.ams.org/journals/bull/1956-62-06/S0002-9904-1956-10082-7/|doi=10.1090/S0002-9904-1956-10082-7|doi-access=free}}

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. He also identified a natural correspondence between certain classes of regular languages called varieties and pseudovarieties of finite monoids, a result which is now known as Eilenberg's theorem.

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.{{citation |last=Pace |first=Eric |title=Samuel Eilenberg, 84, Dies; Mathematician at Columbia | newspaper=The New York Times |date=February 3, 1998 |url=https://www.nytimes.com/1998/02/03/nyregion/samuel-eilenberg-84-dies-mathematician-at-columbia.html}}{{Cite web |title=The Lotus Transcendent: Indian and Southeast Asian Art from the Samuel Eilenberg Collection - The Metropolitan Museum of Art |url=https://www.metmuseum.org/met-publications/the-lotus-transcendent-indian-and-southeast-asian-art-from-the-samuel-eilenberg-collection |access-date=2024-07-26 |website=www.metmuseum.org |language=en}} In reciprocity, the Metropolitan Museum of Art donated substantially to the endowment of the Samuel Eilenberg Visiting Professorship in Mathematics at Columbia University.{{cite journal|last1=Bass|first1=Hyman|author-link=Hyman Bass|last2=Cartan|first2= Henri|author2-link=Henri Cartan|last3=Freyd|first3= Peter|author3-link=Peter Freyd|last4=Heller|first4= Alex|last5=Mac Lane|first5= Saunders| author5-link=Saunders Mac Lane|title=Samuel Eilenberg (1913–1998)|journal=Notices of the American Mathematical Society|volume=45|issue=10|year=1998|pages=1344–1352|url=https://www.ams.org/notices/199810/mem-eilenberg.pdf}}{{Cite web |last=Yorke |first=Department of Mathematics at Columbia University New |title=Department of Mathematics at Columbia University - FALL 2023 SAMUEL EILENBERG LECTURES |url=https://www.math.columbia.edu/2023/08/18/fall-2023-samuel-eilenberg-lectures/ |access-date=2024-07-26 |language=en}}

File:1-image0.jpg and Eilenberg at a conference in July 1992]]

• {{cite book | last1=Eilenberg | first1=Samuel | year=1974|title=Automata, Languages and Machines, Volume A| publisher=Academic Press |isbn = 0-12-234001-9}}
• {{cite book | last1=Eilenberg | first1=Samuel | year=1976|title=Automata, Languages and Machines, Volume B| publisher=Academic Press |isbn = 0-12-234002-7}}
• {{cite journal|first1=Samuel|last1= Eilenberg|first2= Tudor|last2= Ganea |

author2-link=Tudor Ganea| year=1957|jstor=1970062 |title =On the Lusternik-Schnirelmann category of abstract groups| journal=Annals of Mathematics |series= 2nd Series |volume=65|issue= 3|pages=517–518|mr=0085510|doi= 10.2307/1970062}}

• {{cite journal | last1 = Eilenberg | first1 = Samuel | last2 = Mac Lane | first2 = Saunders | author2-link=Saunders Mac Lane| year = 1945 | title = Relations between homology and homotopy groups of spaces | journal = Annals of Mathematics | volume = 46 | issue = 3| pages = 480–509 | doi=10.2307/1969165| jstor = 1969165 }}
• {{cite journal | last1 = Eilenberg | first1 = Samuel | last2 = Mac Lane | first2 = Saunders | author2-link=Saunders Mac Lane|year = 1950 | title = Relations between homology and homotopy groups of spaces. II | journal = Annals of Mathematics | volume = 51 | issue = 3| pages = 514–533 | doi=10.2307/1969365| jstor = 1969365 }}
• {{Citation | last1=Eilenberg | first1=Samuel | last2=Moore | first2=John C. |author2-link=John Coleman Moore| title=Limits and spectral sequences | year=1962 | journal=Topology | issn=0040-9383 | volume=1 | issue=1 | pages=1–23 | doi=10.1016/0040-9383(62)90093-9 | doi-access=free }}
• {{Cite journal | last1=Eilenberg | first1=Samuel | last2=Niven | first2=Ivan | author-link2=Ivan Niven | title=The "fundamental theorem of algebra" for quaternions | journal=Bulletin of the American Mathematical Society | year=1944 | volume=50 |issue=4 |pages=246–248 | mr=0009588 | doi=10.1090/s0002-9904-1944-08125-1| doi-access=free }}
• {{Cite journal | last1 = Eilenberg | first1=Samuel | last2=Steenrod | first2=Norman E. | author2-link=Norman Steenrod| title=Axiomatic approach to homology theory | year=1945 | volume=31 | pages=117–120 | journal=Proceedings of the National Academy of Sciences of the United States of America | pmc=1078770 | pmid=16578143 | issue=4 | doi=10.1073/pnas.31.4.117| bibcode=1945PNAS...31..117E | doi-access=free }}
• {{Cite book | last1 = Eilenberg | first1=Samuel | last2=Steenrod | first2=Norman E. | author2-link=Norman Steenrod| year=1952|title=Foundations of Algebraic Topology|publisher= Princeton University Press|location= Princeton, New Jersey|mr=0050886}}{{cite journal|last=Spanier|first= Edwin H.|author-link=Edwin Spanier|title=Review: Foundations of Algebraic Topology, by S. Eilenberg and N. Steenrod|journal=Bulletin of the American Mathematical Society|year=1958|volume=64|issue=4|pages=190–192|url=http://www.ams.org/journals/bull/1958-64-04/S0002-9904-1958-10204-9/|doi=10.1090/s0002-9904-1958-10204-9|doi-access=free}}

• Stefan Banach
• Stanislaw Ulam
• Eilenberg–Montgomery fixed point theorem

{{Reflist}}

• {{MacTutor Biography|id=Eilenberg}}
• [https://archive.today/20060831114317/http://newton.nap.edu/html/biomems/seilenberg.html Eilenberg's biography] − from the National Academies Press, by Hyman Bass, Henri Cartan, Peter Freyd, Alex Heller and Saunders Mac Lane.

{{Wolf Prize in Mathematics}}

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Category:1913 births

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Category:20th-century American mathematicians

Category:Category theorists

Category:Columbia University faculty

Category:Nicolas Bourbaki

Category:Scientists from New York City

Category:Warsaw School of Mathematics

Category:People from Warsaw Governorate

Category:Polish emigrants to the United States

Category:20th-century Polish Jews

Category:Topologists

Category:University of Warsaw alumni

Category:Wolf Prize in Mathematics laureates

Category:Members of the United States National Academy of Sciences

Category:Mathematicians from New York (state)