Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish-American mathematician who co-founded category theory (with

Saunders Mac Lane Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg. Early life and education Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftvill ...

) and

homological algebra Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology ...

Early life and education

He was born in

Warsaw Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is official ...

, Kingdom of Poland to a

Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...

family. He spent much of his career as a professor at

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manha ...

. He earned his Ph.D. from

University of Warsaw The University of Warsaw ( pl, Uniwersytet Warszawski, la, Universitas Varsoviensis) is a public university in Warsaw, Poland. Established in 1816, it is the largest institution of higher learning in the country offering 37 different fields of ...

in 1936, with thesis ''On the Topological Applications of Maps onto a Circle''; his thesis advisors were

Kazimierz Kuratowski Kazimierz Kuratowski (; 2 February 1896 – 18 June 1980) was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics. Biography and studies Kazimierz Kuratowski was born in Warsaw, ...

and Karol Borsuk. He died in

New York City New York, often called New York City or NYC, is the most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the most densely populated major city in the U ...

in January 1998.

Career

Eilenberg's main body of work was in

algebraic topology Algebraic topology is a branch of mathematics that 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 classif ...

. He worked on the axiomatic treatment of

homology theory In mathematics, homology is a general way of associating a sequence of algebraic objects, such as abelian groups or modules, with other mathematical objects such as topological spaces. Homology groups were originally defined in algebraic topol ...

with Norman Steenrod (and the

Eilenberg–Steenrod axioms In mathematics, specifically in algebraic topology, the Eilenberg–Steenrod axioms are properties that homology theories of topological spaces have in common. The quintessential example of a homology theory satisfying the axioms is singular hom ...

are named for the pair), and on

with

. 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''. Later in life he worked mainly in pure category theory, being one of the founders of the field. The

Eilenberg swindle Eilenberg is a surname, and may refer to: * Samuel Eilenberg (1913–1998), Polish mathematician * Richard Eilenberg (1848–1927), German composer Named after Samuel * Eilenberg–MacLane space * Eilenberg–Moore algebra * Eilenberg–Steenro ...

(or ''telescope'') is a construction applying the

telescoping cancellation In mathematics, a telescoping series is a series whose general term t_n can be written as t_n=a_n-a_, i.e. the difference of two consecutive terms of a sequence (a_n). As a consequence the partial sums only consists of two terms of (a_n) after c ...

idea to projective modules. Eilenberg contributed to

automata theory Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science. The word ''automata'' comes from the Greek word αὐτόματο� ...

and algebraic automata theory. In particular, he introduced a model of computation called

X-machine The X-machine (''XM'') is a theoretical model of computation introduced by Samuel Eilenberg in 1974.S. Eilenberg (1974) ''Automata, Languages and Machines, Vol. A''. Academic Press, London. The ''X'' in "X-machine" represents the fundamental d ...

and a new prime decomposition algorithm for finite state machines in the vein of

Krohn–Rhodes theory In mathematics and computer science, the Krohn–Rhodes theory (or algebraic automata theory) is an approach to the study of finite semigroups and automata that seeks to decompose them in terms of elementary components. These components correspond ...

Art collection

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 The Metropolitan Museum of Art of New York City, colloquially "the Met", is the largest art museum in the Americas. Its permanent collection contains over two million works, divided among 17 curatorial departments. The main building at 100 ...

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''. In reciprocity, the Metropolitan Museum of Art donated substantially to the endowment of the Samuel Eilenberg Visiting Professorship in Mathematics at Columbia University.

Selected publications

* * * * * * * * *

Footnotes

External links

*
Eilenberg's biography
− from the

National Academies Press The US National Academies Press (NAP) was created to publish the reports issued by the National Academies of Sciences, Engineering, and Medicine, the National Academy of Engineering, the National Academy of Medicine, and the National Research C ...

, by Hyman Bass, Henri Cartan, Peter Freyd, Alex Heller and