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

category theory Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, ca ...

(with Saunders Mac Lane) 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 topolo ...

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 officiall ...

, 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 Manhatt ...

. 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 and Karol Borsuk. He died in

New York City New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the L ...

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 classify ...

. 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 topolog ...

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 homo ...

are named for the pair), and on

with Saunders Mac Lane. In the process, Eilenberg and Mac Lane created

. Eilenberg was a member of Bourbaki and, with

Henri Cartan Henri Paul Cartan (; 8 July 1904 – 13 August 2008) was a French mathematician who made substantial contributions to algebraic topology. He was the son of the mathematician Élie Cartan, nephew of mathematician Anna Cartan, oldest brother of c ...

, 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 (or ''telescope'') is a construction applying the telescoping cancellation idea to

projective module In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, by keeping some of the main properties of free modules. Various equivalent characteriz ...

s. Eilenberg contributed to automata theory 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 da ...

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 1000 ...

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 ...

, by Hyman Bass,