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

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

who co-founded

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

(with Saunders Mac Lane) and

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

Early life and education

He was born in

Warsaw Warsaw, officially the Capital City of Warsaw, is the capital and List of cities and towns in Poland, largest city of Poland. The metropolis stands on the Vistula, River Vistula in east-central Poland. Its population is officially estimated at ...

, Kingdom of Poland to a

Jewish Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of History of ancient Israel and Judah, ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, rel ...

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

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

. 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 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. He worked as a professor at the University of Warsaw and at the Ma ...

and Karol Borsuk. He died in

New York City New York, often called New York City (NYC), is the most populous city in the United States, located at the southern tip of New York State on one of the world's largest natural harbors. The city comprises five boroughs, each coextensive w ...

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 invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

. He worked on the axiomatic treatment of

homology theory In mathematics, the term homology, originally introduced in algebraic topology, has three primary, closely-related usages. The most direct usage of the term is to take the ''homology of a chain complex'', resulting in a sequence of abelian grou ...

with Norman Steenrod (and the Eilenberg–Steenrod axioms are named for the pair), and on

with Saunders Mac Lane. As a result of this work, Eilenberg and Mac Lane developed the field of

, for which they are now best known. 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 (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 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 correspon ...

. 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.

Art collection

Eilenberg was also a prominent collector of Asian art. His collection mainly consisted of small sculptures and other artifacts from

India India, officially the Republic of India, is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area; the List of countries by population (United Nations), most populous country since ...

Indonesia Indonesia, officially the Republic of Indonesia, is a country in Southeast Asia and Oceania, between the Indian Ocean, Indian and Pacific Ocean, Pacific oceans. Comprising over List of islands of Indonesia, 17,000 islands, including Sumatra, ...

Nepal Nepal, officially the Federal Democratic Republic of Nepal, is a landlocked country in South Asia. It is mainly situated in the Himalayas, but also includes parts of the Indo-Gangetic Plain. It borders the Tibet Autonomous Region of China Ch ...

Thailand Thailand, officially the Kingdom of Thailand and historically known as Siam (the official name until 1939), is a country in Southeast Asia on the Mainland Southeast Asia, Indochinese Peninsula. With a population of almost 66 million, it spa ...

Cambodia Cambodia, officially the Kingdom of Cambodia, is a country in Southeast Asia on the Mainland Southeast Asia, Indochinese Peninsula. It is bordered by Thailand to the northwest, Laos to the north, and Vietnam to the east, and has a coastline ...

Sri Lanka Sri Lanka, officially the Democratic Socialist Republic of Sri Lanka, also known historically as Ceylon, is an island country in South Asia. It lies in the Indian Ocean, southwest of the Bay of Bengal, separated from the Indian subcontinent, ...

and

Central Asia Central Asia is a region of Asia consisting of Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan, and Uzbekistan. The countries as a group are also colloquially referred to as the "-stans" as all have names ending with the Persian language, Pers ...

. In 1991–1992, the

Metropolitan Museum of Art The Metropolitan Museum of Art, colloquially referred to as the Met, is an Encyclopedic museum, encyclopedic art museum in New York City. By floor area, it is the List of largest museums, third-largest museum in the world and the List of larg ...

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 (formerly known as the National Research Council (United States), National Research Council), the Na ...