Samuel Eilenberg

Samuel Eilenberg was born in Warsaw, Poland on September 30th, 1913. He was awarded his MA from the University of Warsaw in 1934, and received his doctorate in 1936.

Eilenberg’s main interests in college were in the area of mathematics called topology. Topology is the study of properties which are left unchanged by "continuous deformation". The development of topology has had a great influence on many areas of mathematics. Eilenberg’s principle interest was point set topology, also known as general topology. Point set topology is a branch of topology in which one investigates how to put a structure on a set in such a way as to generalize the idea of continuity for maps from the reals R to itself. Eilenberg’s doctoral thesis was published in the math journal Fundamenta Mathematica in 1936, and was very well received in Poland and the United States.

In the late 1930s, Eilenberg eventually joined a group of mathematicians who put together the famous "Scottish Book," in which many mathematicians entered unsolved problems. During this time, he wrote a paper dealing with, "the action of the fundamental group on the higher homotopy groups of a space." His interests had become more algebraic in nature. Algebraic topology is the use of algebra to describe and understand how certain properties of multidimensional forms—such as the number of holes punched through a surface—remain unchanged even when the forms are twisted, bent or stretched.
Eilenberg moved to the United States in 1939. After spending some time at Princeton, he soon was appointed an instructor at the University of Michigan. He spent the next few years in different teaching capacities, then took office at Columbia University in 1948. In that same year, he became an American citizen.

In the United States, Eilenberg became quite famous for his amazing collaborations. His earliest noted collaboration was with André Weil from 1949-1951 as part of the Bourbaki project. He spent two years in France as a visiting professor as part of the project. To fund his time in Paris, Eilenberg had been awarded Guggenheim and Fullbright scholarships to fudn his time abroad.

During that time abroad, Eilenberg met and collaborated with Henri Cartan. The two worked for years to publish their book Homological Algebra, which was finished in 1953 and published in 1956. Together, Eilenberg and Cartan are credited with inventing the term that is the title of their famous text.

From 1940 to 1954, Eilenberg also worked with Saunders McLane to produce papers on category theory, cohomology of groups, the relation between homology and homotopy, Eilenberg-McLane spaces, and generic cycles. "In 1942 the two published a paper in which they introduced Hom and Ext to the math world. They also introduced the terms functor and natural isomorphism and, in 1945, added the terms category and natural transformation." [http://wwwgap.dcs.stand.ac.uk/%7ehistory/
Mathematicians/Eilenberg.html]

Eilenberg collaborated with Norman Earl Steenrod in 1952 to publish their text Foundations of Algebraic Topology. McLane described their book as using "categories to show that they [different versions of homology theory] all could be described conceptually as presenting homology functors from the category of pairs of spaces to groups or to rings, satisfying suitable axioms such as ‘excision’. Thanks to Sammy's insight and his enthusiasm, this text drastically changed the teaching of topology."
Eilenberg wrote a number of other definitive texts on the subjects of topology, homology, and cohomology. He also established himself as an important figure in the foundations of computer science and in applied mathematics in the 1960s and 1970s.

In 1960, Samuel Eilenberg married Natasa Chterenzon. In addition to his contributions to mathematics, Eilenberg was also a leading expert on Indian Art. He donated much of his work to the New York Metropolitan Museum of Art.

Samuel Eilenberg died from cardiac arrest as a result of multiple strokes on January 30, 1998.

For more information, try these websites:
http://www-gap.dcs.st-and.ac.uk/%7ehistory/Mathematicians/Eilenberg.html
http://at.yorku.ca/t/o/p/c/52.htm
http://www.columbia.edu/cu/record/archives/vol23/vol23_iss15/28.html

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Jenna and Drew