Samuel Eilenberg

Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish-American mathematician who made important contributions to modern math. He worked together with another mathematician named Saunders Mac Lane to create something called category theory, a way to organize and understand different mathematical ideas by looking at how they relate to each other.

Eilenberg also helped develop a field of math called homological algebra. This area helps mathematicians study shapes and structures by looking at their properties and how they change. His work has had a big influence on many areas of mathematics and continues to be important today.

Early life and education

Samuel Eilenberg was born in Warsaw, in the Kingdom of Poland, to a Jewish family. He became a professor at Columbia University and spent much of his career there.

He finished his studies and earned his Ph.D. from the University of Warsaw in 1936. His thesis was about maps and circles. Two famous mathematicians, Kazimierz Kuratowski and Karol Borsuk, helped guide his work. He passed away in New York City in January 1998.

Career

Samuel Eilenberg was a mathematician who worked on many important ideas in math. He helped create a new area called category theory with his friend Saunders Mac Lane. They also worked together on homological algebra, which helps us understand shapes and patterns in math.

Eilenberg wrote books and articles about these topics and also helped develop ways to understand how machines follow rules. His work has been very important for many areas of math and computer science.

Art collection

Samuel Eilenberg loved collecting art from Asia. He gathered many small sculptures and other special items from places like India, Indonesia, Nepal, Thailand, Cambodia, Sri Lanka, and Central Asia. In the early 1990s, more than 400 of these items were shown at the Metropolitan Museum of Art in New York. The museum also gave money to support a special math position at Columbia University in Eilenberg's honor.

Selected publications

• Eilenberg, Samuel (1974). Automata, Languages and Machines, Volume A. Academic Press. ISBN 0-12-234001-9.
• Eilenberg, Samuel (1976). Automata, Languages and Machines, Volume B. Academic Press. ISBN 0-12-234002-7.
• Eilenberg, Samuel; Ganea, Tudor (1957). "On the Lusternik-Schnirelmann category of abstract groups". Annals of Mathematics. 2nd Series. 65 (3): 517–518. doi:10.2307/1970062. JSTOR (https://www.jstor.org/stable/1970062). MR (https://mathscinet.ams.org/mathscinet-getitem?mr=0085510).
• Eilenberg, Samuel; Mac Lane, Saunders (1945). "Relations between homology and homotopy groups of spaces". Annals of Mathematics. 46 (3): 480-509. doi:10.2307/1969165. JSTOR (https://www.jstor.org/stable/1969165).
• Eilenberg, Samuel; Mac Lane, Saunders (1950). "Relations between homology and homotopy groups of spaces. II". Annals of Mathematics. 51 (3): 514–533. doi:10.2307/1969365. JSTOR (https://www.jstor.org/stable/1969365).
• Eilenberg, Samuel; Moore, John C. (1962), "Limits and spectral sequences", Topology, 1 (1): 1–23, doi:10.1016/0040-9383(62)90093-9, ISSN 0040-9383
• Eilenberg, Samuel; Niven, Ivan (1944). "The "fundamental theorem of algebra" for quaternions". Bulletin of the American Mathematical Society. 50 (4): 246–248. doi:10.1090/s0002-9904-1944-08125-1. MR (https://mathscinet.ams.org/mathscinet-getitem?mr=0009588).
• Eilenberg, Samuel; Steenrod, Norman E. (1945). "Axiomatic approach to homology theory". Proceedings of the National Academy of Sciences of the United States of America. 31 (4): 117–120. Bibcode:1945PNAS...31..117E. doi:10.1073/pnas.31.4.117. PMC (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1078770). PMID (https://pubmed.ncbi.nlm.nih.gov/16578143).
• Eilenberg, Samuel; Steenrod, Norman E. (1952). Foundations of Algebraic Topology. Princeton, New Jersey: Princeton University Press. MR (https://mathscinet.ams.org/mathscinet-getitem?mr=0050886).