Norman Steenrod
{{short description|American mathematician}}
{{Infobox scientist
| image = Norman Steenrod.jpg
| image_size = 180
| name = Norman Steenrod
| caption =
| birth_date = {{Birth date|1910|4|22}}
| birth_place = Dayton, Ohio, U.S.
| death_date = {{death date and age|1971|10|14|1910|4|22|df=y}}
| death_place = Princeton, New Jersey, U.S.
| nationality = American
| field = Mathematics
| alma_mater = University of Michigan (BA)
Harvard University (MA)
Princeton University (PhD)
| thesis_title = Universal Homology Groups
| thesis_year = 1936
| thesis_url = https://search.worldcat.org/title/1340461451
| doctoral_advisor = Solomon Lefschetz
| doctoral_students = José Adem
Peter J. Freyd
Samuel Gitler
Wu-Chung Hsiang
Jerome Levine
William S. Massey
Paul A. Schweitzer
Edwin Spanier
George W. Whitehead
| work_institution = University of Chicago
University of Michigan
Princeton University
| known_for = Steenrod algebra
Steenrod homology
Steenrod problem
Steenrod squares
Eilenberg–Steenrod axioms
Myers–Steenrod theorem
Local system
| prizes = Guggenheim Fellowship (1950)
Colloquium Lecture (1957)
}}
Norman Earl Steenrod (April 22, 1910{{spaced ndash}}October 14, 1971) was an American mathematician most widely known for his contributions to the field of algebraic topology.Steenrod, Norman, et al. First Concepts of Topology. The Mathematical Association of America New Mathematical Library. Miami: 1966.
Life
He was born in Dayton, Ohio, and educated at Miami University and University of Michigan (A.B. 1932). After receiving a master's degree from Harvard University in 1934, he enrolled at Princeton University. He completed his Ph.D. under the direction of Solomon Lefschetz, with a thesis titled Universal homology groups.
Steenrod held positions at the University of Chicago from 1939 to 1942, and the University of Michigan from 1942 to 1947. He moved to Princeton University in 1947, and remained on the Faculty there for the rest of his career. He was editor of the Annals of Mathematics and a member of the National Academy of Sciences. He died in Princeton, survived by his wife, the former Carolyn Witter, and two children.{{cite web|url=https://www.nytimes.com/1971/10/16/archives/norman-steenrod-xrt-on-opology.html|title=Norman Steenrod, Expert in Topology|newspaper=The New York Times|date=October 16, 1971| page=34|access-date=March 29, 2020}}
Work
Thanks to Lefschetz and others, the cup product structure of cohomology was understood by the early 1940s. Steenrod was able to define operations from one cohomology group to another (the so-called Steenrod squares) that generalized the cup product. The additional structure made cohomology a finer invariant. The Steenrod cohomology operations form a (non-commutative) algebra under composition, known as the Steenrod algebra.
His book The Topology of Fibre Bundles{{cite journal|author=Milnor, John|authorlink=John Milnor|title=Review: Norman Steenrod, The topology of fibre bundles|journal=Bulletin of the American Mathematical Society |year=1958|volume=64|issue=4|pages=202–203| url=http://projecteuclid.org/euclid.bams/1183522568|doi=10.1090/s0002-9904-1958-10211-6|doi-access=free}} is a standard reference. In collaboration with Samuel Eilenberg, he was a founder of the axiomatic approach to homology theory. See Eilenberg–Steenrod axioms.
See also
Publications
- {{cite journal | last=Steenrod | first=Norman E. | title=Homology with local coefficients | journal=Annals of Mathematics | volume=44 | issue=4 | year=1943 | doi=10.2307/1969099 | pages=610–627 | jstor=1969099 | mr=0009114}}
- {{cite journal | last1 = Eilenberg | first1=Samuel | author1-link=Samuel Eilenberg| last2=Steenrod | first2=Norman E. | title=Axiomatic approach to homology theory | year=1945 | volume=31 | pages=117–120 | journal=Proceedings of the National Academy of Sciences of the United States of America | pmc=1078770 | pmid=16578143 | issue=4 | doi=10.1073/pnas.31.4.117| bibcode=1945PNAS...31..117E |mr=0012228| doi-access=free }}
- {{cite journal | last=Steenrod | first=Norman E. | title=Products of cocycles and extensions of mappings | journal=Annals of Mathematics | volume=48 | issue=2 | year=1947 | doi=10.2307/1969172 | pages=290–320 | jstor=1969172 | mr=0022071}}
- {{Citation | last1=Steenrod | first1=Norman E. | editor1-last=Epstein | editor1-first=David B. A. | editor1-link=David B. A. Epstein | title=Cohomology operations | url=https://books.google.com/books?id=CF3bt4oYZ2oC | publisher=Princeton University Press | series= Annals of Mathematics Studies | isbn=978-0-691-07924-0 | mr=0145525 | year=1962 | volume=50}}{{cite journal|last=Szczarba|first= Robert H.|title=Review: Cohomology operations. Lectures by N. E. Steenrod. Written and revised by D. B. A. Epstein|journal=Bulletin of the American Mathematical Society |year=1964|volume=70|issue=4|pages=482–483| url=https://www.ams.org/journals/bull/1964-70-04/S0002-9904-1964-11157-5/|doi=10.1090/s0002-9904-1964-11157-5|doi-access=free}}
References
{{reflist}}
External links
- {{MacTutor Biography|id=Steenrod}}
- {{MathGenealogy|id=7811}}
- Michael Hoffman (2013) [http://www.usna.edu/Users/math/meh/steenrod.html Norman Steenrod] {{Webarchive|url=https://web.archive.org/web/20081231062922/http://www.usna.edu/Users/math/meh/steenrod.html |date=2008-12-31 }} from US Naval Academy
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Category:20th-century American mathematicians
Category:Harvard University alumni
Category:People from Dayton, Ohio
Category:Princeton University alumni
Category:Princeton University faculty
Category:University of Chicago faculty
Category:University of Michigan faculty
Category:University of Michigan alumni
Category:Mathematicians from Ohio
Category:Members of the United States National Academy of Sciences