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Norman Earl Steenrod (April 22, 1910October 14, 1971) was an 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 ...
most widely known for his contributions to the field of
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 ...
.


Life

He was born in
Dayton, Ohio Dayton () is a city in Montgomery County, Ohio, United States, and its county seat. It is the List of cities in Ohio, sixth-most populous city in Ohio, with a population of 137,644 at the 2020 United States census, 2020 census. The Dayton metro ...
, and educated at
Miami University Miami University (informally Miami of Ohio or simply Miami) is a public university, public research university in Oxford, Ohio, United States. Founded in 1809, it is the second-oldest List of colleges and universities in Ohio, university in Ohi ...
and
University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...
(A.B. 1932). After receiving a master's degree from
Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...
in 1934, he enrolled at
Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...
. He completed his Ph.D. under the direction of
Solomon Lefschetz Solomon Lefschetz (; 3 September 1884 – 5 October 1972) was a Russian-born American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equatio ...
, with a thesis titled ''Universal homology groups''. Steenrod held positions at the
University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...
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 The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as t ...
and a member of the
National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...
. He died in Princeton, survived by his wife, the former Carolyn Witter, and two children.


Work

Thanks to Lefschetz and others, the
cup product In mathematics, specifically in algebraic topology, the cup product is a method of adjoining two cocycles of degree p and q to form a composite cocycle of degree p+q. This defines an associative (and distributive) graded commutative product opera ...
structure of
cohomology In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed ...
was understood by the early 1940s. Steenrod was able to define operations from one cohomology group to another (the so-called
Steenrod square Norman Earl Steenrod (April 22, 1910October 14, 1971) was an American mathematician most widely known for his contributions to the field of algebraic topology. Life He was born in Dayton, Ohio, and educated at Miami University and University of ...
s) 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 Norman Earl Steenrod (April 22, 1910October 14, 1971) was an American mathematician most widely known for his contributions to the field of algebraic topology. Life He was born in Dayton, Ohio, and educated at Miami University and University of ...
. His book ''The Topology of Fibre Bundles'' is a standard reference. In collaboration with
Samuel Eilenberg Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish-American mathematician who co-founded category theory (with Saunders Mac Lane) and homological algebra. Early life and education He was born in Warsaw, Kingdom of Poland to ...
, he was a founder of the axiomatic approach to
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 ...
. See
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 homolo ...
.


See also

*
Abstract nonsense In mathematics, abstract nonsense, general abstract nonsense, generalized abstract nonsense, and general nonsense are nonderogatory terms used by mathematicians to describe long, theoretical parts of a proof they skip over when readers are expected ...
*
Fiber bundle In mathematics, and particularly topology, a fiber bundle ( ''Commonwealth English'': fibre bundle) is a space that is a product space, but may have a different topological structure. Specifically, the similarity between a space E and a pr ...


Publications

* * * *


References


External links

* * * Michael Hoffman (2013
Norman Steenrod
from
US Naval Academy The United States Naval Academy (USNA, Navy, or Annapolis) is a federal service academy in Annapolis, Maryland. It was established on 10 October 1845 during the tenure of George Bancroft as Secretary of the Navy. The Naval Academy is the sec ...
{{DEFAULTSORT:Steenrod, Norman 1910 births 1971 deaths 20th-century American mathematicians Harvard University alumni People from Dayton, Ohio Princeton University alumni Princeton University faculty American topologists University of Chicago faculty University of Michigan faculty University of Michigan alumni Mathematicians from Ohio Members of the United States National Academy of Sciences