Richard Donald Schafer (February 25, 1918 – December 28, 2014) was an American mathematician.
Richard Schafer studied at the
University at Buffalo
The State University of New York at Buffalo, commonly called the University at Buffalo (UB) and sometimes called SUNY Buffalo, is a public research university with campuses in Buffalo and Amherst, New York. The university was founded in 1846 ...
, where he received his bachelor's degree in 1938 and his master's degree in 1940. He received in 1942 from the
University of Chicago
The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...
his PhD under
Abraham Adrian Albert
Abraham Adrian Albert (November 9, 1905 – June 6, 1972) was an American mathematician. In 1939, he received the American Mathematical Society's Cole Prize in Algebra for his work on Riemann matrices. He is best known for his work on the Al ...
with dissertation ''Alternative Algebras over an Arbitrary Field''. After service in the U.S. Naval Reserve from 1942 to 1945, he was an instructor at the
University of Michigan
, mottoeng = "Arts, Knowledge, Truth"
, former_names = Catholepistemiad, or University of Michigania (1817–1821)
, budget = $10.3 billion (2021)
, endowment = $17 billion (2021)As o ...
for the academic year 1945–1946. From 1946 to 1948 he was at the
Institute for Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...
. From 1948 to 1953 he was a professor at the
University of Pennsylvania
The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...
. From 1953 to 1958 he was at
University of Connecticut
The University of Connecticut (UConn) is a public land-grant research university in Storrs, Connecticut, a village in the town of Mansfield. The primary 4,400-acre (17.8 km2) campus is in Storrs, approximately a half hour's drive from Hart ...
as professor and head of the mathematics department. He spent the academic year 1958–1959 at the Institute for Advanced Study. From 1959 until his retirement in 1988, he was a professor at the
Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...
. In 2012 he was elected was a Fellow of the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
.
Schafer did research on algebra, specifically on
Jordan algebra
In abstract algebra, a Jordan algebra is a nonassociative algebra over a field whose multiplication satisfies the following axioms:
# xy = yx (commutative law)
# (xy)(xx) = x(y(xx)) ().
The product of two elements ''x'' and ''y'' in a Jordan al ...
s and
Lie algebra
In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...
s. He is best known for his textbook ''An Introduction to Nonassociative Algebras'', first published in 1966,Richard D. Schafer: ''An Introduction to Nonassociative Algebras''. Courier Dover Publications, 1966, which has been freely available since 2008 from
Project Gutenberg
Project Gutenberg (PG) is a Virtual volunteering, volunteer effort to digitize and archive cultural works, as well as to "encourage the creation and distribution of eBooks."
It was founded in 1971 by American writer Michael S. Hart and is the ...
. He also studied the
Cayley–Dickson construction
In mathematics, the Cayley–Dickson construction, named after Arthur Cayley and Leonard Eugene Dickson, produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one. The algebras produced by ...
.
Richard Schafer was married to the mathematician