Abraham Adrian Albert (November 9, 1905 – June 6, 1972) 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 ...

. In 1939, he received the American Mathematical Society's

Cole Prize The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to numbe ...

in Algebra for his work on Riemann matrices. He is best known for his work on the Albert–Brauer–Hasse–Noether theorem on

finite-dimensional In mathematics, the dimension of a vector space ''V'' is the cardinality (i.e., the number of vectors) of a basis of ''V'' over its base field. p. 44, §2.36 It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to d ...

division algebra In the field of mathematics called abstract algebra, a division algebra is, roughly speaking, an algebra over a field in which division, except by zero, is always possible. Definitions Formally, we start with a non-zero algebra ''D'' over a fie ...

s over

number field In mathematics, an algebraic number field (or simply number field) is an extension field K of the field of rational numbers such that the field extension K / \mathbb has finite degree (and hence is an algebraic field extension). Thus K is a ...

s and as the developer of Albert algebras, which are also known as

exceptional Exception(s), The Exception(s), or exceptional may refer to: Arts and entertainment * '' The Exception'', a 2016 British film * ''The Exception'' (2006 novel), a Danish novel (orig. ''Undtagelsen'', 2004) by Christian Jungersen * ''The Excep ...

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 a ...

Professional overview

A first generation

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, p ...

, he was born in

Chicago Chicago is the List of municipalities in Illinois, most populous city in the U.S. state of Illinois and in the Midwestern United States. With a population of 2,746,388, as of the 2020 United States census, 2020 census, it is the List of Unite ...

and most associated with that city. He received his

Bachelor of Science A Bachelor of Science (BS, BSc, B.S., B.Sc., SB, or ScB; from the Latin ') is a bachelor's degree that is awarded for programs that generally last three to five years. The first university to admit a student to the degree of Bachelor of Scienc ...

in 1926, Masters in 1927, and

PhD A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

in 1928, at the age of 22. All degrees were obtained from 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 ...

. He married around the same time as his graduation. He spent his postdoctoral year 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 ...

and then from 1929 to 1931 he was an instructor at

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

. During this period he worked on

Abelian varieties In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a smooth projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular f ...

and their

endomorphism In mathematics, an endomorphism is a morphism from a mathematical object to itself. An endomorphism that is also an isomorphism is an automorphism. For example, an endomorphism of a vector space is a linear map , and an endomorphism of a g ...

algebras. He returned to Princeton for the opening year of the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

in 1933-34 and spent another year in Princeton in 1961-62 as the first Director of the Communications Research Division of the

Institute for Defense Analyses The Institute for Defense Analyses (IDA) is an American non-profit corporation that administers three federally funded research and development centers (FFRDCs) – the Systems and Analyses Center (SAC), Science and Technology Policy Institute, t ...

(IDA). He later served on the Board of Trustees of IDA 1969-1972. From 1931 to 1972, he served on the mathematics faculty at the University of Chicago, where he became chair of the Mathematics Department in 1958 and Dean of the Physical Sciences Division in 1961. As a research mathematician, he is primarily known for his work as one of the principal developers of the theory of linear associative algebras and as a pioneer in the development of linear non-

associative In mathematics, the associative property is a property of some binary operations that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for express ...

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

s, although all of this grew out of his work on endomorphism algebras of Abelian varieties. As an

applied 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, structure, space, models, and change. History One ...

, he also did work for the military during

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

and thereafter. One of his most notable achievements was his groundbreaking work on

cryptography Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), ...

. He prepared a manuscript, "Some Mathematical Aspects of Cryptography," for his invited address at a meeting 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, ...

in November 1941. The theory that developed from this work can be seen in

digital communications Data communication, including data transmission and data reception, is the transfer of data, signal transmission, transmitted and received over a Point-to-point (telecommunications), point-to-point or point-to-multipoint communication chann ...

technologies. After WWII, he became a forceful advocate favoring government support for research in mathematics on a par with physical sciences. He served on policy-making bodies at the

Office of Naval Research The Office of Naval Research (ONR) is an organization within the United States Department of the Navy responsible for the science and technology programs of the U.S. Navy and Marine Corps. Established by Congress in 1946, its mission is to plan ...

, the

United States National Research Council The National Academies of Sciences, Engineering, and Medicine (NASEM), also known as the National Academies, is a congressionally chartered organization that serves as the collective scientific national academy of the United States. The name i ...

, and the

National Science Foundation The U.S. National Science Foundation (NSF) is an Independent agencies of the United States government#Examples of independent agencies, independent agency of the Federal government of the United States, United States federal government that su ...

that funneled research grants into mathematics, giving many young mathematicians career opportunities previously unavailable. Due to his success in helping to give mathematical research a sound financial footing, he earned a reputation as a "statesman for mathematics." Albert was elected a Fellow of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

in 1968.

Publications

Books

* A. A. Albert, ''Algebras and their radicals, and division algebras'', 1928. * . * A. A. Albert, ''Structure of algebras'', 1939. Colloquium publications 24,

, 2003, . * * * * * with Rebeun Sandler: * *

Articles in ''PNAS''

* * * * * * * * * * * * * * * *

References

External links

* *
Abraham Adrian Albert 1905–1972
A Biographical Memoir by

Irving Kaplansky Irving Kaplansky (March 22, 1917 – June 25, 2006) was a mathematician, college professor, author, and amateur musician.O'Connor, John J.; Robertson, Edmund F., "Irving Kaplansky", MacTutor History of Mathematics archive, University of St And ...

National Academy of Sciences Biographical Memoirsearch on author Abraham Adrian Albert
from

Google Scholar Google Scholar is a freely accessible web search engine that indexes the full text or metadata of Academic publishing, scholarly literature across an array of publishing formats and disciplines. Released in Beta release, beta in November 2004, th ...

Guide to the Abraham Adrian Albert Papers 1921-2004
from th
University of Chicago Special Collections Research Center
{{DEFAULTSORT:Albert, A. A. 1905 births 1972 deaths 20th-century American mathematicians 20th-century American Jews American algebraists Fellows of the American Academy of Arts and Sciences Institute for Advanced Study visiting scholars Members of the United States National Academy of Sciences Presidents of the American Mathematical Society Princeton University faculty University of Chicago alumni University of Chicago faculty Columbia University faculty Mathematicians from Chicago