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 number ...

in Algebra for his work on

Riemann matrices In mathematics, the Schottky problem, named after Friedrich Schottky, is a classical question of algebraic geometry, asking for a characterisation of Jacobian varieties amongst abelian varieties. Geometric formulation More precisely, one should co ...

. He is best known for his work on the Albert–Brauer–Hasse–Noether theorem on finite-dimensional

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 f ...

s over

number fields 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 ...

and as the developer of

Albert algebra In mathematics, an Albert algebra is a 27-dimensional exceptional Jordan algebra. They are named after Abraham Adrian Albert, who pioneered the study of non-associative algebras, usually working over the real numbers. Over the real numbers, there ...

s, which are also known as exceptional

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 ...

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, ...

, he was born in

Chicago (''City in a Garden''); I Will , image_map = , map_caption = Interactive Map of Chicago , coordinates = , coordinates_footnotes = , subdivision_type = List of sovereign states, Count ...

and most associated with that city. He received his

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

in 1926,

Masters Master or masters may refer to: Ranks or titles * Ascended master, a term used in the Theosophical religious tradition to refer to spiritually enlightened beings who in past incarnations were ordinary humans *Grandmaster (chess), National Master ...

in 1927, and

PhD PHD or PhD may refer to: * Doctor of Philosophy (PhD), an academic qualification Entertainment * '' PhD: Phantasy Degree'', a Korean comic series * ''Piled Higher and Deeper ''Piled Higher and Deeper'' (also known as ''PhD Comics''), is a newsp ...

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

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

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

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the n ...

and then from 1929 to 1931 he was an instructor at

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manha ...

. 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 projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular func ...

and their endomorphism algebras. He returned to Princeton for the opening year of 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 ...

in 1933-34 and spent another year in Princeton in 1961-62 as the first Director of the Communications Research Division of IDA (the Institute for Defense Analyses). 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 algebra In mathematics, an associative algebra ''A'' is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field ''K''. The addition and multiplica ...

s and as a pioneer in the development of

linear Linearity is the property of a mathematical relationship ('' function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear ...

non-

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

algebra Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathem ...

s, although all of this grew out of his work on

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 ...

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, mathematical structure, structure, space, Mathematica ...

, he also did work for the military during

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great power ...

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

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

. 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 transmission and data reception or, more broadly, data communication or digital communications is the transfer and reception of data in the form of a digital bitstream or a digitized analog signal transmitted over a point-to-point o ...

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 pla ...

, the

United States National Research Council The National Academies of Sciences, Engineering, and Medicine (also known as NASEM or the National Academies) are the collective scientific national academy of the United States. The name is used interchangeably in two senses: (1) as an umbrell ...

, and the

National Science Foundation The National Science Foundation (NSF) is an independent agency of the United States government that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National ...

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 (abbreviation: AAA&S) 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, ...

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 scholarly literature across an array of publishing formats and disciplines. Released in beta in November 2004, the Google Scholar index includes p ...

Guide to the Abraham Adrian Albert Papers 1921-2004
from th
University of Chicago Special Collections Research Center
{{DEFAULTSORT:Albert, Abraham Adrian 1905 births 1972 deaths 20th-century American mathematicians 20th-century American Jews 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 People from Chicago Mathematicians from Illinois