Abraham Adrian Albert
Encyclopedia
Abraham Adrian Albert was an American
mathematician
. In 1939, he received the first American Mathematical Society's Cole Prize
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 division algebras over number fields and as the developer of Albert algebra
s, which are also known as exceptional
Jordan algebra
s.
, he was born in Chicago
and most associated with that city. He received his Bachelor of Science
in 1926, Masters
in 1927, and PhD
in 1928, at the age of 22. All degrees were obtained from the University of Chicago
. He married around the same time as his graduation. He spent his postdoctoral year at Princeton University
and then from 1929 to 1931 he was an instructor at Columbia University
. During this period he worked on Abelian varieties and their endomorphism algebras. He returned to Princeton for the opening year of the Institute for Advanced Study
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 algebras and as a pioneer in the development of linear
non-associative algebra
s, although all of this grew out of his work on endomorphism
algebras of Abelian varieties.
As an applied mathematician, he also did work for the military during World War II
and thereafter. One of his most notable achievements was his groundbreaking work on cryptography
. The theory that developed from this work can be seen in spread spectrum
cell phone technology.
After WWII, he became a forceful advocate favoring government support for research in mathematics on a par with other physical sciences. He served on policy-making bodies at the Office of Naval Research
, the United States National Research Council
, and the National Science Foundation
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
in 1968.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. In 1939, he received the first American Mathematical Society's Cole Prize
Cole Prize
The Frank Nelson Cole Prize, or Cole Prize for short, is one of 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 theory. The prize is named after Frank Nelson Cole, who...
in Algebra for his work on Riemann matrices. He is best known for his work on the Albert–Brauer–Hasse–Noether theorem
Albert–Brauer–Hasse–Noether theorem
In algebraic number theory, the Albert–Brauer–Hasse–Noether theorem states that a central simple algebra over an algebraic number field K which splits over every completion Kv is a matrix algebra over K...
on finite-dimensional division algebras over number fields and as the developer of Albert algebra
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 are two such Jordan algebras up to isomorphism...
s, which are also known as exceptional
Exceptional object
Many branches of mathematics study objects of a given type and prove a classification theorem. A common theme is that the classification results in a number of series of objects as well as a finite number of exceptions that don't fit into any series. These are known as exceptional...
Jordan algebra
Jordan algebra
In abstract algebra, a Jordan algebra is an algebra over a field whose multiplication satisfies the following axioms:# xy = yx # = x ....
s.
Professional overview
A second generation AmericanUnited States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
, he was born in Chicago
Chicago
Chicago is the largest city in the US state of Illinois. With nearly 2.7 million residents, it is the most populous city in the Midwestern United States and the third most populous in the US, after New York City and Los Angeles...
and most associated with that city. He received his Bachelor of Science
Bachelor of Science
A Bachelor of Science is an undergraduate academic degree awarded for completed courses that generally last three to five years .-Australia:In Australia, the BSc is a 3 year degree, offered from 1st year on...
in 1926, Masters
Master's degree
A master's is an academic degree granted to individuals who have undergone study demonstrating a mastery or high-order overview of a specific field of study or area of professional practice...
in 1927, and PhD
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
in 1928, at the age of 22. All degrees were obtained from the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
. He married around the same time as his graduation. He spent his postdoctoral year at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
and then from 1929 to 1931 he was an instructor at Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
. During this period he worked on Abelian varieties and their endomorphism algebras. He returned to Princeton for the opening year of the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
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 algebras and as a pioneer in the development of linear
Linear
In mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...
non-associative algebra
Algebra over a field
In mathematics, an algebra over a field is a vector space equipped with a bilinear vector product. That is to say, it isan algebraic structure consisting of a vector space together with an operation, usually called multiplication, that combines any two vectors to form a third vector; to qualify as...
s, although all of this grew out of his work on endomorphism
Endomorphism
In mathematics, an endomorphism is a morphism from a mathematical object to itself. For example, an endomorphism of a vector space V is a linear map ƒ: V → V, and an endomorphism of a group G is a group homomorphism ƒ: G → G. In general, we can talk about...
algebras of Abelian varieties.
As an applied mathematician, he also did work for the military during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
and thereafter. One of his most notable achievements was his groundbreaking work on cryptography
Cryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...
. The theory that developed from this work can be seen in spread spectrum
Spread spectrum
Spread-spectrum techniques are methods by which a signal generated in a particular bandwidth is deliberately spread in the frequency domain, resulting in a signal with a wider bandwidth...
cell phone technology.
After WWII, he became a forceful advocate favoring government support for research in mathematics on a par with other physical sciences. He served on policy-making bodies at the Office of Naval Research
Office of Naval Research
The Office of Naval Research , headquartered in Arlington, Virginia , is the office within the United States Department of the Navy that coordinates, executes, and promotes the science and technology programs of the U.S...
, the United States National Research Council
United States National Research Council
The National Research Council of the USA is the working arm of the United States National Academies, carrying out most of the studies done in their names.The National Academies include:* National Academy of Sciences...
, and the National Science Foundation
National Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
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
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
in 1968.
Publications
- A. A. Albert, Structure of algebras, Colloquium publications 24, American Mathematical SocietyAmerican Mathematical SocietyThe American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
, 2003, ISBN 0-8218-1024-3.
Further reading
- Nancy E. Albert, A3 and His Algebra: How a Boy from Chicago's West Side Became a Force in American Mathematics, iUniverse, Lincoln, NE, 2005. ISBN 978-0-595-32817-8.