Abraham Adrian Albert

A. A. Albert
Born	(1905-11-09)November 9, 1905 Chicago
Died	Chicago
Nationality	American
Fields	mathematics
Institutions	Columbia University University of Chicago
Alma mater	University of Chicago
Doctoral advisor	L. E. Dickson
Doctoral students	Richard Block Nathan Divinsky Murray Gerstenhaber Anatol Rapaport
Known for	Albert algebras
Notable awards	Cole Prize (1939)

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 Albert–Brauer–Hasse–Noether theorem on finite-dimensional division algebras over number fields and as the developer of Albert algebras, which are also known as exceptional Jordan algebras.

Professional overview

A second generation American, 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 algebras, 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. He prepared a manuscript, "Some Mathematical Aspects of Cryptography," for his invited address at a meeting of the American Mathematical Society in November 1941. The theory that developed from this work can be seen in digital communications technologies.

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.

Publications

Books

• A. A. Albert, Algebras and their radicals, and division algebras, 1928.
• A. A. Albert, Modern higher algebra, 1937.
• A. A. Albert, Structure of algebras, 1939. Colloquium publications 24, American Mathematical Society, 2003, ISBN 0-8218-1024-3.
• with Rebeun Sandler:

Articles in PNAS

• 1957 June 15; 43(6): 506–509.
• 1955 September 15; 41(9): 639–640.
• 1950 July; 36(7): 372–374.
• 1949 June; 35(6): 317–322.
• 1944 June 15; 30(6): 144–146.
• 1944 April 15; 30(4): 90–95.
• 1930 April 15; 16(4): 308–312.
• 1928 December; 14(12): 906–907.
• 1963 September; 50(3): 446–447.
• 1956 September; 42(9): 624–625.
• 1955 July 15; 41(7): 480–482.
• 1934 December; 20(12): 676–681.
• 1931 June; 17(6): 389–392.
• 1930 April 15; 16(4): 313–315.
• 1929 April 15; 15(4): 372–376.
• 1928 December; 14(12): 904–906.

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.

External links

• Abraham Adrian Albert at the Mathematics Genealogy Project
• .
• Abraham Adrian Albert 1905–1972, A Biographical Memoir by Irving Kaplansky
• National Academy of Sciences Biographical Memoir
• search on author Abraham Adrian Albert from Google Scholar