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{{Short description|American mathematician (1905–1972)}} |
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{{Infobox scientist |
{{Infobox scientist |
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|name = A. A. Albert |
|name = A. A. Albert |
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|image = |
|image = |
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|caption = |
|caption = |
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|birth_name = Abraham Adrian Albert |
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|birth_date = {{Birth date |1905|11|09}} |
|birth_date = {{Birth date |1905|11|09}} |
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|birth_place = [[Chicago]] |
|birth_place = [[Chicago]], US |
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|death_date = {{Death date and age|1972|06|06|1905|11|09}} |
|death_date = {{Death date and age|1972|06|06|1905|11|09}} |
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|death_place = Chicago |
|death_place = Chicago, US |
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|residence = |
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|citizenship = |
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|nationality = [[United States|American]] |
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|ethnicity = |
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|fields = [[mathematics]] |
|fields = [[mathematics]] |
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|workplaces = [[Columbia University]]<br>[[University of Chicago]] |
|workplaces = [[Columbia University]]<br>[[University of Chicago]] |
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|doctoral_advisor = [[L. E. Dickson]] |
|doctoral_advisor = [[L. E. Dickson]] |
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|academic_advisors = |
|academic_advisors = |
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|doctoral_students = [[Richard Earl Block|Richard Block]]<br>[[Nathan Divinsky]]<br>[[Murray Gerstenhaber]]<br>[[Anatol Rapaport]]<br>[[Richard D. Schafer]]<br>[[Daniel Zelinsky]] |
|doctoral_students = [[Richard Earl Block|Richard Block]]<br>[[Nathan Divinsky]]<br>[[Murray Gerstenhaber]]<br>[[Anatol Rapaport]]<br>[[Richard D. Schafer]]<br>[[Daniel Zelinsky (mathematician)|Daniel Zelinsky]] |
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|notable_students = |
|notable_students = |
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|known_for = [[Albert algebra]]s |
|known_for = [[Albert algebra]]s |
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|influenced = |
|influenced = |
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|awards = [[Cole Prize]] <small>(1939)</small> |
|awards = [[Cole Prize]] <small>(1939)</small> |
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|religion = |
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|signature = <!--(filename only)--> |
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|footnotes = |
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'''Abraham Adrian Albert''' (November 9, 1905 – June 6, 1972) was an |
'''Abraham Adrian Albert''' (November 9, 1905 – June 6, 1972) was an American [[mathematician]].<ref>{{cite web |url=http://www.jinfo.org/Mathematics_Comp.html |title = Jewish Mathematicians}}</ref> In 1939, he received the American Mathematical Society's [[Cole Prize]] in Algebra for his work on [[Riemann matrices]].<ref>[http://www.jinfo.org/Cole_Mathematics.html Jewish recipients of the Frank Nelson Cole Prizes in algebra and number theory (43% of recipients)]</ref> He is best known for his work on the [[Albert–Brauer–Hasse–Noether theorem]] on finite-dimensional [[division algebra]]s over [[number fields]] and as the developer of [[Albert algebra]]s, which are also known as [[exceptional object|exceptional]] [[Jordan algebra]]s. |
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==Professional overview== |
==Professional overview== |
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A first generation [[United States|American]], he was born in [[Chicago]] and most associated with that city. He received his [[Bachelor of Science]] in 1926, [[Master's degree|Masters]] in 1927, and [[Doctor of Philosophy|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 |
A first generation [[United States|American]], he was born in [[Chicago]] and most associated with that city. He received his [[Bachelor of Science]] in 1926, [[Master's degree|Masters]] in 1927, and [[Doctor of Philosophy|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 [[Institute_for_Defense_Analyses#Center_for_Communications_and_Computing|Communications Research Division]] of the [[Institute for Defense Analyses]] (IDA). He later served on the Board of Trustees of IDA 1969-1972.<ref> |
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{{cite web |
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| url=https://celebratio.org/Albert_AA/article/34/ |
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| title=Abraham Adrian Albert: 1905–1972 |
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| last=Kaplansky |
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| first=Irving |
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| author-link=Irving Kaplansky |
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| website=[[Celebratio Mathematica]] |
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| publisher=[[Mathematical Sciences Publishers]] |
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| access-date=2023-11-04 |
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}}</ref> |
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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. |
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. |
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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. |
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. |
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After WWII, he became a forceful advocate favoring government support for research in mathematics on a par with |
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 [[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.<ref name=AAAS>{{cite web|title=Book of Members, 1780-2010: Chapter A|url=http://www.amacad.org/publications/BookofMembers/ChapterA.pdf|publisher=American Academy of Arts and Sciences|access-date=6 April 2011| archive-url= https://web.archive.org/web/20110510021801/http://www.amacad.org/publications/BookofMembers/ChapterA.pdf| archive-date= 10 May 2011 | url-status= live}}</ref> |
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==Publications== |
==Publications== |
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{{Scholia}} |
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===Books=== |
===Books=== |
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* A. A. Albert, ''Algebras and their radicals, and division algebras'', 1928. |
* A. A. Albert, ''Algebras and their radicals, and division algebras'', 1928. |
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* {{Citation | last1=Albert | first1=A. Adrian | title=Modern higher algebra | url={{Google books|iVwZCgAAQBAJ|Modern higher algebra|plainurl=yes}} | publisher=[[Cambridge University Press]] | isbn=978-1-107-54462-8 | year=2015 |orig-year=1938 }}.<ref>{{cite journal|author=Brinkmann, H. W.|title=Review: ''Modern Higher Algebra'' by A. Adrian Albert|journal=Bull. Amer. Math. Soc.|year=1938|volume=44|issue=7|pages=471–473|url= |
* {{Citation | last1=Albert | first1=A. Adrian | title=Modern higher algebra | url={{Google books|iVwZCgAAQBAJ|Modern higher algebra|plainurl=yes}} | publisher=[[Cambridge University Press]] | isbn=978-1-107-54462-8 | year=2015 |orig-year=1938 }}.<ref>{{cite journal|author=Brinkmann, H. W.|title=Review: ''Modern Higher Algebra'' by A. Adrian Albert|journal=Bull. Amer. Math. Soc.|year=1938|volume=44|issue=7|pages=471–473|url=https://www.ams.org/journals/bull/1938-44-07/S0002-9904-1938-06758-4/S0002-9904-1938-06758-4.pdf|doi=10.1090/s0002-9904-1938-06758-4|doi-access=free}}</ref> |
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* A. A. Albert, ''Structure of algebras'', 1939.<ref>{{cite journal|author=Baer, Reinhold|author-link=Reinhold Baer|title=Review: A. Adrian Albert, ''Structure of Algebras''|journal=Bull. Amer. Math. Soc.|year=1940|volume=46|issue=7|pages=587–591|url=http://projecteuclid.org/euclid.bams/1183502777|doi=10.1090/s0002-9904-1940-07233-7}}</ref> Colloquium publications '''24''', [[American Mathematical Society]], 2003, {{ISBN|0-8218-1024-3}}. |
* A. A. Albert, ''Structure of algebras'', 1939.<ref>{{cite journal|author=Baer, Reinhold|author-link=Reinhold Baer|title=Review: A. Adrian Albert, ''Structure of Algebras''|journal=Bull. Amer. Math. Soc.|year=1940|volume=46|issue=7|pages=587–591|url=http://projecteuclid.org/euclid.bams/1183502777|doi=10.1090/s0002-9904-1940-07233-7|doi-access=free}}</ref> Colloquium publications '''24''', [[American Mathematical Society]], 2003, {{ISBN|0-8218-1024-3}}. |
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* {{Citation |title=Introduction to algebraic theories|year=1941}}<ref>{{cite journal|year=1941|title=Review of ''Introduction to algebraic theories'' by A. Adrian Albert|journal=The Mathematical Gazette|volume=25|issue=265|pages=184|doi=10.2307/3607394|jstor=3607394|s2cid=4088670 |url=https://www.cambridge.org/core/journals/mathematical-gazette/article/abs/introduction-to-algebraic-theories-by-a-adrian-albert-pp-viii-137-10s-6d-1941-university-of-chicago-press-cambridge-university-press/CA43785D85543234DA9A83AD94D30C11}}</ref> |
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* {{Citation |title=Introduction to algebraic theories|year=1941}} |
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* {{Citation |title=College algebra|year=1946}} |
* {{Citation |title=College algebra|year=1946}} |
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* {{Citation |title=Solid analytic geometry|year=1949}} |
* {{Citation |title=Solid analytic geometry|year=1949}} |
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* {{Citation |title=Fundamental concepts of higher algebra|year=1956}}<ref>{{cite journal|author=Mattuck, Arthur|title=Review: ''Fundamental concepts of higher algebra'' by A. Adrian Albert|journal=Bull. Amer. Math. Soc.|year=1957|volume=63|issue=5|pages=323–325|url= |
* {{Citation |title=Fundamental concepts of higher algebra|year=1956}}<ref>{{cite journal|author=Mattuck, Arthur|title=Review: ''Fundamental concepts of higher algebra'' by A. Adrian Albert|journal=Bull. Amer. Math. Soc.|year=1957|volume=63|issue=5|pages=323–325|url=https://www.ams.org/journals/bull/1957-63-05/S0002-9904-1957-10130-X/S0002-9904-1957-10130-X.pdf|doi=10.1090/s0002-9904-1957-10130-x|doi-access=free}}</ref> |
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* with Rebeun Sandler: {{cite book|title=Introduction to finite projective planes|year=1968}} |
* with Rebeun Sandler: {{cite book|title=Introduction to finite projective planes|year=1968}} |
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*{{Citation | last1=Albert | first1=A. Adrian | editor1-last=Block | editor1-first=Richard E. | editor2-last=Jacobson | editor2-first=Nathan | editor2-link=Nathan Jacobson | editor3-last=Osborn | editor3-first=J. Marshall | editor4-last=Saltman | editor4-first=David J. | editor5-last=Zelinsky | editor5-first=Daniel | title=Collected mathematical papers. Part 1. Associative algebras and Riemann matrices.| url=https://books.google.com/books?isbn=0821800051 | publisher=[[American Mathematical Society]] | location=Providence, R.I. | isbn=978-0-8218-0005-8 | year=1993 | mr=1213451}} |
*{{Citation | last1=Albert | first1=A. Adrian | editor1-last=Block | editor1-first=Richard E. | editor2-last=Jacobson | editor2-first=Nathan | editor2-link=Nathan Jacobson | editor3-last=Osborn | editor3-first=J. Marshall | editor4-last=Saltman | editor4-first=David J. | editor5-last=Zelinsky | editor5-first=Daniel | title=Collected mathematical papers. Part 1. Associative algebras and Riemann matrices.| url=https://books.google.com/books?isbn=0821800051 | publisher=[[American Mathematical Society]] | location=Providence, R.I. | isbn=978-0-8218-0005-8 | year=1993 | mr=1213451}} |
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===Articles in PNAS=== |
===Articles in PNAS=== |
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*{{cite journal|title=The Norm Form of a Rational Division Algebra|journal=Proc Natl Acad Sci U S A|pmc=528485 | pmid=16590045|volume=43|year=1957|pages=506–9|doi=10.1073/pnas.43.6.506 }} |
*{{cite journal|title=The Norm Form of a Rational Division Algebra|journal=Proc Natl Acad Sci U S A|pmc=528485 | pmid=16590045|volume=43|year=1957|pages=506–9|doi=10.1073/pnas.43.6.506 |last1=Albert|first1=A. A.|issue=6|bibcode=1957PNAS...43..506A|doi-access=free}} |
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*{{cite journal|title=On Hermitian Operators over the Cayley Algebra|journal=Proc Natl Acad Sci U S A|pmc=528152 | pmid=16589719|volume=41|year=1955|pages=639–40|doi=10.1073/pnas.41.9.639 }} |
*{{cite journal|title=On Hermitian Operators over the Cayley Algebra|journal=Proc Natl Acad Sci U S A|pmc=528152 | pmid=16589719|volume=41|year=1955|pages=639–40|doi=10.1073/pnas.41.9.639 |last1=Albert|first1=A. A.|issue=9|bibcode=1955PNAS...41..639A|doi-access=free}} |
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*{{cite journal|title=A Note on the Exceptional Jordan Algebra|journal=Proc Natl Acad Sci U S A|pmc=1063206 | pmid=15430315|volume=36|year=1950|pages=372–4|doi=10.1073/pnas.36.7.372 }} |
*{{cite journal|title=A Note on the Exceptional Jordan Algebra|journal=Proc Natl Acad Sci U S A|pmc=1063206 | pmid=15430315|volume=36|year=1950|pages=372–4|doi=10.1073/pnas.36.7.372 |last1=Albert|first1=A. A.|issue=7|bibcode=1950PNAS...36..372A|doi-access=free}} |
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*{{cite journal|title=A Theory of Trace-Admissible Algebras|journal=Proc Natl Acad Sci U S A|pmc=1063026 | pmid=16588897|volume=35|year=1949|pages=317–22|doi=10.1073/pnas.35.6.317}} |
*{{cite journal|title=A Theory of Trace-Admissible Algebras|journal=Proc Natl Acad Sci U S A|pmc=1063026 | pmid=16588897|volume=35|year=1949|pages=317–22|doi=10.1073/pnas.35.6.317|last1=Albert|first1=A. A.|issue=6|bibcode=1949PNAS...35..317A|doi-access=free}} |
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*{{cite journal|title=The Minimum Rank of a Correlation Matrix|journal=Proc Natl Acad Sci U S A|pmc=1078686 | pmid=16588638|volume=30|year=1944|pages=144–6|doi=10.1073/pnas.30.6.144 }} |
*{{cite journal|title=The Minimum Rank of a Correlation Matrix|journal=Proc Natl Acad Sci U S A|pmc=1078686 | pmid=16588638|volume=30|year=1944|pages=144–6|doi=10.1073/pnas.30.6.144 |last1=Albert|first1=A. A.|issue=6|bibcode=1944PNAS...30..144A|doi-access=free}} |
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*{{cite journal|title=The Matrices of Factor Analysis|journal=Proc Natl Acad Sci U S A|pmc=1078675 | pmid=16578117|volume=30|year=1944|pages=90–5|doi=10.1073/pnas.30.4.90 }} |
*{{cite journal|title=The Matrices of Factor Analysis|journal=Proc Natl Acad Sci U S A|pmc=1078675 | pmid=16578117|volume=30|year=1944|pages=90–5|doi=10.1073/pnas.30.4.90 |last1=Albert|first1=A. A.|issue=4|bibcode=1944PNAS...30...90A|doi-access=free}} |
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*{{cite journal|title=On the Structure of Pure Riemann Matrices with Non-commutative Multiplication Algebras|journal=Proc Natl Acad Sci U S A|pmc=526637 | pmid=16587573|volume=16|year=1930|pages=308–12|doi=10.1073/pnas.16.4.308}} |
*{{cite journal|title=On the Structure of Pure Riemann Matrices with Non-commutative Multiplication Algebras|journal=Proc Natl Acad Sci U S A|pmc=526637 | pmid=16587573|volume=16|year=1930|pages=308–12|doi=10.1073/pnas.16.4.308|last1=Albert|first1=A. A.|issue=4|bibcode=1930PNAS...16..308A|doi-access=free}} |
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*{{cite journal|title=The Group of the Rank Equation of Any Normal Division Algebra|journal=Proc Natl Acad Sci U S A|pmc=1085796 | pmid=16587420|volume=14|year=1928|pages=906–7|doi=10.1073/pnas.14.12.906 }} |
*{{cite journal|title=The Group of the Rank Equation of Any Normal Division Algebra|journal=Proc Natl Acad Sci U S A|pmc=1085796 | pmid=16587420|volume=14|year=1928|pages=906–7|doi=10.1073/pnas.14.12.906 |last1=Albert|first1=A. A.|issue=12|bibcode=1928PNAS...14..906A|doi-access=free}} |
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*{{cite journal|title=On the Nuclei of a Simple Jordan Algebra|journal=Proc Natl Acad Sci U S A|pmc=221198 | pmid=16578544|volume=50|year=1963|pages=446–7|doi=10.1073/pnas.50.3.446 }} |
*{{cite journal|title=On the Nuclei of a Simple Jordan Algebra|journal=Proc Natl Acad Sci U S A|pmc=221198 | pmid=16578544|volume=50|year=1963|pages=446–7|doi=10.1073/pnas.50.3.446 |last1=Albert|first1=A. A.|issue=3|bibcode=1963PNAS...50..446A|doi-access=free}} |
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*{{cite journal|title=A Property of Special Jordan Algebras|journal=Proc Natl Acad Sci U S A|pmc=534263 | pmid=16589918|volume=42|year=1956|pages=624–5|doi=10.1073/pnas.42.9.624 }} |
*{{cite journal|title=A Property of Special Jordan Algebras|journal=Proc Natl Acad Sci U S A|pmc=534263 | pmid=16589918|volume=42|year=1956|pages=624–5|doi=10.1073/pnas.42.9.624 |last1=Albert|first1=A. A.|issue=9|bibcode=1956PNAS...42..624A|doi-access=free}} |
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*{{cite journal|title=On Involutorial Algebras|journal=Proc Natl Acad Sci U S A|pmc=528119 | pmid=16589700|volume=41|year=1955|pages=480–2|doi=10.1073/pnas.41.7.480 }} |
*{{cite journal|title=On Involutorial Algebras|journal=Proc Natl Acad Sci U S A|pmc=528119 | pmid=16589700|volume=41|year=1955|pages=480–2|doi=10.1073/pnas.41.7.480 |last1=Albert|first1=A. A.|issue=7|bibcode=1955PNAS...41..480A|doi-access=free}} |
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*{{cite journal|title=Involutorial Simple Algebras and Real Riemann Matrices|journal=Proc Natl Acad Sci U S A|pmc=1076512 | pmid=16587930|volume=20|year=1934|pages=676–81|doi=10.1073/pnas.20.12.676 }} |
*{{cite journal|title=Involutorial Simple Algebras and Real Riemann Matrices|journal=Proc Natl Acad Sci U S A|pmc=1076512 | pmid=16587930|volume=20|year=1934|pages=676–81|doi=10.1073/pnas.20.12.676 |last1=Albert|first1=A. A.|issue=12|bibcode=1934PNAS...20..676A|doi-access=free}} |
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*{{cite journal|title=Normal Division Algebras of 2<sup>2m </sup>|journal=Proc Natl Acad Sci U S A|pmc=1076070 | pmid=16587641|volume=17|year=1931|pages=389–92|doi=10.1073/pnas.17.6.389 }} |
*{{cite journal|title=Normal Division Algebras of 2<sup>2m </sup>|journal=Proc Natl Acad Sci U S A|pmc=1076070 | pmid=16587641|volume=17|year=1931|pages=389–92|doi=10.1073/pnas.17.6.389 |last1=Albert|first1=A. A.|issue=6|doi-access=free}} |
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*{{cite journal|title=On Direct Products, Cyclic Division Algebras, and Pure Riemann Matrices|journal=Proc Natl Acad Sci U S A|pmc=526638 | pmid=16587574|volume=16|year=1930|pages=313–5|doi=10.1073/pnas.16.4.313}} |
*{{cite journal|title=On Direct Products, Cyclic Division Algebras, and Pure Riemann Matrices|journal=Proc Natl Acad Sci U S A|pmc=526638 | pmid=16587574|volume=16|year=1930|pages=313–5|doi=10.1073/pnas.16.4.313|last1=Albert|first1=A. A.|issue=4|bibcode=1930PNAS...16..313A|doi-access=free}} |
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*{{cite journal|title=The Rank Function of Any Simple Algebra|journal=Proc Natl Acad Sci U S A|pmc=522469 | pmid=16587486|volume=15|year=1929|pages=372–6|doi=10.1073/pnas.15.4.372 }} |
*{{cite journal|title=The Rank Function of Any Simple Algebra|journal=Proc Natl Acad Sci U S A|pmc=522469 | pmid=16587486|volume=15|year=1929|pages=372–6|doi=10.1073/pnas.15.4.372 |last1=Albert|first1=A. A.|issue=4|bibcode=1929PNAS...15..372A|doi-access=free}} |
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*{{cite journal|title=Normal Division Algebras Satisfying Mild Assumptions|journal=Proc Natl Acad Sci U S A|pmc=1085795 | pmid=16587419|volume=14|year=1928|pages=904–6|doi=10.1073/pnas.14.12.904 }} |
*{{cite journal|title=Normal Division Algebras Satisfying Mild Assumptions|journal=Proc Natl Acad Sci U S A|pmc=1085795 | pmid=16587419|volume=14|year=1928|pages=904–6|doi=10.1073/pnas.14.12.904 |last1=Albert|first1=A. A.|issue=12|bibcode=1928PNAS...14..904A|doi-access=free}} |
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==References== |
==References== |
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{{Authority control}} |
{{Authority control}} |
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{{DEFAULTSORT:Albert, |
{{DEFAULTSORT:Albert, A. A.}} |
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[[Category:1905 births]] |
[[Category:1905 births]] |
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[[Category:1972 deaths]] |
[[Category:1972 deaths]] |
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[[Category:20th-century American mathematicians]] |
[[Category:20th-century American mathematicians]] |
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[[Category:American Jews]] |
[[Category:20th-century American Jews]] |
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[[Category:Algebraists]] |
[[Category:Algebraists]] |
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[[Category:Fellows of the American Academy of Arts and Sciences]] |
[[Category:Fellows of the American Academy of Arts and Sciences]] |
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A. A. Albert
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| Born | Abraham Adrian Albert (1905-11-09)November 9, 1905
Chicago, US
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| Died | June 6, 1972(1972-06-06) (aged 66)
Chicago, US
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| Alma mater | University of Chicago |
| Known for | Albert algebras |
| Awards | Cole Prize (1939) |
| Scientific career | |
| Fields | mathematics |
| Institutions | Columbia University University of Chicago |
| Doctoral advisor | L. E. Dickson |
| Doctoral students | Richard Block Nathan Divinsky Murray Gerstenhaber Anatol Rapaport Richard D. Schafer Daniel Zelinsky |
Abraham Adrian Albert (November 9, 1905 – June 6, 1972) was an American mathematician.[1] In 1939, he received the American Mathematical Society's Cole Prize in Algebra for his work on Riemann matrices.[2] 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.
A first 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 the Institute for Defense Analyses (IDA). He later served on the Board of Trustees of IDA 1969-1972.[3]
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 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.[4]
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