Nathan Jacobson
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Jacobson.html
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Born: 8 Sept 1910 in Warsaw, Russian Empire (now Poland)
Died: 5 Dec 1999 in Hamden, Connecticut, USA
Nathan Jacobson was known as Jake by all around him. His mother was
Pauline Rosenberg and his father was Charles Jacobson (at least this
was what Jacobson calls his "Ellis Island name"). It was a Jewish
family, and Nathan was born in the Jewish ghetto of Warsaw. In fact he
was actually born on 5 October but this was wrongly converted to 8
September which is now the date which appears on all official
documents and the latter incorrect date has now been accepted as his
official birthday. Nathan had a brother Solomon who was about eighteen
months older. The two boys began their elementary schooling in Warsaw
where they encountered discrimination with Jewish children required to
sit on special benches separated from Polish children.
When Nathan was five years old his father emigrated to the United
States leaving his family behind in Warsaw until he had earned
sufficient money for them to make the trip. Charles bought a small
grocery store in Nashville, Tennessee and there he lived in a small
room at the rear. It took him two years to save enough money to pay
for his family's passage and then Nathan, with his mother and brother,
made the trip [4]:-
It was a long journey from Warsaw to New York: in a sealed freight car
through Germany to Rotterdam where we had to wait four months for a
Dutch ship to take us across the U-boat infested Atlantic. ... After a
brief visit with relatives in New York, our family was reunited in
Nashville where we squeezed into the modest quarters that my father
had occupied.
The family soon moved to Birmingham, Alabama, where Nathan attended
elementary school, and then High School. The Jacobson family moved to
Columbus, Mississippi where Nathan completed the two final years of
his school career at the S D Lee High School. Jacobson entered the
University of Alabama in 1926 and, in 1930, was awarded a B.A. [4]:-
I had intended to study law to follow in the footsteps of a maternal
uncle who had come to the United States a few years before my father
and had obtained a degree in law from the University of Alabama. My
initial objective of law as well as my interests at the time led me to
a curriculum that was heavily weighted in the humanities especially
history. However, I also took the mathematics courses that were
offered (not a large number). Apparently I had distinguished myself in
these, for I was offered a teaching assistantship in mathematics in my
junior year. This marked a turning point in my college career since I
decided then to major in mathematics and to pursue this study beyond
college ...
Having applied to Princeton, Harvard and Chicago for financial support
to undertake graduate studies, he went to Princeton where he was
awarded a research assistantship to study for his doctorate under
Wedderburn's supervision. For his second and third years Jacobson was
awarded a part-time instructorship, and in his fourth year he was a
Procter Fellow with a good stipend:-
The mathematics students formed a closely knit group. We lived in
Graduate College and we ate together, particularly dinner at Procter
Hall where academic gowns were required attire. Much to the annoyance
of the other students, our dinner talk was almost exclusively confined
to mathematics. This was an important part of our learning process ...
Having attended a course by Wedderburn on matrices in which he ended
by developing his classical structure theory of finite dimensional
algebras over finite fields, Jacobson was given the task of studying
division algebras which were idealizers of one-sided ideals of
polynomial rings. His doctorate was awarded in 1934 for a thesis on
this topic entitled Non-commutative polynomials and cyclic algebras,
the main results from which were published in the Annals of
Mathematics. He spent 1934-35 at the Institute of Advanced Study at
Princeton during which time he read Wedderburn's paper Algebras which
do not possess a finite basis. This paper would lead him to his
important results on the structure of rings some years later.
Having saved from his salary he was able to visit Europe in the summer
of 1935 with two fellow colleagues from Princeton. He made a short
visit by himself to Poland where he was able to see an uncle, aunts
and cousins [4]:-
This was the last time I would see them. All were killed by the Nazis
in the death camps after the German invasion of Poland in 1939.
Jacobson's career began with relatively short periods in a number of
universities throughout the United States. Jacobson had heard Emmy
Noether lecture on class field theory in Princeton in the spring
semester of 1935 and again at the summer meeting of the American
Mathematical Society where she made comments on Jacobson's thesis
results which he presented there. Jacobson also met Noether at the
Brauers' home where they were invited for dinner on several occasions.
When she died in the spring of 1935 Jacobson was invited to take up a
one year post at Bryn Mawr to give Noether's advertised lecture
courses so session 1935-36 was spent at Bryn Mawr.
The year 1935 saw the publication of Jacobson's first paper on Lie
algebras and over the four years up to 1938 he published five further
papers on the topic as well as two papers on topological rings. During
these four years, Jacobson worked at three different universities.
After session 1935-36 at Bryn Mawr, he spent 1936-37 at the University
of Chicago, financed by a National Research Council Fellowship, where
Dickson and A A Albert were working. Then the University of North
Carolina was home to him for a number of years.
In fact this was a particularly difficult period due to the
depression, which affected everyone, and anti-Semitism which meant
that the top research universities were not taking on staff from
Jewish backgrounds. He was lucky that North Carolina had a liberal
policy and was also looking for young research mathematicians who
would be given a light teaching load. Appointed in 1937 as an
instructor, he became an assistant professor there in 1938, then in
1941 an associate professor.
Soon after the United States entered World War II a training programme
was set up in Chicago to train teachers for the Navy Pre-Flight
School. Jacobson undertook the training, then taught at the Navy
school for pilots. While in Chicago, Jacobson mixed with the
algebraists at the University and there he met Florence Dorfman (known
as Florie) who was a doctoral student working under A A Albert. They
married on 25 August 1942 and Florence gave up her doctoral studies.
Florie did not give up mathematics for she was a joint author with her
husband on their 1949 paper Classification and representation of
semi-simple Jordan algebras.
In 1943 civilian instructors were asked to leave the Navy Pre-Flight
School and Jacobson was appointed to a two year post at Johns Hopkins
University where Zariski was on the Faculty. Together with his wife,
he moved to Baltimore in September 1943 to take up this post. He
writes in [5]:-
My research at Hopkins during the years 1943-46 was mainly in the area
of Galois theory and the general structure of rings. I also wrote my
first paper on Jordan rings during this period.
After four years at Johns Hopkins University he moved to Yale in 1947.
This was made possible since discrimination against Jews lessened in
the United States after the end of World War II [6]:-
I accepted and became the first Jew to hold a tenured position in the
mathematics department.
Two years after his appointment to Yale he was promoted to full
professor, then in 1961 he was appointed as James E English Professor,
and in 1963 as Henry Ford II Professor. He remained at Yale until he
retired in 1981, but when he was offered a position at Chicago in 1960
he certainly had to make a difficult decision. He wrote to A A Albert
[7]:-
... I am convinced that there would have been many scientific
advantages to making this move. However, after a good deal of thought
on the subject, I still feel that for me these are outweighed by the
advantages of living in New Haven and the difficulties of uprooting
myself and my family from an environment we have found congenial for
so many years.
During his years at Yale, Jacobson spent time on visits to other
universities. For example he spent the summer of 1947 at Chicago,
1951-52 as a Guggenheim Fellow in Paris living in André Weil's
apartment, the summer of 1956 as visiting professor at the University
of California at Berkeley, and 1957-58 in Paris for a second visit. He
attended the Fourth All-Union Congress of Mathematicians of the USSR
in 1961, attending the International Congress of Mathematicians in the
same year. After taking unpaid leave from Yale to visit Chicago and
Japan in 1964-65 he lectured in St Andrews Scotland in 1968 [8]:-
We had a very pleasant summer in 1968, lecturing in Scotland and
sight-seeing in Scotland and Ireland. I was invited to give a course
of lectures at the St Andrews Colloquium of the Edinburgh Mathematical
Society.
I [EFR] attended Jacobson's course that he gave on Quadratic Jordan
algebras at the Colloquium and learnt much, not only about Jordan
algebras, but also on how to lecture combining both excitement and
clarity.
We have made a number of references to Jacobson's Jewish background in
this article and there is one further episode we should mention which
illustrates the tensions that resulted. From 1972 to 1974 Jacobson and
Pontryagin were both vice-presidents of the International Mathematical
Union. They argued over the Soviet Union's refusal to allow invited
Jewish speakers to attend and lecture at conferences in the West. In
1978 Jacobson was attacked by Pontryagin who made the following
infamous anti-Semitic statement (we quote from [9]):-
There was an attempt by Zionists to take the International
Mathematical Union into their hands. They attempted to raise N
Jacobson, a mediocre scientist but an aggressive Zionist, to the
presidency. I managed to repel this attack.
This attack Jacobson answered at length with a reply which appears in
the June 1980 Notices of the American Mathematical Society.
Jacobson is well known for his outstanding contributions to ring
theory. Seligman writes in [2]:-
... his contributions have become a part of the daily vocabulary and
working equipment of many of us. ... he earned his dominance by
recasting whole theories of algebraic systems and by insisting on the
module theoretic viewpoint in their study.
Jacobson discovered a deep structure theory for rings and has given
his name to the Jacobson radical, the intersection of the maximal
ideals of a ring. He also made very substantial contributions to
nonassociative algebras, in particular Lie algebras and Jordan
algebras. He worked on rings satisfying conditions of the type xn = x
in 1945. Herstein was to carry on the study of rings satisfying this
type of condition.
The collection of Jacobson's sixteen algebra books are beautifully
written, presenting deep results which are accessible to advanced
undergraduate and postgraduate students. They include The theory of
rings (1943) and the three volume work Lectures in abstract algebra
(1951-64) covering basic concepts, linear algebra and the theory of
fields and Galois theory. In 1956 his book Structure of rings
appeared. Kaplansky writes in [2] that this volume:-
... includes his account of his structure theory. It was definitive
when it appeared. It remains indispensable today; I think it will
continue to be indispensable for a long time.
He wrote two books which rapidly became classics on Lie algebras, Lie
algebras (1962) and Exceptional Lie algebras (1971). On Jordan
algebras he wrote Structure and representations of Jordan algebras
(1968) and another major work on algebra was PI-algebras : an
introduction (1975).
Many honours have been bestowed on this outstanding algebraist.
Besides the award of a Guggenheim Fellowship, he has been elected to
the National Academy of Sciences and the American Academy of Arts and
Sciences. He also has served as president of the American Mathematical
Society from 1971 to 1973, and was vice-president of the International
Mathematical Union from 1972 to 1974. He was made an honorary member
of the London Mathematical Society in 1972 and the University of
Alabama designated him Sesquicentennial Honorary Professor in 1981. He
received the Leroy P Steele Prize for Lifetime Achievement from the
American Mathematical Society in 1998.
Article by: J J O'Connor and E F Robertson |