# Nathan Jacobson

### Quick Info

Born
8 September 1910
Warsaw, Russian Empire (now Poland)
Died
5 December 1999
Hamden, Connecticut, USA

Summary
Nathan Jacobson was an American algebraist who is best known for his work in ring theory and for his text-books.

### Biography

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 $x^{n} = x$ 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.

### References (show)

1. N Jacobson, Collected Mathematical Papers (3 Vols.) (Boston-Basel-Berlin, 1989).
2. G Benkart, I Kaplansky, K McCrimmon, D J Saltman and G B Seligman, Nathan Jacobson (1910 -1999), Notices Amer. Math. Soc. 47 (9) (2000), 1061-1071. http://www.ams.org/notices/200009/mem-jacobson.pdf
3. P M Cohn, Nathan Jacobson (1910 -1999), Bull. London Math. Soc. 33 (5) (2001), 623-630.
4. N Jacobson, A personal history and commentary 1910-1943, in N Jacobson, Collected Mathematical Papers I (Boston-Basel-Berlin, 1989), 1-11.
5. N Jacobson, A personal history and commentary 1943-1946, in N Jacobson, Collected Mathematical Papers I (Boston-Basel-Berlin, 1989), 276-284.
6. N Jacobson, A personal history and commentary 1947-1955, in N Jacobson, Collected Mathematical Papers II (Boston-Basel-Berlin, 1989), 1-16.
7. N Jacobson, A personal history and commentary 1956-1965, in N Jacobson, Collected Mathematical Papers II (Boston-Basel-Berlin, 1989), 269-288.
8. N Jacobson, A personal history and commentary 1965-1970, in N Jacobson, Collected Mathematical Papers III (Boston-Basel-Berlin, 1989), 1-12.
9. N Jacobson, A personal history and commentary 1970-1980, in N Jacobson, Collected Mathematical Papers III (Boston-Basel-Berlin, 1989), 42-61.
10. N Jacobson, A personal history and commentary 1980-1988, in N Jacobson, Collected Mathematical Papers III (Boston-Basel-Berlin, 1989), 215-239.