# Hans Samelson

### Quick Info

Born
3 March 1916
Strassburg, Germany, now Strasbourg, France
Died
22 September 2005
Palo Alto, California, USA

Summary
Hans Samelson was a German-born American mathematician who worked in differential geometry, topology and Lie groups and algebras.

### Biography

Hans Samelson's parents were Siegfried Samelson and Irmgard Engel. We should say a little about the family background, particularly because of the connection to Moritz Pasch. Siegfried Samelson was the son of Adolf Samelson and Moritz Pasch's younger sister Henriette Pasch. The Samelson family were Jewish but Siegfried, who was professor of pediatrics and director of the school health system in Strassburg, married Irmgard Engel who was also a paediatrician. Irmgard was a Christian and not Jewish. It is a sad fact that Siegfried and Irmgard's ethnicity had such a major effect on their lives and those of their children Hans, Klaus and Franz.

When Hans was born in Strassburg the city was in Germany and World War I was taking place. In November 1918, when Hans was two years old, following the defeat of Germany, French troops entered Strassburg and declared the city to be part of France. Hans's younger brother was born in Strasbourg (as it had been renamed) in December 1918 shortly after the French occupation and before international recognition of the city's transfer to France in the Treaty of Versailles in June 1919. The Samelson family were expelled from Strasbourg by the new French authorities and, after a brief stay in the Black Forest, they returned to Siegfried's hometown of Breslau, where Siegfried became a professor of paediatrics and director of school health system. His wife Irmgard also found work as a paediatrician. Hans's youngest brother Franz was born in Breslau in 1923.

Hans Samelson was educated in Breslau but after the Nazis came to power in 1933 not only did his father lose his position in the university but all three boys, being half-Jewish, also began to have restrictions imposed on their education. Although Hans studied at the University of Breslau, advanced studies were restricted and he left Germany in 1936 to study for his doctorate in mathematics at the Eidgenössische Technische Hochschule in Zürich. At this time his brother Klaus, unable to undertake university studies, began an apprenticeship in Hamburg. Hans worked for his doctorate advised by Heinz Hopf but also attended lectures by Michel Plancherel and George Pólya. In 1938 Samelson's paper Über die Drehung der Tangenten offener ebener Kurven was published and, in the same year, a joint paper Zum Beweis des Kongruenzsatzes für Eiflächen written with Heinz Hopf appeared. However, tragedy struck the family in this year of 1938 for on 9 November the Nazis launched attacks on synagogues, Jewish businesses and home of Jews across Germany. Following Kristallnacht, as this event had been called, Siegfried Samelson decided that the only way he could help his family was to commit suicide. By taking his own life he did manage to ensure that his wife Irmgard and his two sons still in Germany, Klaus and Franz, were able to survive under slightly less severe conditions. Hans Samelson continued his research in Switzerland and in 1940 published Über die Sphären, die als Gruppenräume auftreten in which he gave a topological proof that a compact Lie group of rank one (that is a Lie group in which maximal abelian subgroups are of dimension one is homeomorphic to the circle, the 3-sphere or projective 3-space. He was awarded his doctorate in 1940 for his thesis Beiträge zur Topologie der Gruppen-Mannigfaltigkeiten . In the thesis, writes André Weil:-
... some notable progress is made in the study of the topological structure of compact Lie-groups and of the corresponding homogeneous spaces. ... the methods are those of "classical" topology, combined with an extensive use of Hopf's inverse homomorphism, and with some of the simpler results concerning fibre-spaces.
Samelson married Renate Reiner in 1940 but he had no reason to be in Switzerland after the award of his doctorate. He wrote (see [1]):-
It was clear from the beginning that my only chance was eventual immigration into the USA; in Switzerland my stay was definitely temporary, but as long as I got enough money from home or otherwise to live on - but not from work - they let me stay.
However, he wrote [5]:-
... the Fremdenpolizei [Immigration Office] called me in frequently to ask me why I was still there.
He was fortunate that money was found to enable him to spend 1941-42 at the Institute of Advanced Study in Princeton. However, there was still a major problem for Samelson and his wife had to escape from Europe. He was still liable for military service in Germany and so had to avoid contact with German troops. Samelson and his wife escaped by making for Spain and then taking a boat to New York. He arrived at Princeton with his wife Renate in June 1941. Soon after he arrived, Hermann Weyl wrote to Heinz Hopf in Zürich (see [1]):-
The Samelsons arrived safely, though after quite an unpleasant journey. He makes an excellent impression on everyone around here. In one of your earlier letters you wrote that his probability of surviving Switzerland was zero.
At first the Samelsons sublet an apartment of William "Ted" Martin, who was just leaving Princeton, but then found their own place to live. Samelson writes about this year at the Institute for Advanced Study in [6]:-
It wasn't difficult to meet and get to know everybody who was there; in fact it seems to me that a good deal of the time all of us were together. [Paul Halmos,] Jimmy Savage, Ellis Kolchin, David Blackwell, Warren Ambrose, George Mackey, Erdős, Kakutani, Arthur Stone, Dorothy Maharam, Irving Segal, Bob Thrall, Abe Taub, Alfred Brauer, and Deane Montgomery (with whom I soon started collaborating). I am not quite sure I have everybody. The permanent members - those famous names that I had never thought of as people: Hermann Weyl, Oswald Veblen, Marston Morse, J W Alexander, von Neumann, also (invisible, to me at any rate) Gödel, and, somehow floating above this group all by himself and out of reach for me, the serene figure of Einstein. Actually I didn't see much of the permanent members. I wish I had had more contact with Alexander. He was quite aristocratic, with intensely blue eyes, and rather elusive; but the few times I talked to him he gave me excellent answers to my questions.
The United States entered World War II while Samelson was at the Institute of Advanced Study in Princeton but, despite the fact that he was German and the United States was at war with Germany, he suffered little difficulty [6]:-
There were in that period two people in our group who were not allowed into Fine Hall at the University, myself (as a German citizen I was an "enemy alien" and might endanger the war work being done there) and David Blackwell (as a black American).
Of course it was vital to Samelson that he remain in the United States after the year in Princeton so he applied for every possible position. He received an offer from the University of Wyoming in Laramie and arrived there in September 1942 to take up the post [6]:-
Laramie was a hospitable place, interesting and quite different from anything I had known; it consisted in those days of the University people, the railroad people ("Union Pacific"), and the people on the other side of the tracks. The teaching load then was 18 hours per week. The most interesting mathematical event was a visit and talk by G D Birkhoff. The year went by fast, and the question of what to do next year came up again. It could have been Laramie, or Smith College where Deane Montgomery was on leave now, but it turned out to be Syracuse, New York, where Ted Martin was starting to build up the Mathematics Department. His first appointment was Paul Halmos. Spurred on by Paul he made me an offer, and Paul persuaded me to accept it. The third member that year was Abe Gelbart.
Samelson took up his appointment at Syracuse University in 1943. World War II was still taking place and he was involved teaching in the Army's Specialized Training Program where soldiers attended for a six-week crash course in calculus. However, he now had a permanent position at Syracuse and he could begin to influence building up a strong mathematics department there [6]:-
Life at Syracuse was quite hectic. The idea of building up a department was quite exciting, even though the physical aspect - the somewhat dark and dank basement of the old Hall of Languages - was not so great. ... Many people were coming to the department, for a shorter or longer time. Among them were Loewner, Bers, Ralph Fox, Henry Scheffé, Arthur Milgram (Jim Milgram's father), and many more later. It almost seemed as if anybody who was anything must have spent some time at Syracuse. We had many discussions whom to approach next and how. Paul was of course quite involved in this, since he was very up to date and in touch with the mathematical community, and Ted Martin listened carefully to his suggestions. It was quite an education for me.
In 1946 Samelson moved to Ann Arbor and took up an appointment at the University of Michigan. A year later his mother left Germany and joined him in Ann Arbor. Hans' younger brother Franz also came to Ann Arbor and studied social psychology at the University of Michigan. In 1956 Samelson married his second wife Nancy Morse. He left Ann Arbor in 1960 when he took up a professorship at Stanford University. He served as chair of the Stanford Mathematics Department from 1979 to 1982. In 1986 he retired and was made professor emeritus.

Let us look briefly at his outstanding contributions to research [5]:-
His earliest work was in the area of transformation groups, and, together with D Montgomery, he published the very influential paper 'Transformation groups of spheres' in the 1944 Annals of Mathematics. In 1954 he described and analyzed one of the first homotopy operations in the seminal paper A connection between the Whitehead product and the Pontryagin product. Today, that operation is called the Samelson product. Perhaps Hans Samelson's most important results were contained in his joint work with R Bott. The most famous of these papers is 'Applications of the theory of Morse to Symmetric Spaces', American Journal of Mathematics, 1958. The ideas developed here lead to some of the most important developments in topology and geometry during the last 50 years. Above all, they were key in R Bott's proof of the Bott periodicity theorems.
All those interested in Lie algebras will know Samelson's wonderful book Notes on Lie algebras (1969). The Preface begins as follows:-
These notes are a slightly expanded version of lectures given at the University of Michigan and Stanford University. Their subject, the basic facts about structure and representations of semisimple Lie algebras, due mainly to S Lie, W Killing, E Cartan, and H Weyl, is quite classical. My aim has been to follow as direct a path to these topics as I could, avoiding detours and side trips, and to keep all arguments as simple as possible. As an example, by refining a construction of Jacobson's, I get along without the enveloping algebra of a Lie algebra. (This is not to say that the enveloping algebra is not an interesting concept; in fact, for a more advanced development one certainly needs it.)
B Kolman begins a review of the book by writing:-
The brief set of notes ... deals with the structure and representation theory of semi-simple Lie algebras and succeeds in covering a good deal of material. The subject is treated in the classical fashion, concentrating primarily on Lie algebras over the field $\mathbb{C}$ of complex numbers. The arguments lean heavily on linear algebra; the writing style is clear and the presentation is neither too terse nor too lengthy.
Twenty years after this first edition was published Samelson produced a revised edition. He begins the Preface:-
This is a revised edition of my "Notes on Lie Algebras" of 1969. Since that time I have gone over the material in lectures at Stanford University and at the University of Crete (whose Department of Mathematics I thank for its hospitality in 1988). The purpose, as before, is to present a simple straightforward introduction, for the general mathematical reader, to the theory of Lie algebras, specifically to the structure and the (finite dimensional) representations of the semisimple Lie algebras. I hope the book will also enable the reader to enter into the more advanced phases of the theory.
Samelson also published a linear algebra text An introduction to linear algebra (1974). George Barker writes in a review:-
The present text is suitable for a course in linear algebra at the senior or first year graduate level. ... [It] has features which make it a good choice for a course. The author's style is pleasant to read. The chapters and sections are of reasonable size and each section has a collection of problems. However, the stylistic device of putting definitions and notation within the statements of theorems is one which I feel should be avoided.
James Milgram said (see [4]):-
Hans was a marvellous expositor. His book on Lie algebras presents all the basic material in a wonderfully compact yet accessible form. In fact, that thin little book has become one of the basic references in the theory. And it was the same when I would go to his office to ask him questions. The answers were always concise, yet got to the heart of what mattered.
The quality of his writing, and Milgram's words about his skill in answering questions, would lead one to expect that he would be an excellent teacher and indeed this was the case. He received the Dean's Award for Distinguished Teaching in 1977. In 1981-82 he served as Section Chair of the Northern California Section of the Mathematical Association of America.

Away from mathematics Samelson had many other interests. He loved a wide range of music, in particular classical, opera and jazz. He played instruments, in particular the bassoon and recorder. He was a member of a number of local orchestras such as the Mid-Peninsula Recorder Orchestra. He was also interested in politics and made many contributions to various political campaigns of Democrats. Being outdoors was a great joy to him and he often went hiking and skiing. He loved travelling and wrote a number of historical articles, most notably using his mathematical skills to investigate an architectural puzzle in [7]. This letter begins:-
I would like to report an observation on Brunelleschi's cupola of S Maria del Fiore in Florence that may interest readers of the Journal of the Society of Architectural Historians. It has to do with the curvature of the groin vaults of the cupola. ...
He was a Quaker, active in the Palo Alto Friends Meeting after he retired, serving as treasurer for several years. He died peacefully in his sleep of natural causes in Palo Alto.

### References (show)

1. R Siegmund-Schultze, Mathematicians fleeing from Nazi Germany: individual fates and global impact (Princeton University Press, Princeton, 2009).
2. D Tamari, Moritz Pasch (1843-1930) (German) (Shaker Verlag, Aachen, 2007).
3. Hans Samelson: Mathematician and Musician, Stanford Magazine (March/April 2006).
4. D Levy, Hans Samelson, renowned mathematician, dead; Nov 6 memorial service set, Stanford University News Service (21 October 2005).
5. R J Milgram, R L Cohen and Y Eliashberg, Memorial Resolution. Hans Samelson, Stanford University.
6. H Samelson, Some early memories around Paul Halmos, in J H Ewing and F W Gehring (eds.), Paul Halmos: Celebrating 50 years of mathematics (Springer-Verlag, New York-Berlin-Heidelberg-London, 1991), 79-86.
7. H Samelson, Letter, Journal of the Society of Architectural Historians 57 (3) (1998), 360-361.
8. C Sturrock, Hans Samelson - Stanford professor, The Chronicle (4 November 2005).

Written by J J O'Connor and E F Robertson
Last Update July 2011