Professor am Courant Institute of Mathematical Sciences of New York University (1950 bis 1973)
Hans Heinrich Wilhelm Magnus, er publizierte als Wilhelm Magnus, (* 5. Februar 1907 in Berlin; † 15. Oktober 1990 in New York City) war ein deutscher Mathematiker, der sich vor allem mit Gruppentheorie, speziellen Funktionen und mathematischer Physik beschäftigte.
Leben[Bearbeiten | Quelltext bearbeiten]
Wilhelm Magnus studierte nach seinem Abitur in Tübingen von 1925 bis 1930 Mathematik und Physik an den Universitäten Tübingen und Frankfurt am Main und wurde 1930 bei Max Dehn promoviert. 1933 wurde er in Frankfurt habilitiert und war bis 1938 Privatdozent an der Universität Frankfurt. Als Stipendiat der Rockefeller Stiftung war er 1934/35 an der Princeton University. Ab 1939 war er an der Albertina in Königsberg tätig und wechselte 1940 an die Technische Hochschule Berlin-Charlottenburg, wo er 1942 zum apl. Professor ernannt wurde. Er war zudem in der Forschungs-Abteilung der Kriegsmarine Berlin-Wannsee eingesetzt. Da er sich weigerte, der Nationalsozialistischen Partei beizutreten, kam seine Karriere jedoch zum Stillstand. Er befasste sich in dieser Zeit mit mathematischen Tafelwerken für die speziellen Funktionen der mathematischen Physik, was ihm später in den USA zugutekam. 1944 wurde er zum ordentlichen Professor ab der Königsberger Universität ernannt.
Von 1946 bis 1949 war Magnus ordentlicher Professor an der Universität Göttingen; 1947/48 war er Gastprofessor am Institute of Technology Pasadena (heute CalTech) in Kalifornia, USA. 1948 wurde er zum auswärtigen Mitglied der Göttinger Akademie der Wissenschaften gewählt. 1950 wechselte er an das Courant Institute of Mathematical Sciences of New York University und 1973 auf einen Lehrstuhl am Polytechnic Institute of New York, wo er 1978 emeritiert wurde.
Wirken[Bearbeiten | Quelltext bearbeiten]
Sein Hauptforschungsgebiet war die kombinatorische Gruppentheorie. In Amerika war er ab 1948 Mitarbeiter des Bateman Manuscript Projects des Caltech (der nachgelassenen Manuskripte über spezielle Funktionen von Harry Bateman), dessen Hauptherausgeber Arthur Erdélyi war (weitere Mitarbeiter waren Fritz Oberhettinger und Francesco Tricomi). Er befasste sich auch mit Funktionen der mathematischen Physik wie den Lösungen der Mathieu-Gleichung und der Hill-Gleichung.
1932 löste er das Wortproblem für Gruppen mit einer Relation.
Er galt als ein hervorragender Lehrer, hatte zahlreiche Doktoranden, unter anderem Fritz Oberhettinger, Friedrich Wilhelm Schäfke, Joan Birman, Bruce Chandler, Abe Shenitzer, Seymour Lipschutz, Harry Hochstadt, Donald Solitar und Herbert Keller, und erhielt 1969 den Great Teacher Award der New York University. Er war 1934 Rockefeller-Stipendiat, 1969 Guggenheim Fellow und 1973/74 Fulbright-Hayes Senior Research Scholar. Er war Mitglied der Deutschen Mathematiker-Vereinigung von 1932 bis 1934 und von 1938 bis zu seinem Tode.
Schriften[Bearbeiten | Quelltext bearbeiten]
- Collected Papers. Herausgeber Bruce Chandler, Gilbert Baumslag. Springer 1984.
- mit Israel Grossman: Gruppen und ihre Graphen. Klett Verlag 1971, zuerst englisch bei Random House 1964.
- Hill’s equation. Wiley 1966.
- mit Fritz Oberhettinger: Formeln und Lehrsätze für die speziellen Funktionen der mathematischen Physik. Springer 1943, 2. Aufl.1948, 3. Auflage (englisch) 1966.
- mit Fritz Oberhettinger: Anwendungen der elliptischen Funktionen in Physik und Technik. Springer 1949.
- Noneuclidean tessellations and their groups. Academic Press 1974.
- mit Abraham Karrass, Donald Solitar: Combinatorial group theory -presentations of groups in terms of generators and relations. Interscience, New York 1966, 2. Auflage, Dover 1976.
- mit Bruce Chandler: The History of Combinatorial Group Theory. A Case Study in the History of Ideas. Springer 1982.
Literatur[Bearbeiten | Quelltext bearbeiten]
- Abe Shenitzer: Memory of my friend Wilhelm Magnus. Mathematical Intelligencer Nr. 2, 1995.
Weblinks[Bearbeiten | Quelltext bearbeiten]
- Literatur von und über Hans Heinrich Wilhelm Magnus im Katalog der Deutschen Nationalbibliothek
- John J. O’Connor, Edmund F. Robertson: Hans Heinrich Wilhelm Magnus. In: MacTutor History of Mathematics archive.
- Eintrag von Wilhelm Magnus bei der DMV
- Hochstadt zu Magnus, pdf-Datei (18 kB)
Einzelnachweise[Bearbeiten | Quelltext bearbeiten]
- ↑ Holger Krahnke: Die Mitglieder der Akademie der Wissenschaften zu Göttingen 1751–2001 (= Abhandlungen der Akademie der Wissenschaften zu Göttingen, Philologisch-Historische Klasse. Folge 3, Bd. 246 = Abhandlungen der Akademie der Wissenschaften in Göttingen, Mathematisch-Physikalische Klasse. Folge 3, Bd. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1, S. 158.
Wilhelm Magnus’s parents were Alfred Magnus and Paula Kalkbrenner. Wilhelm attended the Gymnasium in Tübingen from 1916 and was awarded his Abitur in 1925. He had studied Latin throughout the nine years at the Gymnasium but his favourite subjects were mathematics and physics. At this stage he decided that physics was the subject for him and he began his university studies with that in mind. He entered the University of Tübingen in the autumn of 1925 but, even in the year he entered, he was studying advanced mathematics :-
I became interested in Number Theory and, in 1925 during my first semester at a university, I started to read the ‚Disquisitiones Arithmeticae‘ Ⓣ by Gauss. … the language was not difficult but Gauss’s style was and I never really became initiated into his theory of quadratic forms. So I was happy to see the publication of the first volume of Edmund Landau’s ‚Vorlesungen aber Zahlentheorie‘ Ⓣ which appeared shortly afterwards. The publication date given in the three volumes is 1927, but the first volume appeared somewhat earlier. Landau was known to be the leading number theorist in Germany, and I started reading his book with great expectations. All went well up to page 93, theorem 152 … I could follow the proof, but I did not see through it, and I felt that if this was number theory it was too difficult for me.
After two semesters at the University of Tübingen, Magnus went to the Johann-Wolfgang-Goethe-University of Frankfurt. He had already decided that he wanted to specialise in mathematics rather than physics when he was taught by Cornelius Lanczos who had been appointed to Frankfurt in 1924. Magnus wrote :-
When I attended a course taught by Lanczos for the first time, I had already changed my original plan to become a physicist, realizing that I was more at home and at ease in mathematics. Perhaps, this was fortunate, because Lanczos might have made me stay in physics if I had met him earlier. To work in theoretical physics requires an uncanny combination of talents: a specific type of intuitive understanding of the realities of physics and a well developed ability to handle the necessary mathematical tools with complete ease. What made Lanczos such a fascinating teacher for a mathematician was his ability to inject some of the intuition of the physicist into mathematics. Even the supreme clarity of Lanczos’s lectures would not have sufficed to produce this effect. What one really could learn from him was the over-riding importance of motivation for the development of a theory.
Magnus was also taught by Carl Siegel, who had been appointed to Frankfurt in 1922 to fill Arthur Schönflies’s chair, and by Ernst Hellinger, who had been appointed to a chair at the University of Frankfurt in 1914. He wrote about his experiences in their classes in :-
Instinctively, everyone in the class knew that none of us would ever be as powerful a mathematician as Siegel. Contrary to all the talk from psychologists and educators who warn against oppressing the developing student, this need not be a depressing experience at all. The opposite is true: it is beneficial to know early what high standards really mean. And Siegel was encouraging when he felt that this was justified. And his word then carried weight. … Hellinger was the most widely appreciated teacher among the mathematicians. He, too, was very well prepared. His lectures were highly polished but he never forgot to mention the motivation for a theorem.
Magnus completed the work for his first degree in Mathematics, Theoretical Physics and Experimental Physics and was awarded the degree on 18 November 1929 with the grade of „excellent“. He was appointed as an assistant at the Mathematical Seminar at Frankfurt from 1 October 1929, holding this position until 30 September 1930.
Despite the other outstanding teachers he had at Frankfurt, it was Max Dehn, who held the chair of Pure and Applied Mathematics at the University of Frankfurt from 1921 until 1935, who had become Magnus’s Ph.D. advisor in 1928. Magnus wrote :-
Max Dehn was my Ph.D. advisor and I have been influenced deeply by him. I took courses taught by him only in my last year at the university, and they had a lasting effect on me in spite of the fact that they were not as polished and smooth as those which I had attended before. Dehn communicated ideas. One had to be ready for this. In fact, one had to be able to enter into a dialogue with him. Even if one had only a tiny contribution to make, and even if one expressed it in a confused way, this was enough. Dehn always understood. He had the ability which Socrates claimed for himself: to act as a midwife at the birth of an idea. This ability went far beyond mathematics. Dehn had an extensive knowledge of philosophy and of history, and he used it to gain the proper perspective for any particular fact or occurrence. He was very undogmatic and did not belong to any philosophical school, but he always tried to see the significance of ideas and facts within the general framework of human experience.
In 1928 Dehn asked Magnus various questions about one-relator groups. He was able to answer these questions and published his results on one-relator groups in 1930 in the paper Über unendliche diskontinuierliche Gruppen mit einer definierenden Relation (Der Freiheitssatz) Ⓣ. In this he proves that certain subgroups of one-relator groups are free groups. The results of this paper formed his Ph.D. thesis and he was awarded the degree on 13 January 1931. From 1 November 1930 to 31 July 1932 he was an assistant at the Mathematical Institute at the University of Göttingen. In 1932 he published Das Identitätsproblem für Gruppen mit einer definierenden RelationⓉ containing a major result in combinatorial group theory, namely that the word problem for one-relator groups is soluble. In this paper Magnus introduced a method of breaking a one-relator group into simpler one-relator groups. This method became the main tool in attacking one-relator groups in later research.
Magnus was appointed to the staff in Frankfurt serving from 1933 until 1938. During this time he spent nine months of session 1934/35 at Princeton University in the United States supported with a Scholarship from the Rockefeller Foundation. At Princeton he attended a course given by his former teacher Carl Siegel, who was spending a year at the Institute for Advanced Study at Princeton. Magnus writes :-
My attendance at Siegel’s lectures resulted in the publication of my only number theoretical paper (on the class number of quadratic forms).
During this period Magnus introduced Lie ring methods to study the lower central series of free groups. He studied the automorphism groups of free groups in 1934. In 1935 Magnus gave examples of finitely presented groups which were isomorphic to proper factor groups of themselves. Heinz Hopf had originally asked whether such groups exist and, although Jakob Nielsen had shown that free groups of finite rank have this property ten years before Hopf asked the question, nobody – including Jakob Nielsen himself – noticed the question had already been answered.
He was appointed as an assistant at the University of Königsberg on 1 April 1939. Later that year, on 5 August, he married Gertrud Remy; they had three children, Jutta, Bettina, and Alfred. However his career was to hit problems when he refused to join the Nazi Party and, as a consequence of this, was not allowed to hold an academic post during World War II. Instead he had to work in industry :-
I had joined Telefunken (a radio firm), and there I met Arnold Sommerfeld, the famous physicist, who had been induced by the management of the firm to act as a consultant on theoretical problems. I became fascinated by his work on diffraction problems and by his „radiation condition“ which enforces uniqueness for their solutions. Sommerfeld was at least as much – if not more – a mathematician as a physicist. How else would he have taken pride in solving the diffraction problem for a half-plane by introducing a branched covering of physical three-space with edge of a half-plane as a branch line and the half-plane as a branch cut? Now special functions, especially Bessel functions, are used extensively and effectively in Sommerfeld’s papers. From him I learned how to apply them as useful tools for the solution of certain problems. I started collecting them. I am not sure how far these functions may have appealed to my collector’s instinct, an instinct which manifests itself in many people with application to diverse objects, regardless of any consideration of usefulness.
During the war, Magnus also undertook military research in the Department of War Marines situated at Berlin-Wannsee. In 1944 he became an ordinary professor at the University of Königsberg but Königsberg was bombed by the Royal Air Force in August 1944 and during the first three months of 1945 the Russian army bombarded the city resulting in its capitulation on 9 April 1945. By this time 80% of university buildings had been destroyed. The staff fled and many were given positions at the University of Göttingen. Magnus was offered an ordinary professorship at the University of Göttingen in 1946 but he was not to remain there for long.
In 1946 Harry Bateman died and Edmund Whittaker was asked to recommend someone who could undertake the project of organising and publishing Bateman’s manuscripts. Whittaker’s advice was that Arthur Erdélyi should lead the project and, in 1947, Erdélyi went to the California Institute of Technology. The project was a major one and other collaborators were needed. Magnus left Göttingen in 1947 and joined the Bateman project in 1948, first as a visiting researcher. He wrote :-
In the case of Harry Bateman there is very little doubt in my mind that he was, at least in part, motivated by a pure collector’s instinct. I became acquainted with his incredible collection of formulas for special functions and definite integrals when working from 1948 to 1950 on the handbook of higher transcendental functions, which is commonly known as the „Bateman Project.“
Magnus collaborated with Arthur Erdélyi, Fritz Oberhettinger and Francesco G Tricomi on the production of three volumes of Higher Transcendental Functions and two volumes of Tables of Integral Transforms. All five volumes appeared in print between 1953 and 1955. For more information, see THIS LINK.
I first met Wilhelm Magnus in 1950, when I came to the New York University graduate school and enrolled in Magnus’s course in algebra. I took an immediate liking to this polite, somewhat shy, and strikingly intelligent man. I was older than most of the students in the class and I approached him without hesitation. The fact that I was a good student helped, and I found myself talking to Magnus about nonmathematical matters as well as mathematical issues. One day he said to me: „You’ve done more for me than any person can do for another.“ He was visibly moved and I was utterly perplexed. „Yes,“ he said, „you are a Jew who was in German concentration camps and I am a German.“ „But I deal with individual people, not with labels“ was my response. This was the beginning of our friendship.
He spent 23 years at the Courant Institute before moving to a chair at the Polytechnic Institute of New York in 1973. He held this post for five years before retiring.
In  Magnus’s research is described in these terms:-
Magnus’s mathematical expertise was exceptionally wide ranging. In addition to research in group theory and special functions, he worked on problems in mathematical physics, including electromagnetic theory and applications of the wave equation.
It was not only in the breadth and depth of research that Magnus excelled. He was also one of the best supervisors of doctoral students, supervising 61 doctoral students during his career. One of his students was Seymour Lipschutz who dedicated a paper to Magnus with the words:-
The author dedicates this paper to his teacher, advisor and friend Wilhelm Magnus (1907–1990); he was a shining example of a kind, considerate and concerned human being.
Shenitzer writes :-
Magnus was a creative mathematician and, as he told me, he liked best to work with gifted doctoral students. On the other hand, he was far too intelligent not to function occasionally as a critic who sheds light on a whole area with a single aphoristic remark. When, as a rank beginner, I asked him what made groups of automorphisms important, he replied, „They are the algebraic counterpart of symmetries in geometry.“ He began his first lecture in a course on geometry with the remark: „The fundamental difference between Hilbert and Euclid is that Hilbert realized that you can study form without substance.“
His teaching is described in  as ‚outstanding‘ and this is confirmed by his receipt of the Great Teacher Award of New York University in 1969.
His nine books cover a wide range of mathematical topics such as elliptic functions, tessellations (Noneuclidean tessellations and their groups (1974)), combinatorial group theory (a major work Combinatorial group theory (1966) written jointly with A Karrass and D Solitar) and mathematical physics.
For more information about these books and extracts from some reviews see THIS LINK.
It is unusual for a 20th century mathematician to work in two mathematical areas as far apart as the ones on which Magnus worked. But he was also deeply interested in other topics outside mathematics :-
He was deeply versed in history, philosophy, and literature, but he had a special passion for poetry. His learning was an integral part of his mind. He was the epitome of a cultivated person. He once told me that if he got tired of algebra, then he could always teach a course on Plato. I was present when the philosopher Hans Jonas, the mathematician Fritz John, and Magnus got together to listen to Jonas’s report on a conference on gnosticism which he had just attended. There ensued an animated discussion by three people who seemed equally at home in history and in philosophy. An outsider would have found it hard to believe that two of the three participants were eminent mathematicians.
You can read Magnus’s ideas on „What Makes a Mathematician?“ at THIS LINK.
He was awarded a number of honours including a Rockefeller Fellowship in 1934, a Guggenheim Fellowship in 1969 and Fulbright-Hays Senior Research Scholarship in 1973/74. He was a member of the Göttingen Academy of Sciences and the American Mathematics Society. He was awarded an honorary Doctor of Science from the Polytechnic Institute New York in 1980.
Article by: J J O’Connor and E F Robertson
Click on this link to see a list of the Glossary entries for this page
List of References (12 books/articles)
Additional Material in MacTutor
- Combinatorial group theory
- Wilhelm Magnus’s books
- Noneuclidean Tesselations and Their Groups
- What Makes a Mathematician?
Cross-references in MacTutor
- History Topics: A history of the Burnside problem
- History Topics: Word problems for groups
- Chronology: 1930 to 1940
Other Web sites
What Makes a Mathematician?
|Wilhelm Magnus, in his paper „The Significance of Mathematics: The Mathematicians‘ Share in the General Human Condition“, Amer. Math. Monthly 104 (3) (1997), 261-269, asks „What Makes a Mathematician?“ We give below a version of Magnus’s answer to his own question:|
What Makes a Mathematician?
There exists a widespread resentment against mathematics. It is supposed to deal only with quantity (not true, since most of mathematics deals with structure and relations), or with computing (again not true, but I cannot explain that in a few words) and, on the whole, it is more worthy of a machine than of a human being. As an aid to science and technology, it does not provide values and is therefore dehumanizing. Even the claim of the mathematician to be concerned with truth is frequently answered by saying that mathematical statements are not true but merely correct. Nevertheless, it is undoubtedly true that the results of mathematics are found by human beings. Can anything be said about them?
The answer is: Not enough to enable us to recognize a mathematician if we meet one at a party. Nevertheless, there exist properties without which a mathematician cannot exist. One of them is, of course, a specific talent. But this is far from being enough. It must be supplemented by an interest in the matter, in fact by a fascination with the problems of the field. And the talent must be supported by persistence and by the willingness to spend the large amounts of time and energy needed to master a difficult craft. And the mathematician needs an exceptionally great ability to stand up under frustration. This is due to the fact (pointed out to me by a colleague) that ours is the only field with an all-or-nothing alternative. A painting or a piece of furniture may be more or less perfect. A theorem and a proof are either true or false. If either the proof or the theorem is false, we have absolutely nothing. Finally, we must be satisfied with the production of something intangible. I have found house painting to be a gratifying supplement to mathematical research. At least one can see and touch what one has done.
It follows that the mathematician needs the support of a civilization that acknowledges as valuable the products of theory, of pure thought. Although we do not set a scale of values, we would not exist without such a scale. I can be brief here, since the arguments given by the philosopher Enrico Cantore for the humanistic significance of science apply, with small modifications, to mathematics as well.
Let me conclude by pointing out one advantage that the mathematician (and, with him, the representative of the exact sciences) has. Our thoughts are eminently communicable. Not, perhaps, from person to person. But certainly from nation to nation. Mathematicians understand each other no matter where they come from. Even across many centuries we understand each other. We may not see clearly what a particular expression in Euclid means. But we are confident that, could we talk with him, we would be able to clear up the matter quickly. Nothing is more international than the community of mathematicians.
Ph.D. Johann Wolfgang Goethe-Universität Frankfurt am Main 1931
Dissertation: Über Unendlich diskontinuierliche Gruppen von einer definirenden Relation (der Freiheitssatz)
Advisor: Max Wilhelm Dehn
Click here to see the students listed in chronological order.
|Bachman, George||New York University||1956||89|
|Bachmuth, Seymour||New York University||1963|
|Bernstein, Herbert||New York University||1968|
|Birman, Joan||New York University||1968||54|
|Blumenson, Leslie||New York University||1962|
|Briggs, James||New York University||1969|
|Brigham, Robert||New York University||1970||4|
|Chandler, Bruce||New York University||1962|
|Chein, Orin||New York University||1968||1|
|Cohen, David||New York University||1973|
|Czerniakiewicz-Kerzman, Anastasia||New York University||1971|
|Drillick, Albert||New York University||1971|
|Dyer, Joan||New York University||1965|
|Enright, Dennis||New York University||1968|
|Epstein, David||New York University||1956|
|Epstein, Irving||New York University||1956|
|Feuer, Richard||New York University||1970|
|Fine, Benjamin||New York University||1973||3|
|Fischer, Emanuel||New York University||1964|
|Forastiero, Diane||Polytechnic University||1977|
|Fox, David||New York University||1961|
|Frederick, Karen||New York University||1961|
|Freilich, Esther||New York University||1973|
|Gassner, Betty||New York University||1957|
|Ginsburg, Karen||New York University||1973|
|Gold, Phillip||New York University||1961|
|Greendlinger, Martin||New York University||1960||21|
|Hellman, Morton||New York University||1954|
|Hochstadt, Harry||New York University||1956||18|
|Horowitz, Robert||New York University||1970|
|Jagerman, David||New York University||1962||5|
|Kalka-Grossman, Edna||New York University||1972|
|Katz, Robert||New York University||1968|
|Keller, Herbert||New York University||1954||119|
|Kotin, Leon||New York University||1958|
|Kuiken, Kathryn||Polytechnic University||1976|
|Kushner, Harvey||Temple University||1976|
|LaBudge, Donald||New York University||1959|
|Landman, Joan||New York University||1965|
|Ledlie, John||New York University||1969|
|Levinger, Bernard||New York University||1960|
|Levinson, Henry||New York University||1970|
|Lewin, Jacques||New York University||1964||7|
|Lieberman, Sidney||New York University||1965|
|Lipschutz, Seymour||New York University||1960||1|
|Mariani, John||New York University||1960|
|Matthews, Jane||New York University||1964|
|McCarthy, Donald||New York University||1965|
|Newman, Nathan||New York University||1959|
|Oberhettinger, Fritz||Universität Berlin||1943||13|
|Peluso, Ada||New York University||1966|
|Pflumm, Eugene||New York University||1959|
|Poss, Samuel||New York University||1969|
|Preiser, Stanley||New York University||1958||4|
|Rosenthal, Richard||Polytechnic University||1975|
|Schäfke, Friedrich||Georg-August-Universität Göttingen||1947||115|
|Segal, Martin||New York University||1963|
|Shenitzer, Abe||New York University||1954|
|Sleator, Frederick||New York University||1957|
|Socci, Patrick||Polytechnic University||1978|
|Sohmer, Bernard||New York University||1958|
|Solitar, Donald||New York University||1958||53|
|Spellman, Dennis||New York University||1971|
|Stebe, Peter||New York University||1968|
|Steinberg, Arthur||New York University||1963|
|Stevenson, Jr., John||Polytechnic University||1976|
|Stork, Daniel||New York University||1970|
|Strasser, Elvira||New York University||1956||5|
|Struik, Ruth||New York University||1955||2|
|Traina, Charles||Polytechnic University||1978|
|Tretkoff, Carol||New York University||1974||1|
|Tretkoff, Marvin||New York University||1971||3|
|Weinbaum, Carl||New York University||1963|
|Winkler, Stanley||New York University||1958|
|Zumoff, Nancy||New York University||1973|
If you have additional information or corrections regarding this mathematician, please use the update form. To submit students of this mathematician, please use the new data form, noting this mathematician’s MGP ID of 12042 for the advisor ID.
JOC/EFR May 2017
The URL of this page is: