Friedrich Wilhelm Levi
Quick Info
Mülhausen, Alsace, Germany (now Mulhouse, France)
Freiburg im Breisgau, Germany
Biography
Friedrich Levi, also known as F W Levi, was the son of Georg Levi (1856-1942) and Emma Laura Blum (1859-1943). The family were Jewish which, as we detail below, led to many tragedies after the Nazis came to power in 1933. Georg Levi, born in Landau, Rheinland-Pfalz, Germany, was a prominent lawyer, the son of Simon Levi, a National Liberal politician and member of the Bavarian Parliament, and Fanni Roos. Emma Laura Blum, born in Strasbourg, Alsace, France, was the daughter of the banker Alexander Blum and Rosalie Kramer. Georg and Emma Levi had (probably) four children, but we only have details of three: Franziska Sara "Fanni" Levi (1882-1943), born in Alsace; Friedrich Wilhelm Daniel "Fritz" Levi (1888-1966), the subject of this biography, born in Mulhouse, Alsace; and Eva Felicitas Emma Maria "Fee" Levi (1894-1982), born in Strasbourg, Alsace. If the details in [11] are correct, then there was one further sister who:-... took her own life after the November 1938 massacre.By 1894 the Levi family had moved to Strasbourg where Eva Levi was born and where, in that year, Friedrich Levi began his schooling at a private school. We should say a little about Alsace, and in particular Strasbourg, since the reader may be confused as to whether this is in Germany or in France. The Alsace region was French from 1681 when it was conquered by the army of Louis XIV. Following the Franco-Prussian war in 1870-71, Alsace became German and the city of Strasbourg became known by the name Straßburg. Following World War I, Alsace again became French. This explains how Emma Levi was born in France but her children were born in Germany, despite all being born in Alsace.
After two years at the private school in Strasbourg, from 1894 to 1896, Levi entered a humanistic Gymnasium in that same city. He studied at the Gymnasium from 1896 to 1904 but, before completing his studies, his father was transferred to Colmar where he became President of the Senate at the Higher Regional Court of Colmar. Friedrich Levi completed his schooling at the municipal Lyceum in Colmar. He passed his Arbitur examination in the spring of 1906 and in October of that year, he went to Würzburg where he undertook his one-year military service. While doing his military service he also enrolled in the University of Würzburg where he began his studies of mathematics and physics. After he was discharged from military service in October 1907, he enrolled in the University of Strasbourg to continue his studies. He attended lectures by Heinrich Weber, Friedrich Schur and Richard von Mises. He was taught algebra by Heinrich Weber and this quickly became his favourite topic.
Friedrich Schur (1856-1932) had been taught by Heinrich Schröter and Jacob Rosanes at the University of Breslau before going to Berlin where he was influenced by Leopold Kronecker, Karl Weierstrass, Ernst Kummer, and Gustav Kirchhoff. He then went to Leipzig where he habilitated in 1881. He taught at the University of Dorpat, then RWTH Aachen and the Technical University of Karlsruhe before being appointed a full professor at Strasbourg in 1909. He would play a large part in Friedrich Levi's career but in Strasbourg it was Heinrich Weber who became Levi's thesis advisor. He was awarded his doctorate in October 1911 having submitted his thesis Integritätsbereiche und Körper dritten Grades Ⓣ. This was an exceptional piece of work and it was given the grade summa cum laude, which is the highest possible.
After the award of his doctorate, Levi wanted to habilitate in mathematics and become a university professor. He decided, however, before beginning work for his habilitation thesis he should broaden his mathematical knowledge. The leading place in the world for mathematics at this time was Berlin so Levi spent the year 1912-13 in Berlin where he took courses and attended seminars run by David Hilbert, Edmund Landau, Otto Töplitz and Hermann Weyl. Certainly given Levi's love of algebra, it is quite likely that he would have planned to return to Strasbourg after his year in Berlin and work under Heinrich Weber. This was not an option, however, since Heinrich Weber died in May 1913. Andreas Speiser had worked at Strasbourg where, advised by Heinrich Weber, he had habilitated with the thesis Über die Komposition der binären quadratischen Formen Ⓣ in 1911. With Strasbourg not an option for his habilitation, Levi sought advice from Friedrich Schur on how he should proceed.
Levi's first attempt was to approach Eduard Study in June 1913 at the University of Bonn. Study had accepted the chair of mathematics at the University of Bonn in 1904 which had been left vacant on the death of Rudolf Lipschitz in October 1903. The response from Study left Levi with no hope of habilitating at Bonn so he turned again to Friedrich Schur for advice. Friedrich Schur had become friends with Karl Rohn during his time at the University of Leipzig and, with Rohn having returned to Leipzig to the chair of mathematics in 1905, Schur suggested that Levi contact Leipzig about habilitating there. After discussions with his colleague Otto Hölder, Rohn gave Levi an encouraging reply. Friedrich Schur suggested that Levi spend the winter semester of 1913-14 at Leipzig and see if things went well for him. Rohn was undertaking research in geometry and Levi thought this might make a good topic for his habilitation but Friedrich Schur advised him against this and suggested he work on a topic in algebra.
Otto Hölder had been appointed as an Ordinary Professor of Mathematics at the University of Leipzig in 1899, succeeding to the chair that had been occupied by Sophus Lie. He was at that time working on group theory problems so was an excellent person for Levi to talk to about his habilitation thesis on abelian groups. He submitted his thesis Abelsche Gruppen mit abzählbaren Elementen Ⓣ to the University of Leipzig in July 1914. This, however, was the time when events leading to World War I were taking place. By the time that Otto Hölder approved Levi's habilitation thesis, in December 1914, and indicated that he should complete the remaining requirements to habilitate, Levi had been called up for military duty and had already served three months as a soldier in the field artillery arm of the Royal Saxon Army, part of the Imperial German Army.
Levi requested leave of absence from military service to give the required trial lecture before the faculty so that he might receive the venia legendi Ⓣ. He was refused leave of absence so, in December 1916, Otto Hölder, Karl Rohn and Gustav Herglotz made a request to the Ministry of Culture asking for permission to have Levi's thesis printed so that his priority could be established. They made a successful request "in consideration of the extraordinary wartime conditions." Levi was decorated several times for his bravery in action at the front, including being awarded the Iron Cross II. He had reached the rank of Second Lieutenant by the time he was discharged. Levi continued his military service until November 1918 and only then was he able to prepare to give the required trial lecture, and complete the formalities for the habilitation. He gave the lecture Die Bedeutung der Dimensionszahl bei der axiomatischen Begründung der Geometrie Ⓣ and habilitated in March 1919.
Although Levi had been unable to complete the habilitation process for five years after his thesis was approved, he was able to marry during these years. On 6 December 1917 he married Barbara Caroline Fitting (1894-1992), the daughter of Lieutenant Colonel Karl Fitting and Anna Kuhn. Barbara Fitting, had a cousin Hans Fitting, a mathematician with a biography in this archive. Friedrich and Barbara Levi had three children: Paul Georg Carl Levi (1919-2008); Charlotte Bertha Emma Levi (1920-2012); and Susanne Ursula Levi (1924-2006). All three children were born in Leipzig; we give some further details below.
Levi published relatively little in the years following his habilitation. He was appointed as an assistant at the Mathematical Institute in Leipzig in 1920 and became an Associate Professor in 1923. He was appointed to a (badly paid) teaching position in 1926. He published Geometrische Konfiguratione Ⓣ in 1929 and H D Ursell writes in a review of the book [31]:-
The author of this book, starting entirely from scratch, gives an adequate and very readable introduction to two-dimensional topology and an excellent discussion of various simple geometrical figures and their groups of self-transformations.Charles F Rupp writes in the review [28]:-
The bulk of the energy of the American graduate student of mathematics is used in learning the essentials of algebra, analysis, and geometry. After he gets settled in his life-work, he seldom feels the urge to go through a lot of memoirs in the periodical literature to find out what a certain branch of his study is about. In the absence of a comprehensive, unified theory, there will be few texts to guide his path, and probably he will forego exploration in that direction altogether.Helmut Hasse offered Reinhold Baer a post at Halle University in 1928 and Baer accepted, partly because he would then be living close to Leipzig where his wife's parents lived. Friedrich Levi had been a friend of Baer's wife's family since she was a young girl and Baer and Levi soon began a mathematical collaboration which lasted until Levi's death. Their first joint papers included: Stetige Funktionen in topologischen Räumen Ⓣ (1930), Vollständige irreduzible Systeme von Gruppenaxiomen Ⓣ (1932), and Freie Produkte und ihre Untergruppen Ⓣ (1936).
Until the publication of Dr Levi's text, this has been the case with reference to configurations. The author, in his preface, expresses the hope that the few topics he has selected will beguile more mathematicians into a study of configurations. He bears in mind the necessity of assuming more maturity than knowledge in his readers, and promises to unveil the hidden connections be-tween group theory and analysis situs, combinatorial topology and geometric figures. He plans a second book, to cover gaps in the present text.
...
The mathematical world is indebted to Dr Levi for making this first text upon a fascinating topic.
Bartel van der Waerden was appointed professor of mathematics at the University of Leipzig in 1931 as Otto Hölder's successor. Levi and van der Waerden published the joint paper Über eine besondere Klasse von Gruppen Ⓣ (1932) which solved a special case of Burnside's problem of whether a finitely generated group with a finite exponent is finite. In the paper:-
... the case of exponent 3 is treated, namely, the order of the group is determined as a function of the number of generators, the structure of the group is examined, and a complete enumeration of the characteristic subgroups is given.The Nazis came to power in Germany in January 1933 and on 7 April passed a law which excluded Jews from the civil service, which included university faculty. There were exemptions, for example anyone who was a World War I veteran would not be dismissed. Levi fell under that exemption but, despite this, was told in July that he had to leave the profession at the end of September. A newspaper article pointing out inconsistencies in those being dismissed led to his dismissal being postponed to the end of January 1934. Pleas on his behalf led to him being given a paid teaching position in December 1933. For a while it looked as if he was secure for he was even given permission to make a trip to England in the summer of 1934 to visit Reinhold Baer who, being Jewish, had been dismissed from Halle and had fled to England where he secured the position of Honorary Research Fellow at Manchester. Back in Leipzig, Levi was one of five who were dismissed in April 1935. Five members of the Faculty of Philosophy, including van der Waerden and Heisenberg, protested at a faculty meeting stating correctly that the dismissals were contrary to the law (because of their World War I service). Their protest was in vain and Levi's dismissal stood.
Van der Waerden made many enquiries in an attempt to find a position for Levi in Holland, Belgium, France and Switzerland, but was not successful. After months of worry, Levi was offered a professorship at the University of Calcutta in India; he went to India with his wife and youngest daughter and took up his post as Hardinge Professor of Higher Mathematics in January 1936. He began teaching algebra to postgraduate students and in August 1936 brought out a provisional edition of an Algebra textbook subtitled Systems of Linear Equations. He writes in the Preface:-
Upon introducing a course of lectures in Algebra, I realised after delivering a few lectures that the students of this country should have a book covering the entire subject matter. In order to make my lectures successful, I had no other alternative than to write a textbook and publish it in different parts as quickly as possible.In 1937 a second provisional Algebra volume appeared with subtitle General Algebra. The first volume of the full textbook on Algebra mentioned in the above quote was published in 1942. László Fuchs and Rüdiger Göbel write in [17] that it:-
So a provisional edition of this textbook was taken into hand. References to the original papers, examples, explanations of details, everything that caused delays in publication had to be omitted in these "lectures." Later, a full textbook on Algebra will be published.
... is an introduction to abstract algebra for graduate students. It discusses the basic algebraic structures and some number theory (like continued fractions). A few topics which are usually not included in graduate algebra texts are also studied, e.g., approximation of roots, Sturm's and Budan-Fourier's theorems etc. Important features are the numerous examples which make the book especially useful for students. Levi completed the manuscript of the second volume in which abelian groups, finite groups, Galois theory, commutative and non-commutative rings were discussed at length, but this volume has never been printed in book form.Richard Brauer writes [5]:-
The book is well written, and many examples should further increase its value as a text book.A 'Dialogue' from this book is reproduced at THIS LINK.
Let us say a little about Levi's children. When Levi went to India, he sent his son Paul Levi to Blundell's School in Devon, England, where he developed an interest in carving and architecture, winning a BBC schools' prize for sculpture. Being a German national in England, after war broke out with Germany in 1939 he was interned on the Isle of Man in 1940. While there he became friends with Hermann Bondi. Paul Levi went on to become famous as a picture framer. Charlotte Levi was sent to the United States to join her mother's cousin, the physicist and later Nobel laureate Hans Bethe. They had the same maternal grandparents, having Abraham Kuhn, the Professor of Otology at Strasbourg, as their grandfather. Charlotte's high school mathematics teacher introduced her to Martha's Vineyard, a picturesque Massachusetts island located just seven miles off the coast of Cape Cod, in 1936. While studying for a Ph.D. in bacteriology at the University of Rochester she met Mortimer Litt (1925-2024) whom she later married on Martha's Vineyard. We have no details of Susanne Levi's life except the fact that she died in London, England in 2006.
We have seen how the Nazis affected Friedrich Levi's life, but let us say a little about how other members of his family suffered. His father Georg Levi died in Darmstadt in January 1942. One year later, in February 1943, his mother Emma Levi, by that time 84 years old, blind and incapacitated, was sent to the concentration camp in Theresienstadt where she starved to death three weeks later. Levi's sister Fanni was arrested in Darmstadt in March 1943 and sent to Auschwitz, where she was later murdered. Eva Levi married Hans Ulrich Wrede in 1913. At the end of 1939, Eva Wrede was denounced and from then on often commanded to hearings by the Gestapo. In 1945 she avoided deportation to a camp since her Aryan husband was extremely ill and she was able to produce a certificate to say that he was dependent on her for care at home. After her husband went to hospital she had to hide and although friends gave her food they would not let her stay with them. Eventually the Americans liberated the city and she was found hiding in her husband's hospital room.
Hubert Cremer (1897-1983), who had written a doctoral thesis advised by Ludwig Bieberbach and Issai Schur, had been a friend of Friedrich Levi's and, after the war ended, they re-established contact exchanging letters. Cremer wrote that Levi's letter [16]:-
... moved me deeply through the terrible news it contained. As I so lightly sent you 'cordial greetings', I had no idea that also your poor mother and your sister were killed by those murderers' hands which have disgraced the German name forever. If this possibility had been known to me, I would never have dared to write in such a harmless fashion to you. I did not know the dead, however I had a mother, and have a sister, and it is possible for me to have some feeling what such a loss in such a way must mean. And I feel myself guilty as well. To be sure, we knew nothing of these horrors, however, indeed, we dimly suspected them, we had immeasurable and pitiable fear and because of this fear for our own lives, we were silent. Today I feel that we should have stood up and spoken out, even in the certainty of being murdered ourselves. At the time I silenced my conscience with the impoverished objection that such a sacrifice were indeed senseless, and with secret gifts of money to Jews in need. Even such actions were always in the fear that someone would find out and it would land us also in a concentration camp.Friedrich Levi made a major contribution to mathematics in India. Between 1939 and 1947 he had over 30 publications. He took part in meetings of the Calcutta Mathematical Society and, as President, delivered the presidential address Topology to the Society in 1942 and the presidential address Modern Algebra in 1943. He also played a major role in the Indian Mathematical Society being president of the Society from 1942 to 1947. At the Twelfth Conference of The Indian Mathematical Society held at Aligarh Muslim University in December 1941, Levi was the chairman of a Symposium on Group Theory. He delivered the lecture Report on the Combinatorial Theory of Groups. The report of the Symposium begins as follows [33]:-
Opening the general discussion on group theory, Professor Levi pointed out that the automorphisms of a system of any kind form a group, and that every group can be considered a group of automorphisms. This interconnection seems to be the reason for the central position of group theory. Starting from the idea of automorphism, i.e. of generalised permutations - a review was given of the development of the theory in recent times.Also speaking at this Symposium on Group Theory was Mohammad Abdul Jabbar who delivered the lecture Theory of p-groups. Jabbar had studied the new M.Sc. (Hons) in Pure Mathematics set up by Levi at the University of Calcutta and had graduated with First Class Honours in 1938. He went on to become the first registrar of the East Pakistan University of Engineering and Technology.
Besides this main line of progress, a certain by-way has gained enhanced importance, where the idea of combination prevails. This theory is the subject of the report.
Also at the Twelfth Conference of The Indian Mathematical Society Levi made a suggestion to the Business Meeting. This is reported in [34] as follows:-
At the suggestion of Prof Levi, the desirability of students who had completed a course of advanced study in one University being given facilities for work in other Universities was discussed.Levi delivered the Presidential address Why Mathematics? at the Thirteenth Conference of the Indian Mathematical Society held at Annamalainagar in December 1943. He said during this address:-
It was agreed that
(i) Universities be requested to arrange for research scholars to be sent to specialists and that each University should pay the expenses of its students.
(ii) that Universities and Colleges be requested, whenever possible, to arrange special courses of lectures open to the post-graduate students of all Universities.
(iii) that intimation of such lectures be sent to Heads of departments of mathematics of various Universities, at least six months before the commencement of the lectures.
I like to remember the harmony and the spirit of good fellowship prevailing at the meetings of this Society at Lucknow, Hyderabad and Aligarh and the kindness shown by distinguished mathematicians of this country to me as newcomer; moreover I feel much indebted to many mathematicians of other countries - living or deceased - to my teachers and to those with whom I used to exchange ideas.You can read a version of the full address at THIS LINK.
He gave the presidential address Relations and operations at the Fourteenth Conference of the Indian Mathematical Society held at the University of Delhi in December 1945.
In 1948 Levi reached the retirement age of 60 and he left his chair in Calcutta and became a researcher at the Tata Institute for Fundamental Research in Bombay. Although he had enjoyed his time in India, Levi was still keen to return to Europe. While still based in India, he made European trips giving a series of talks in England, the Netherlands, and Germany in 1950. While in Germany, he attended a group theory meeting in Oberwoldfach in June 1950. He held visiting professorships in Freiburg (1951) and in Berlin (1952). At the newly founded Freie Universität in Berlin Alexander Dinghas was determined to hire Levi and succeeded in doing this in 1952 in spite of the opposition of the administration because Levi was close to retirement. He retired from the position in Berlin in 1956 but continued to teach in Freiburg as an honorary professor.
In 1956 Lázló Fuchs attended a meeting in Oberwolfach which was also attended by Levi. He said:-
I had a long walk in the forest with Friedrich Levi, the nestor of abelian group theorists. Besides mathematics, he also told me about his escape from Germany to India.He continued to lecture at Freiburg until February 1963 when he gave his last lecture on his 75th birthday. He died in Freiburg after a walk on New Year's Day 1966.
Let us end with a quote from Raghavan Narasimhan ([25] or [26]). He writes that Levi's:-
... influence on mathematics in India was considerable. He introduced Indians to algebra (which used to be called modern algebra). He was an active participant in mathematical meetings. Levi played an important part in the acceptance of algebra in university curricula all over India.
Additional Resources (show)
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Written by J J O'Connor and E F Robertson
Last Update July 2026
Last Update July 2026