> 7 bjbjUU .77lp0P4448lLd.("$k/ 1x.].D+o.D+D+D+F D+D+D+`KcX4(.0.2*d2D+Herman Mntz: A Mathematicians Odyssey
Eduardo L. Ortiz and Allan Pinkus
EMBED Equation.3
Introduction
In 1885 Weierstrass [1] proved that every continuous function on a finite interval can be uniformly approximated by algebraic polynomials. In other words, algebraic polynomials are dense in C[a,b] (for any "<a<b<+"). This is a theorem of major importance in mathematical analysis and a foundation for approximation theory.
One of the first outstanding generalizations of the Weierstrass Theorem is due to Ch. H. Mntz, who answered a conjecture posed by S. N. Bernstein in a paper [2] in the proceedings of the 1912 International Congress of Mathematicians held at Cambridge, and in his 1912 prizewinning essay [3]. Bernstein asked for exact conditions on an increasing sequence of positive exponents n, so that the system EMBED Equation.3 is complete in the space C[0,1]. Bernstein himself had obtained some partial results. On p. 264 of [2] Bernstein wrote the following: It will be interesting to know if the condition that the series 1/ n diverges is necessary and sufficient for the sequence of powers EMBED Equation.3 to be complete; it is not certain, however, that a condition of this nature should necessarily exist.
It was just two years later that Mntz [M7] was able to provide a solution confirming Bernsteins qualified guess. What Mntz proved is the following:
Theorem. The system EMBED Equation.3 , EMBED Equation.3 where 0 EMBED Equation.3 0 < 1 <2 < .... , is complete in C[0,1] if and only if 0 = 0 and
EMBED Equation.3
Today there are numerous proofs and generalizations of this theorem, widely known as the Mntz Theorem. In fact a quick glance at Mathematical Reviews, that is, at papers from 1940, shows nearly 150 papers with the name Mntz in the title. All these articles mention Mntzs name in reference to the above theorem, except one referring to his thesis. Mntzs name with his theorem appears in numerous books and papers. In addition there are Mntz polynomials, Mntz spaces, Mntz systems, Mntz type problems, Mntz series, MntzJackson Theorems, and MntzLaguerre filters. The Mntz Theorem is at the heart of the Tau Method and the Chebyshevlike techniques introduced by Cornelius Lanczos [4]. In other words, Mntz has come the closest a mathematician can get to attaining a little piece of immortality.
Notwithstanding, a quick search of the mathematical literature will also show that essentially nothing is known about Mntz, the person and the mathematician. The purpose of this paper is to try to redress this oversight. Mntzs life, mathematically and otherwise, makes for an illuminating and dramatic journey through the first half of the twentieth century. It is unfortunate it was not a more pleasant journey.
Early Years (18841914)
Herman Mntz (officially named Chaim) was born in Lodz on August 28, 1884. Mntzs family was bourgeois and Jewish, though not religious. At that time Lodz was a part of Congress Poland under Russian rule. It was an important industrial city at the western boundary of this area. In the last decades of the nineteenth century, when Mntz was born, it had a vibrant Jewish community, mainly engaged in textiles and other related trades, as well as in business in general. In official documents, Mntzs father is described as in trade, with the suggestion that he was an estate agent. The family name was spelt in the German manner rather than the more common Minc. Herman was the eldest of five children, all of whom (except for the youngest) were sent to study at German and Swiss universities. The turbulent economic times were such that the family was generally, though not always, comfortably well off. A noticeable decline was associated with the depression of the late 1920s. Mntz started his studies at the Hhere Gewerbeschule in Lodz, the top technical high school in that city, with a bias toward textiles, textile machinery and chemistry. He was fluent in Polish and had a reasonably good command of German and Russian.
In 1902 Mntz went to Berlin to study at the FriedrichWilhelmsUniversitt, generally referred to as the University of Berlin (called Humboldt Universitt Berlin since 1948), where he studied mathematics, the natural sciences and philosophy. In 1906 he earned his matriculation degree. He named Frobenius, Knoblauch, Landau, Schottky and Schwarz as his teachers, singling out Frobenius and Schwarz as his main influences.
From 1906 to 1910 Mntz was in Berlin where he worked, wrote and studied. In 1912 he married Magdalena (Magda) Wohlman who was from the area of Zlotkow near Poznan, an area of Poland under German control. Magda had come to Berlin to study biology. While the marriage would remain childless it was, by all accounts, an unusually harmonious union. During this early period Mntz was involved in the private teaching of mathematics. Money was always a pressing problem. For much of his life Mntz remained engaged in pedagogy in one form or another teaching elementary and higher mathematics, partly in private schools and partly as a private tutor.
Mntz was an intellectual who was intensely interested in philosophy, poetry, art and music. He was especially taken with Goethe but, more particularly, with Nietzsches philosophy, which was to have a profound influence on him. He attended university lectures given by the philosopher Alois Riehl, and he seems to have written a thesis on Nietzsche.
In these years he also became interested in a reassessment of Jewish culture and the position of Jews in society. In 1907 he published a 124 page book called Wir Juden [6] in which the influence of Nietzsche, and especially his Also sprach Zarathustra, is discernible. The book, dedicated to Friedrich Nietzsche, is about the need for a basic reform of the Jewish people in the postorthodox religious period, and a reconsideration of the position of Jews in contemporary society.
Mntz discussed, in detail, what he called the new Jew, the contribution Jewish people had made and could make to humanity, and characterized Jews not as a pure race but as a diversity of many peoples emphasizing the past and present connections between Jews and a variety of other people. The book also aspired to help the young Jewish generation of the time to achieve its religious and political selfdefinition. It embraced a view of Zionism, not uncommon at the time, in which socialist viewpoints were discernible. At a time when racism and antiSemitism were rampant there were remarks in Mntzs text that are very much racebased. This makes for a book very discomforting to read today. The book was advertised in the Berlin Jewish/Zionist weekly Jdische Rundschau in its list of Zionistische Literatur. These advertisements continually misspelt the authors name as Mntzer, which might well be considered as a measure of the perceived importance of the book.
Aside from a mathematical text mentioned later, this was the only book by Mntz that was ever published. However, we have found various items of correspondence indicating that he also wrote at least three other (nonmathematical) texts. All written from about 1911 to 1924, they were: a) ber Ehe und Treue (On marriage and fidelity); b) A book about Psalms, and c) Der Jdische Staat (The Jewish state). The three manuscripts were sent to different publishers, but for a variety of reasons, including the war and lack of paper, none seems to have been published. However, parts of the lastnamed book appeared as articles in a journal.
Despite these varied activities, Mntzs main goal in the period 19061910 seems to have been his mathematical studies, which were under the supervision of Hermann Amandus Schwarz. His first results were of a geometric character, having to do with rational tetrahedra. However he soon began to produce results on the main topic of his doctoral dissertation, namely minimal surfaces defined by closed curves in space that mathematically involved the approximate solution of nonlinear partial differential equations. On October 1, 1910, Mntz was awarded a doctorate, Dr. Phil., magna cum laude. His official reviewers were Schwarz and Schottky. His dissertation, under the title of On boundary value problems of partial differential equations of minimal surfaces was published in Crelles journal [M1]. This work is still occasionally referenced.
In this thesis Mntz studied the Plateau problem in some detail. He used potential theory and the method of successive approximation, two tools he would return to in subsequent papers. When Mntz was near the end of this dissertation work, Schwarz advised him that Arthur Korn, who was working in the same area, had submitted for publication a paper on the subject of his thesis, which was later published [7]. In his Crelle paper Mntz acknowledged Korns work. Although their results had a common ground, the techniques used by each author and the final results were sufficiently diverse to merit independent publication. Mntz seems to have been the last of Schwarzs doctoral students. Other doctoral students of Schwarz included Leopold Fejr, Ernst Zermelo, Paul Koebe, and Leon Lichtenstein. The latter became a close friend of Mntz.
In late 1911 Mntz went to Munich to give a lecture at the seminar of Ferdinand von Lindemann. He was also accepted into Aurel Vosss circle. These were two of the three mathematics professors at the Karl LudwigMaximilians Universitt, in Munich, the third was Alfred Pringsheim. The Mntzes decided to move to Munich primarily on the basis of this visit, which seemed to open some opportunities. But they were also undoubtedly influenced by the fact that two of Mntzs brothers were also then residing in Munich. However, Mntzs aim and that of any young aspiring mathematician in Germany at this stage of his career, was to secure a position as a Privatdozent. The next stage was to gain a Habilitation and eventually an academic position at a university. At that time, and the same is essentially true today, the Habilitation was necessary for a professorship, and a professorship is what Mntz wanted then and throughout his life. According to his correspondence Mntz, who was not the only candidate, obtained the support of the three mathematics professors. It seems, however, that there were also what he termed some strange regulations, and serious formal problems. The matter dragged on, seemingly interminably, but to no avail. In the end, Mntz was unsuccessful in gaining the dozent position.
While in Munich Mntz was again earning his living privately as a teacher at various levels. His wife also worked parttime and there was some financial help from the family. Mntz also attended lectures and seminars given by von Lindemann and Voss and was actively engaged in mathematics research. From 1912 to 1914 he published four papers on problems in the field of modern projective geometry, and the axiomatics of geometry, two of which appeared in Mathematische Annalen. His 1912 paper on the construction of geometry on the basis of only projective axioms was read by Voss at a meeting of the Bavarian Academy. In 1913 he published two notes in Comptes Rendus in connection with the use of iterative techniques for the solutions of algebraic equations. It is very possible that Mntz was the first to develop an iterative procedure for the determination of the smallest eigenvalue of a positive definite matrix. It certainly predates the more generally quoted result of R. von Mises of 1929 [8]. In 1914 he published an additional two papers on approximation theory. The first is a note on properties of Bernoulli polynomials published in Comptes Rendus. The other is the paper in which the Mntz Theorem appeared. This last work was written as a contribution to the Festschrift in honour of his teacher Hermann Schwarzs 70th birthday.
In this period reference is already made in Mntzs correspondence to serious problems in one of his eyes. Eye problems would continually plague Mntz throughout his life.
Boarding Schools and Martin Buber (1914  1919)
In early 1914, probably through socialist and feminist common friends, Mntz started a correspondence with the pedagogue Paul Geheeb, who ran a boarding school called the Odenwaldschule near Heppenheim in southern Hessen. Mntz moved to Geheebs school in 1914 as a mathematics teacher, with the understanding that he would be able to devote a considerable amount of his time to his mathematical research. It was agreed that he would have at most three hours of teaching a day. This was to be the first time he taught very young children.
In a letter to Geheeb written by Mario Jona, who interviewed him for the position, there is the following passage: He [Mntz] is perfectly aware of what he is worth and shows it, which face to face is not so unpleasant as in writing. As it was I imagined him from his letter to be much more terrible. He is short, pleasant and with a very serious appearance and sometimes a little clumsy in politeness, ...... For him the most important thing is his scientific work. He is in a period of important scientific activity, but would like also to work in a school like ours if he also has time to work for himself.
Geheeb was a liberal humanist, profeminist and much opposed to antiSemitism. He and his schools hold a special place in the history of progressive education in Germany. At one of his earlier schools, in Wickersdorf, he had established the first coeducational boarding school in Germany. His wife, Edith Cassirer, was a progressive young teacher, the daughter of the wealthy Berlin Jewish industrialist Max Cassirer. With his fatherinlaws financial backing, Geheeb founded the Odenwaldschule in 1910. It was a large boarding school with modern or specially modernized buildings. Coeducation, an emphasis on physical education and flexibility in the curriculum, were among its innovations. The new school was run with a fair amount of selfgovernment. The teachers, and especially Geheeb, supposedly guided rather than led. The students were called Kameraden, comrades, and the teachers Mitarbeiter, coworkers. In 1914, the time we are talking about, there were 68 fulltime students, many of whom were children of the liberal, affluent, German intelligentsia. The children of Thomas Mann and of other noted writers and artists were among the pupils and were not necessarily easy to handle. Much has been written about this school and Geheeb. The school survived both wars and exists today, but the Geheebs left in 1934 and moved to Switzerland, when the influence of Nazi activists reached the school. There, he and his wife established a school of a related character: cole dHumanit.
According to some, Mntz included, life in Odenwaldschule seemed anarchic on occasions. Mntz and Geheeb parted ways in the summer of 1915. Nonetheless Mntz kept in touch with some of the schools faculty and remained on speaking terms with Geheeb.
Mntz then found a similar position at another school, Drerschule, which does not exist today, in Hochwaldhausen also in Hessen. Mntz seems to have enjoyed his teaching, and was particularly interested in the teaching of mathematics and science to younger children, developing very definite opinions thereon. Another teacher who joined him at the Drerschule was his friend and brotherinlaw Herman Schmalenbach, married to his sister Sala. He later became a Professor of Philosophy at the University of Basel.
The war was also having its impact. Mntz was regarded as an alien with Hessian residency, but no German citizenship, and he was generally restricted in his travels. This had prevented a move to Heidelberg planned in 1915. In a letter dated August 1917 Mntz wrote that he had to stay in Hessen to avoid difficulties with the authorities. However as an alien he did not take part in the war. Although happy at the school, he was forced to leave as a consequence of being subjected to antiSemitic remarks by the director.
Many pupils, especially the Jews, also did not return to Drerschule after the holiday. Mntz felt he had a responsibility for some of these children and decided to return as a private scholar to Heppenheim where he had friends, but not to Odenwaldschule. With his wife, he managed a small boarding house for students: a Schlerpensionat.
Despite his many obligations and worries Mntz still managed to carry on with his mathematics research. During this period he published five more papers, concerning problems in projective geometry, and the solution of algebraic equations and algebraic eigenvalue problems.
While still at the Odenwaldschule, Mntz had begun to correspond with Martin Buber, the enlightened and broadminded philosopher, Zionist thinker and writer, who was then in Berlin. Buber was the spiritual leader of an entire generation of Germanspeaking Jewish intellectuals. He adhered to a form of tolerant utopian socialism he called Hebrew humanism.
In 1915 Mntz helped Buber find a house in the town of Heppenheim, where Buber and his family lived from 1916 until 1938. Buber then left for Palestine to take a Chair in Social Philosophy at the Hebrew University and subsequently had a distinguished career there. During the years of the First World War the two families kept in close contact and exchanged fairly intense and interesting correspondence.
In 1915 Buber founded and coedited a journal called Der Jude [10] that for eight years was the most important organ of Germanreading Jewish intellectuals. In a letter dated in November of that year, Buber invited Mntz to become one of his collaborators on this journal. He wrote You are, of course, amongst the first whom I am asking to participate. Mntz wrote 18 articles and notes for this journal, some quite lengthy, which he published under the pseudonym of Herman Glenn. It is an indication of the way in which Mntzs contributions were valued that in the very first issue of Der Jude, the first article was signed by Buber, while the second was signed by Glenn (Mntz).
Gttingen and Berlin (1919  1929)
Around 1919 or 1920 Mntz seems to have had a nervous breakdown and was placed at a sanatorium in Gandersheim near Gttingen. We do not know exactly how long Mntz was in the sanatorium. The few letters available from this period are rather bleak. In a letter to Buber in September of 1923 Mntz recalled that he suffered a personal collapse in 19191920 and said he learnt from the experience to look at things from a distance, and in this way they are no longer dangerous to me.
Toward the end of 1920 Mntz and his wife moved to his wifes family farm in Poland to recuperate for some eight to ten months. Letters show that during this period the Mntzes, together with his wifes brothers, considered emigrating to Palestine. But the economic situation there was far from encouraging and the idea was dropped. As he recuperated, Mntz took up mathematics again and from the farm traveled to Warsaw to attend seminars and to lecture on his research. This activity is reflected in a number of publications in the journal of the then recently founded Polish Mathematical Society.
In October of 1921 the Mntzes returned to Germany, moving into a boarding house in Gttingen. At that time the Schmalenbachs also lived in that city. It is not clear how the Mntzes supported themselves in Gttingen, but it was again probably through private teaching and with the help of their family. While in Gttingen Mntz did a considerable amount of mathematical research. During this time he wrote eleven papers, that were published between 1922 and 1927. They range over a number of topics including integral equations, the nbody problem, summability, Plateaus problem, and quite a few papers on number theory, possibly under the influence of Edmund Landau.
By this time Mntz seems to have made a name for himself within both mathematical and Jewish/Zionist circles. He was a member of the editorial board of the mathematics and physics section of the shortlived journal Scripta Universitatis founded by Immanuel Velikovsky from Jerusalem. The one and only issue of the mathematics and physics section was edited by Einstein and published in 1923. He also cooperated with Hertz, Kneser and Ostrowski in a German translation of some lectures of LeviCivita [M21].
In April 1924 the Mntzes moved to Berlin, while maintaining scientific contacts in Gttingen. In Berlin they rented an apartment and seemed to live happily. Mntz also returned to writing on Jewish matters. He sent contributions to Der Jude some of which were excerpts from the third of his unpublished books on Jewish matters.
Mntz does not seem to have favored scientific collaboration, although he had at least one student in this period. Divsha Amir (ne Itine) from Palestine was a geometer who officially obtained her doctorate from the University of Geneva in 1924. She collaborated with Mntz whilst residing in Gttingen. In 1925 she published a memoir [12] on a projective synthesis of Euclidean geometry. Mntz had attempted a construction of algebraic Euclidean geometry using what he called Basisfiguren. In her memoir Divsha extended Mntzs ideas to the general Euclidean plane considering, instead, sets of straight lines. She discussed elementary constructions, congruence axioms and the axiomatic construction of geometry. Divsha was generous in her remarks to Mntz and to his research. Although not her formal thesis supervisor, Mntz clearly was her mentor. Divshas husband Benjamin, who also obtained his doctorate from the University of Geneva, was a student of Edmund Landau.
The first meeting of the board of governors of the new Hebrew University in Jerusalem took place in April of 1925. At that meeting it was decided to establish an institute devoted to research in pure mathematics, staffed by one professor and two assistants. The board of governors also authorized the President and Chancellor to offer Edmund Landau the professorship in pure mathematics. The involvement of Landau in the Hebrew University started well before the First World War, and lasted into the 1930s. He was the person who had the major say in the choice of who would be appointed to the mathematics institute. At a meeting of the board of governors in September 1925, Landau was asked to draw up plans for the establishment of a mathematical institute to be opened as soon as funding became available. At the suggestion of Landau, it was decided to appoint Benjamin Amir as the first assistant.
In October of 1925 Mntz was in Berlin and was busy trying to find a position, either in or outside Germany. The creation of the Hebrew University undoubtedly interested him as a mathematician, as someone without proper employment and as a Zionist. Mntz saw himself as the professor and thus the director of this new mathematical institute. In a rather manipulative way he used his connections, particularly Schmalenbachs everlasting good disposition towards him. He asked his wellpositioned brotherinlaw to contact Buber, Landau and Courant on his behalf. Schmalenbach reported that Courant was emphatic in stating that he had no doubts as to Mntzs qualifications, which he exhibited in his papers and in his lectures at the meetings of the local mathematical society. However he indicated that not having a Habilitation was a serious drawback in his case. The Jerusalem matter was resolved negatively in early November. In retrospect, it seems Mntz had misread, or been misled, concerning the entire situation. At this early stage in 1925 Landau probably was saving the professorship for himself. In any case the academic leadership of the Hebrew University was looking for an established star to take up the professorship. At the very least they were looking for someone with a Habilitation and also a chair somewhere else. They were actually looking for a person like Landau, who in fact moved to Jerusalem with his family for the initial academic year of 192728. However, for various reasons things did not work out and he returned to Gttingen the following year.
Throughout this period Mntz was constantly seeking an academic appointment, while at the same time attempting to obtain his Habilitation. In 1925 Voss and von Lindemann recommended him for a Habilitation in Giessen, but nothing came of it. That same year it appears he was recommended, by A. A. Fraenkel, for a position at the University of Cairo. Again he was unsuccessful.
As we said, according to Courant, the fact that Mntz had not been given the Habilitation in Gttingen was not as a consequence of his lack of qualifications. There were other reasons. On the one hand there was Gttingens hierarchy. As in the cases of Bernays, Hertz, and E. Noether, if he were not to be called by a university, Gttingen would feel morally obliged to provide for his maintenance. On the other hand there was the question of his origin, which Mntz did not try to hide. Mntz had heard essentially the same from Hilbert years earlier. To all this Mntz justifiably complained that he was in an impossible situation. If he was guaranteed a position then he would have no problems being given Habilitation, but without the Habilitation it was almost impossible to obtain a position. His case was not unique.
One source of income for Mntz we have identified is the Jahrbuch ber die Fortschritte der Mathematik (FdM). This annual review, published from 1869 until the end of the Second World War, was in the format adopted by the Zentralblatt fr Mathematik, and later shared by Mathematical Reviews, except that it appeared each year as a single volume. As a consequence of the First World War, the work on the annuals was severely backlogged and remained so for many years thereafter. A count of the reviews signed by Mntz, shows he wrote nearly 800 reviews for the FdM, mainly during the mid 1920s. In fact he was still registered among the journals regular reviewers up to 1929 when he had already left Germany. Reviewers were paid 1 Reichsmark per review. The average salary at the time seems to have been about 120 Reichsmark per month.
The reviews by Mntz cover an extensive mathematical, as well as linguistic, area. Besides the languages he was brought up in, namely Polish, German, and Russian, Mntz reviewed papers in English, French, Italian, Dutch and Swedish. The topics frequented by him, besides function theory, and differential equations, were probability theory, fluid mechanics, the theory of electricity and magnetism, including its geophysical applications, numerical methods of calculation and the history of mathematics.
At the end of 1927 Mntz wrote to Buber that for several months he has been the professional scientific collaborator of Einstein, and added This, of course, compensates me a great deal for what has been in Germany an almost impossible situation as the official professionals are more official than professional. He was probably alluding to the fact that he had been unable to obtain a Habilitation. It is not totally clear when Mntz started to work with Einstein and for how long this collaboration continued. From his wifes correspondence it seems he met Einstein socially in January 1927. For much of the time that Mntz worked with/for Einstein, another subsequently wellknown mathematician, Cornelius Lanczos, also worked with Einstein. Both seem to have been supported by grants from a fund supporting promising young scientists. Mntz published no joint papers with Einstein. But Einsteins archive has an extensive collection of correspondence between Mntz and Einstein on a range of mathematical ideas. Moreover Mntz, as well as Lanczos, are mentioned and thanked in two of Einsteins papers on distant parallelism.
In describing to his sister his work under Einstein in September of 1927, Mntz indicated that it was running normally and for reasons of convenience I have submitted myself; for in these fields it is he who is the extraordinary master while I am only the technical assistant. Nevertheless I am very happy to be working with him. On more than one occasion, however, Einstein politely expressed reservations regarding Mntzs work. Einstein sometimes indicated that he did not believe there were sufficient reasons for Mntzs assumptions, or he did not regard Mntzs reasoning as being justified, or he did not think that Mntzs arguments made any obvious experimentalphysical sense.
Toward the end of 1928 Mntz was again considering the possibility of taking a chair outside Germany. However, he purposely kept these discussions from many of his close friends and colleagues, including Lichtenstein and Einstein, which suggests that he still expected that they might be able to help him find a job within Germany.
Leningrad (1929  1937)
In May of 1929 Mntz finally obtained an academic appointment, something he had yearned for for many years. He was invited to fill the position of Professor of Mathematics and Head of the Chair of Differential Equations at the Leningrad State University. In Leningrad Mntz was also put in a group of exceptional scientists, and given a personal salary. From 1933 he is listed as Head of the Chair of Differential and Integral Equations.
In a letter written a few years later, Mntz stated that in 1927 he was also offered the Lobatschevsky Chair in Kazan, and that during the technical period of waiting was offered the Chair for Higher Analysis in Leningrad. According to Mntz he exchanged the chair in Kazan with that in Leningrad (initially offered to Bernstein), while his friend N. G. Chebotarev took the Kazan Chair. We have found no direct documentation to support this claim, but the fact is that Chebotarev became professor at Kazan University in 1928 after having been offered posts at both Kazan and Leningrad.
G. G. Lorentz, who was an undergraduate at the time, recalled [13] that in 1930, shortly after his arrival in Leningrad, Mntz was called upon to present a lecture sponsored by the Leningrad Physical and Mathematical Society on the socalled crisis of the exact sciences. The subject matter was the foundational debate in mathematics, and Hilberts attack on the intuitionism of Brouwer and Weyl. Mntz was an ideal candidate to deliver the lecture because of his research background on the foundations of mathematics; and having recently arrived from Germany, he was perceived as the carrier of the latest advances on this controversy.
The lecture was well attended. Of course Mntz stated that the crisis was only in the foundations and did not in any way affect the work of most mathematicians. However, because of an underlying power struggle between N. M. Gnter, V. I. Smirnov and Ya. V. Uspensky, on the Societys traditional side, and L. A. Leifert and E. S. Rabinovich, of an alternative young Communist league, the meeting turned rowdy and undisciplined. The Leningrad Physical and Mathematical Society subsequently ceased to exist in its previous form, being amalgamated into a new organization under Rabinovich.
The row does not seem to have affected Mntzs subsequent career. From 1931 Mntz was also in charge of mathematical analysis at the Scientific and Research Institute in Mathematics and Mechanics (Nauchna Issledovatelskii Institut Mathematiski i Mechanika, or NIIMM) at Leningrad State University. Furthermore, in 1932, Mntzs position in Russia seems to have been quite firm, since he was given the singular distinction of being sent to the International Congress of Mathematicians in Zurich as one of four of the Soviet Unions official delegates. The other three were Chebotarev, representing Kazan State University, who gave a plenary lecture on Galois Theory (on the occasion of the centenary of the death of Galois), the famous topologist P. S. Aleksandrov from Moscow State University, who talked about Dimension Theory, and . Ya. Kolman, a mathematician and a member of the Communist Academy, in Moscow. The Academy was an institution created in 1918 which had been given the task of developing Marxist views in the fields of philosophy and science. Kolman, the ideologist in this delegation, gave two talks, the first about quaternions and the second about the foundations of differential calculus in the works of Karl Marx. Mntz, representing NIIMM at Leningrad State University, read a paper on boundary value problems in Mathematical Physics.
While Mntz had been unable to obtain his Habilitation in Germany, he was far more successful in Russia. In 1935, at the recommendation of Leningrad State University, VAK, the committee that gave these higher (or second) doctorates in Russia, awarded Mntz a higher degree without requiring the submission of a written thesis. Mntz would later write that he had been awarded an honorary doctorate, and that could be one possible interpretation of this degree. All the above testifies to the fact that without doubt Mntz held a senior position in Leningrad State University and had the respect of his colleagues. He had fulfilled his ambition.
Mntz seems to have been active administratively, pedagogically and mathematically. In a later letter to Einstein he wrote about working on a uniform theory of the solutions of nonstationary boundary value problems in homogeneous and nonhomogeneous spaces. However he also talked about the heavy teaching and administrative load, and the unfortunate state of his eyes that hindered him greatly. In 1934 he published a textbook on Integral Equations [M32] which is still sometimes referenced, and in 1935 he edited a Russian edition of Liapounoffs important monograph on General Problems of Stability of Motion [M35]. The fact that Mntz was given this task, of historical as well as scientific importance, is another indication of the high regard in which he was held at the time. He also wrote some half dozen research papers, mainly on boundaryvalue problems, integral equations and on topics of Mathematical Physics. Furthermore, he was asked to write a review of his own work for the Second AllUnion Mathematical Congress held in Leningrad in 1934. The latter was a definite honour, awarded at a time when he began to recover from further eye problems.
While in the Soviet Union Mntz kept a low, neutral, profile visvis internal politics. Although he kept his German citizenship, obtained in 1919, at some stage he was given a former foreigner status within the Soviet Union. He also seems to have traveled abroad widely in the company of his wife, visiting Finland, Germany, Switzerland and Poland. Generally visits were related to vacations or had to do with mathematics research or meetings, but sometimes they were motivated by his and his wifes health.
While visiting Berlin on vacations, by March 1930 Mntz was again working under Einstein. His work related to a question of compatibility of partial differential equations which Einstein indicated had been solved by Cartan, in a wonderful fashion, but had not yet been published. He indicated to Mntz You will take pleasure from it.
Magda had suffered a cerebral thrombosis in 1934. Mntz himself, as has been mentioned, suffered from severe problems in one eye and around 1934, at the beginning of term, he suffered damage in the retina of the other eye. This kept him away from his academic duties for several months. As he began to recover, his department provided a secretary to help him with his research and when in a position to teach, his students helped him by writing on the blackboard before each lecture the formulae he needed.
F. I. Ivanov, who was a graduate student in the 1930s, recalls that Mntz conducted a seminar in Mathematical Physics. Ivanov remembers Mntz as being very actively occupied with science, but both accessible and sociable. He writes that Mntz was stout, had lightgrey hair and very strong glasses because of his poor eyesight. For this reason Mntzs wife would bring him to the seminar.
According to Mntz he also helped, sometimes directly and sometimes indirectly, mathematicians from Central Europe obtain positions in the Soviet Union. He said that the appointments of CohnVossen, a former collaborator of Hilbert who died of pneumonia shortly after arriving in Moscow, and of the number theorist Walfisz, who went to Tbilissi, were the result of his suggestions. With others he helped both Plessner and Bergman obtain positions.
In October 1937 Mntz was expelled from the Soviet Union without, according to him, any apparent reason. However this was part of a wide movement sweeping the country, which turned the tide against foreigners, including teachers and engineers. It even affected those, like Mntz, who had helped develop different areas of activity in the Soviet Union. The Mntzes were given a few weeks to leave.
Sweden (1937  1956)
Leaving the Soviet Union was a shock to Mntz who was then 53 years old. He had lost the position he had worked most of his life to obtain. The Mntzes were permitted to take their personal possessions with them, but no financial recompense was offered for his eight years as a professor at Leningrad State University.
Travelling long distances was risky because of his wifes thrombosis. The Mntzes left Russia and first went to Tallinn in Estonia. According to Mntz, the MathematicsMechanics Faculty of the Technical University in Tallinn offered him a visiting professorship for the spring semester. But since neither German nor Russian were then acceptable teaching languages  ministry regulations required lectures to be given in Estonian  this was not a possibility. In February of 1938, the Mntzes moved to Sweden where they later requested political asylum.
Immediately after being expelled from Russia, Mntz asked for help in obtaining an academic position from a number of colleagues and former teachers. He also asked family and personal friends for financial help. Mntzs file at the Society for the Protection of Science and Learning and files on him in other scientific refugee organizations indicate that he contacted, among others, Harald Bohr, Einstein, Landau, LeviCivita, Volterra, Weyl and Courant.
Finding an academic position for a scientist of Mntzs age was not easy. Technically he was not a refugee from Hitlers Germany, since he had left in 1929. This put him outside the purview of relief organizations such as the Notgemeinschaft Deutscher Wissenschaftler im Ausland. Furthermore, he was already in Sweden, a relatively safe place. Because of earlier emigration from Germany, competition for academic positions in Europe and in the United States was fierce and involved a large number of parameters to overcome the resistance and antiforeign feeling, often as intense as the generosity of those many prepared to help. Seniority in the field, age of the candidate, area of research, even personality, without leaving aside the strength of his personal network of scientific contacts, were among these parameters.
While Mntz was referred to as a mathematician of the highest rank, in the dossiers of agencies dealing with displaced scientists, he was not considered a star. There were other drawbacks in Mntzs prospects for employment. Crucially, Einstein had concerns regarding Mntzs personality, dating from their association in the late 1920s, which we have briefly outlined. In a letter to a colleague, Einstein explained his reservations in terms of what he regarded as Mntzs inability to submit his ideas to a proper level of critical analysis and his previous mental illheath. Einstein thought that, in a period of general distress, he should reserve his influence to more clearcut cases. An imbalance in his personality, probably associated with his nervous breakdown of 20 years earlier, was now a serious drawback in Mntzs prospects for employment.
Mntz resented Einsteins attitude and especially Einsteins suggestion (in 1938!) that Mntz should look for work in his native Poland. Mntz indicated that he was now in exile from Poland, Germany and the Soviet Union, and in Germany he had not been forgiven for his former cooperation with Einstein. The tremendous competitiveness for jobs in America at the time may not have been entirely clear to Mntz, as the jobdescription of his aspirations suggest. In a possibly lost letter, Einstein may have pointed to such difficulties. Only Mntzs reply to this letter is available. Mntz responded that it was painful and unjust after so many years to conclude that my present fate is to be judged only by the statistics of supply and demand. Even if Mntz was right, this last matter was clearly not in Einsteins hands.
In Sweden, as previously in Germany, Mntz had less success in penetrating official academic circles than in the Soviet Union. However, from the first days of his arrival there he had the support of Professor Gran Liljestrand, chairman of the funding committee for exiled intellectuals, who helped him financially in 1939 and 1940. A number of distinguished Swedish academics also offered their help and friendship, among them Professors Folke K.G. Odqvist, a mechanics specialist, Hugo Valentin, a physicist, Marcus Ehrenpreis, a pediatrician surgeon, and David Katz, a psychologist.
Initially, in 194042, he received research grants from the Karolinska Institutet for work on mathematical problems related to haemodynamics, the study of the dynamics of blood flow, whose problems involved the solution of complex nonlinear partial differential equations. Research on this subject was carried out at the Maria Hospital, in Stockholm, in collaboration with a young medical doctor, Dr. A. Apria. Mntz published a note on haemodynamics in Comptes Rendus, submitted by Hadamard, that appeared in the February 1939 issue. In 1942 Apria died and this research came to an abrupt end.
Although he was on good terms with some leading Swedish scientists and intellectuals, Mntz was not able to forge a working contact with the small but active Swedish mathematical community of the time. Nevertheless, for some years he remained interested in various mathematical problems. In correspondence with Einstein and others he indicated he was interested in problems of integral equations, turbulence, knot theory, actuarial mathematics and, of course, haemodynamics. However, possibly due to the severity of his circumstances, no subsequent scientific papers of Mntz have come to light from this last period.
While in Stockholm Mntz returned to private teaching, and the couple moved to an apartment in Solna, a pleasant district of Stockholm. They had a telephone in their name, which suggests that their financial circumstances had improved. It seems that they did have some outside financial resources. Mntz later received a small pension from the Warburgfonden, a foundation controlled by the Mosaic community in Sweden.
His wife Magdalena died of hemiplegia on January 19, 1949. Mntz became a Swedish citizen in 1953 and died on April 17, 1956, at the age of 71. He was blind for the last few years of his life. But for an obituary in Svenska Dagbladet, the leading Swedish newspaper, written by Odqvist, his death passed almost unnoticed to the mathematical community of Sweden and the rest of the world. In this obituary Professor Odqvist summarized the last years of Mntzs life in a short but poignant paragraph: Herman Mntz is dead. In spite of the fact that he lived in Sweden for 18 years, the last five years as a Swedish citizen, there are probably not many Swedes outside his nearest circle of acquaintances, that knew that we had among us a mathematician of international fame who was thrown up on our calm shore by the storms of the times, his life saved but with his scientific activities broken. He ended the obituary with these words: Herman Mntz lived in an exceptionally harmonious marriage and his wife Magda meant much to him, not in the least in order to keep his floating spirit down to earth. After her death in 1949 he only seldom saw his friends and he went every day to her grave in the Jewish cemetery with fresh flowers as long as he could. Now he is gone. Let this be a modest flower of memory from his Swedish friends. Let his memory be blessed.
Acknowledgement: A paper such as this could not have been written without the help of many, many people and of various institutions. While it is impossible to name them all here we hope to acknowledge them by name at a later opportunity.
Herman Mntz: List of Mathematical Publications
[M1] Zum Randwertproblem der partiellen Differentialgleichung der Minimalflchen, J. Reine Angew. Math., 139 (1911), 5279.
[M2] Aufbau der gesamten Geometrie auf Grund der projektiven Axiome allein, Mnchener Sitz., (1912), 223260.
[M3] Das Euklidische Parallelenproblem, Math. Ann., 73 (1913), 241244.
[M4] Das Archimedische Prinzip und der Pascalsche Satz, Math. Ann., 74 (1913), 301308.
[M5] Solution directe de lquation sculaire et de quelques problmes analogues transcendants, C. R. Acad. Sci. Paris, 156 (1913), 4346.
[M6] Sur la solution des quations sculaires et des quations intgrales, C. R. Acad. Sci. Paris, 156 (1913), 860862.
[M7] ber den Approximationssatz von Weierstrass, in H. A. SchwarzFestschrift, Berlin, 1914, 303312.
[M8] Sur une proprit des polynmes de Bernoulli, C. R. Acad. Sci. Paris, 158 (1914), 18641866.
[M9] Ein nichtreduzierbares Axiomensystem der Geometrie, Jber. Deutsch Math. Verein, 23 (1914), 5480.
[M10] Approximation willkrlicher Funktionen durch Wurzeln, Archiv Math. Physik, 24 (1916), 310316.
[M11] Zur expliziten Bestimmung der Hauptachsen quadratischer Formen und der Eigenfunktionen symmetrischer Kerne, Gtt. Nachr., (1917), 136140.
[M12] On projective analytical geometry (in Polish and German), Prac. Mat.Fiz., 28 (1917), 87100.
[M13] The problem of principal axes for quadratic forms and symmetric integral equations (in Polish and German), Prac. Mat.Fiz., 29 (1918), 109177.
[M14] A general theory for the direct solution of equations (in Polish), Prac. Mat.Fiz., 30 (1919), 95119.
[M15] Die hnlichkeitsbewegungen beim allgemeinen nKrperproblem, Math. Z., 15, 12 (1922), 169187.
[M16] Allgemeine independente Auflsung der Integralgleichungen erster Art, Math. Ann., 87, 13 (1922), 139149.
[M17] Beziehungen der Riemannschen (Funktion zu willkrlichen reellen Funktionen, Mat. Tidsskrift B, (1922), 3947.
[M18] Absolute Approximation und Dirichletsches Prinzip, Gtt. Nachr., 2 (1922), 121124.
[M19] Allgemeine Begrndung der Theorie der hheren (Funktionen, Abhdl. des Sem. Hamburg, 3 (1923), 111.
[M20] Der Summensatz von Cauchy in beliebigen algebraischen Zahlkrpern und die Diskriminante derselben, Math. Ann., 90, 13 (1923), 279291.
[M21] Fragen der klassischen und relativistischen Mechanik. Vier Vortrge gehalten in Spanien im Januar 1921, by T. LeviCivita; authorized translation by P. Hertz, H. Kneser, Ch. H. Mntz, and A. Ostrowski, pp. VI + 110, J. Springer, Berlin, 1924.
[M22] Umkehrung bestimmter Integrale und absolute Approximation, Math. Z., 21 (1924), 96110.
[M23] ber den Gebrauch willkrlicher Funktionen in der analytischen Zahlentheorie, Sitzungsberichte der Berliner Math. Gesellschaft, 24, 2 (1925), 8193.
[M24] Die Lsung des Plateauschen Problems ber konvexen Bereichen, Math. Ann., 94, 12 (1925), 5396.
[M25] Zur Gittertheorie ndimensionaler Ellipsoide, Math. Z., 25 (1926), 150165.
[M26] Zum Plateauschen Problem. Erwiderungen auf die vorstehende Note des Herrn Rado, Math. Ann., 96, 34 (1927), 597600.
[M27] ber die Potenzsummation einer Entwicklung nach Hermiteschen Polynomen, Math. Z., 31, 23 (1929), 350355.
[M28] Sur la rsolution du problme dynamique de llasticit, C. R. Acad. Sci. Paris, 194 (1932), 14561459.
[M29] ber die Lsung einiger Randwertaufgaben der mathematischen Physik, Verhandlungen des Internationalen MathematikerKongress Zrich 1932, Dr. Walter Saxer, ed., Zurich, 1932, 109110.
[M30] Integralgleichungen der Elastodynamik, Rec. Math. Moscou, 39, 4 (1932), 113132.
[M31] Zum dynamischen Wrmeleitungsproblem, Math. Z., 38, 3 (1934), 323337.
[M32] Integral Equations, Vol. I, Volterras Linear Equations, (in Russian), pp. 330, Leningrad, 1934.
[M33] Sur les problmes mixtes dans lespace htrogne. quation de la chaleur n dimensions, C. R. Acad. Sci. Paris, 199 (1934), 821824.
[M34] Functional Methods for Boundary Value Problems (in Russian), Works of the 2nd AllUnion Mathematical Congress, Leningrad, LeningradMoscow, 1 (1935), 318337.
[M35] General problems of stability of motion, by A. Liapounoff, (in Russian), Ch. H. Mntz, ed., LeningradMoscow, 1935.
[M36] Zur Theorie der Randwertaufgaben bei hyperbolischen Gleichungen, Prace Mat.Fiz., (Gedenkschrift fr L. Lichtenstein), 43 (1936), 289305.
[M37] Les lois fondamentales de lhmodynamique, C. R. Acad. Sci. Paris, 280 (1939), 600602.
References
[1] K. Weierstrass, ber die analytische Darstellbarkeit sogenannter willkrlicher Funktionen einer reellen Vernderlichen, Sitzungsberichte der Akademie zu Berlin, 1885, 633639 and 789805.
[2] S. Bernstein, Sur les recherches rcentes relatives la meilleure approximation des fonctions continues par des polynmes, Proceedings of the Fifth International Congress of Mathematicians, (Cambridge, 2228 August 1912), E. W. Hobson and A. E. H. Love, eds., Cambridge, 1913, Vol. I, 256266.
[3] S. N. Bernstein, Sur lordre de la meilleure approximation des functions continues par les polynmes de degr donn, Mem. Cl. Sci. Acad. Roy. Belg., 4 (1912), 1103.
[4] E. L. Ortiz, Canonical polynomials in the Lanczos Tau Method, B. P. K. Scaife, ed., Studies in Numerical Analysis, New York, 1974, 7393, on 75.
[5] E. L. Ortiz, The Society for the Protection of Science and Learning and the Migration of Scientists in the late 1930s, Panels Chairmans lecture, Proceedings of the 113th annual meeting of the American Historical Association, Washington, 93 (1999), 128.
[6] Ch. Mntz, Wir Juden, Oesterheld and Co., Berlin, 1907.
[7] A. Korn, ber Minimalflchen, deren Randkurven wenig von ebenen Kurven abweichen Abhdl. Kgl. Akad. Wiss., Physmath, Berlin, (1909), 137.
[8] R. von Mises and H. PollaczekGeiringer, Praktische Verfahren der Gleichungsauflsung, Zeitschrift fr Angewandte Mathematik und Mechanik, 9 (1929), 5877 and 152164.
[9] L. Butschli, Hochwaldhauser Diary, 39, 39a.; quoted in KarlAugust Helfenbein, Die Sozialerziehung der Drerschule Hochwaldhausen, Hochhausmuseum and Hohhasubibliotek, Lauterbach, 1986, p.15.
[10] Der Jude, Jdischer Verlag, Berlin, 19161928.
[11] E. C. Titchmarsh, The Theory of the Riemann ZetaFunction, Oxford, 1951, p. 28.
[12] D. Amir, La Synthse Projective de la Gomtrie Euclidienne, Itine and Shoshani, TelAviv, 1925.
[13] G. G. Lorentz, Mathematics and Politics in the Soviet Union from 1928 to 1953, Journal of Approximation Theory, 116 (2002), 169223.
Mathematics Department, Imperial College London. This author wishes to thank the Royal Society, London, for its financial support while researching on this paper.
Department of Mathematics, Technion, Haifa.
The file on Mntz preserved at the Society for the Protection of Science and Learning, now at the Bodleian Library, Oxford, provided a valuable start in the search for other sources included. On the Mntzs files there see Ortiz [5].
Mntz to Geheeb, March 1, 1914. Archive of the cole dHumanit.
Jona to Geheeb, March 10, 1914. Archive of the cole dHumanit.
In an open meeting in 1917 the headmaster, G. H. Neuendorff, had called him a little Polish Jew. See Butschli [9].
Today called The Martin Buber House, it is home to the International Council of Christians and Jews.
Buber to Mntz, November 11, 1915, Buber Archives, JNUL, Jerusalem.
Now called Bad Gandersheim.
Mntz to Buber, September 18, 1923, Buber Archives, JNUL, Jerusalem.
One of his results from this period is quoted in Titchmarsh [11].
As related by Schmalenbach.
Mntz to Buber, October 30, 1927, Buber Archives, JNUL, Jerusalem.
The Notgemeinschaft Deutscher Wissenschaftler.
Einstein (as well as Lichtenstein) as well as the rest of the insider world shall not learn anything of this. Mntz to Schmalenbach, December 5, 1928.
Letter to his sister Sala, March 28, 1930.
Odqvist is wrong in this point, Mntz was granted Swedish citizenship in 1953. Riksarkivet, Stockholm.
Works by Mntz on religious or philosophical matters, his contributions in the form of articles and notes to Der Jude, and biographical work, such as a note on Einstein, published in the Soviet Encyclopedia in the mid 1930s, are excluded from this list.
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