Richard von Mises’ work for ZAMM until his emigration in 1933 and glimpses of the later history of ZAMM

With the exception of Ludwig Prandtl, Bieberbach and Hencky, all those named so far came from Vienna, Linz (Körner) or (like the Hungarian Theodor (Tódor) von Kármán) from other territories ruled by the Habsburg monarchy until the end of the First World War. RvM's particularly close, even emotional relationship with his Austrian homeland cannot be doubted. He is well known for his intensive occupation (including publications of his own) with the poetic work of Rainer Maria Rilke and the philosophical writings of Ernst Mach. In 1925, in a discussion conducted in ZAMM about the quality of education of mathematics and engineering in Germany and Austria, RvM wrote, undoubtedly including himself:

“I think it is a fact sufficiently well known in professional circles that an extraordinarily large number of engineers originating from Austrian schools work in the German Reich in precisely those places where particularly high theoretical demands are made.” (Mises 1925b, 181)

During her Viennese years, Geiringer was involved politically left-wing in youth, women's and adult education (Volkshochschule) movements, and in 1922 she wrote the book “Die Gedankenwelt der Mathematik” (The intellectual world of mathematics), which was influenced by Ernst Mach and also contained psychoanalytic elements of interpretation (Geiringer 1922). It was a good start of her relationship with RvM that the latter dedicated a very positive review to her book in ZAMM:

“In summary, although one might wish for clearer and more mature judgments here and there, the work is a fine achievement, an original and gratifying enrichment of literature, worthy of attention, worthy of dissemination and, above all, worth reading.” (ZAMM 2: 224)

Three of these four publications appeared between 1927 and 1932 in ZAMM, the fourth in 1928 in the Swedish statistical and actuarial journal Aktuarietidskrift. The most influential of these four papers seems to have been the first one, which appeared in ZAMM in 1927 in German under the title “On the structure of plane frameworks” (Geiringer 1927). In the recent book Graphs and Geometry (2019) by László Lovász one finds under “Stress-free and rigid graphs in the plane”:

“Whether a graph is generically rigid or stress-free is a purely combinatorial property, and one would like to obtain a purely combinatorial characterization of these properties. It is surprising that this basic question is only solved in the planar case, which we present here. … The following important theorem, combining the results of Henneberg 1911, Pollaczek-Geiringer 1927 and Laman 1970 describes stress-free graphs in the plane.” (Lovász 2019, 269)11

Geiringer wrote about the realization of her statistical publication of 1928 (Geiringer 1928) and the habilitation secured by it in her “Mathematische Entwicklung” around 1970:

“The error was corrected by feverish work of Mises and the work was presented and accepted (in a very prestigious journal, the Skandinavisk Aktuarietidskrift 1928. At that time, papers that came from a good school were not evaluated by the editor of the journal) and my habilitation went through, but only for ‘applied mathematics’.” (Siegmund-Schultze 1993, 373/74)

RvM had Russian rocket engineer A.B. Scherschevsky, who lived in Berlin and was associated with Hermann Oberth (1894–1989), report several times in his journal on Russian work on mechanics and applied mathematics.13 RvM had particularly close personal and scientific relations with Russia in general, which were probably also based on the traditionally lower separation between pure and applied mathematics there.14 As late as in June 1933 RvM reported in the following short obituary about another Russian “co-worker” at ZAMM:

“On May 30th in Leningrad our co-worker [Mitarbeiter] S. A. Gerschgorin, professor of theoretical mechanics at the Mechanical Engineering Institute in Leningrad, died at the age of 32. He was one of the most talented and promising of the young Russian mathematicians working in the fields of applied mathematics and mechanics”. (ZAMM 13: 250)

Co-workers without permanent academic positions such as Bergmann, Hencky, Ratzersdorfer and Scherschevsky were undoubtedly also motivated to work for ZAMM by smaller fees from the VDI-Verlag. The best information for the fees paid by ZAMM is contained in RvM's correspondences with Ernst Weinel (1906–1979), and with Max Herzberger.17 In a letter dated October 31, 1931, apparently sent by RvM as a circular letter and addressed as “Dear Colleague”, it says on head sheets of ZAMM among other things:

“The increasing economic hardship in Germany, which hits the publication [Verlag]18 of our journal particularly hard, since it is very much dependent on advertising income, makes it increasingly difficult to maintain the ‘Zeitschrift für angewandte Mathematik und Mechanik’ on the same scale as before. In order to be able to get by with only an insignificant shortening of the text in the next few years, the publisher sees itself compelled to make a change in the fee conditions. As is the case with many mathematical and physical journals, the authors are to receive a certain number of copies of their work free of charge instead of the previous fee.”19

The Odessa-born engineer and doctoral student of RvM Isidore Malkin (1889-?) was probably also dependent on such additional income. In ZAMM he published, among other things, the detailed Short Excerpts “On some recent work in the field of elasticity theory” (ZAMM 10: 182–197). Already in his PhD thesis of 1924 Malkin had written:

“I am particularly indebted to Prof. Dr. R. v. Mises for promoting my studies by offering the possibility of their practical utilization [Verwertung] in industry.”21

With a header from ZAMM, RvM confirmed to von Kármán on July 13, 1921, the receipt of four hydrodynamic manuscripts, all of which were published as soon as in August 1921 in issue 4 of the first volume of ZAMM.30 Especially the works by von Kármán himself and by Karl Pohlhausen (1890–1980) were groundbreaking for the calculation of Prandtl's boundary layer (Millsaps 1984). The leading historian for these topics, Michael Eckert, writes, partly quoting von Kármán's paper:

“Kármán's paper, ‘On laminar and turbulent friction,’ … was a larger attempt ‘to present the basic idea of Prandtl's boundary layer theory as simply as possible both from a mathematical and a physical point of view.’ Kármán's declared goal was to render the boundary layer theory amenable for solving ‘complicated problems with simple mathematical means’ [ZAMM 1: 233]. By integrating over the thickness of the boundary layer, he derived an equation of the incoming and outgoing momentum – a procedure Prandtl's student Karl Pohlhausen had just applied in his doctoral dissertation.” (Eckert 2006, 120)

Thus, using the example of the important work (Kármán 1921), the collaboration of the three great aerodynamicists Prandtl, von Kármán and RvM with each other and with a promising student (Karl Pohlhausen) can be followed in detail. Not only the editorial contribution but also RvM's achievement in terms of content was acknowledged when von Kármán wrote in a footnote of his publication, referring to RvM's book of 1914:

“The only resistance formula to date that takes into account the two decisive variables, relative roughness and Reynolds’ number, is that of R. v. Mises, Elemente der technischen Hydromechanik, Leipzig 1914, p. 50 ff.” (Kármán 1921, 237)

On November 28, 1921, RvM thanked von Kármán for his review of the eighth edition (1920) of the classic book “Elasticity and Strength” by Carl von Bach (1847–1931), but asked for an addition, because the “view of the buckling process there is completely untenable.” Kármán conceded in his reply letter of December 10, 1921:

“I have supplemented Bach's discussion of the buckling question. It has escaped my notice that it is indeed treated very strangely.”32

Von Kármán's review was finally published with a misprint – rare for ZAMM – under the heading “Electricity and Strength.” Regarding the passage complained of by RvM it says:

“The treatment of the buckling problem is by no means adequate. There is no connection to the classical theory of elasticity (consideration of finite curvature), which is required to make the whole situation conceptually clear, and the theory of buckling beyond the limit of proportionality, which is completely secured today, is also missing.” (ZAMM 1: 486)

In other contexts too, von Kármán recognized RvM's broad technical and mathematical competence in his correspondence with him. On March 26, 1926 von Kármán sent RvM a manuscript by C. Vajda “Slipping of the rolling wheel” (“Schlüpfung des rollenden Rades“). Kármán said he was not familiar with the subject, but, judging from RvM's article in Felix Klein's Encyclopedia, he assumed that he was competent. RvM wrote in his reply on April 26:

“The Short Communication [Kleine Mitteilung] of Mr. Vajda about the rolling wheel is not quite understandable to me. I can't very well commit myself to publish it, because I am not convinced that it is in accordance with the basic laws of mechanics.”33

RvM's British doctoral student (1951) in American emigration, Geoffrey Ludford (1928–1987), later went so far as to suggest that RvM's versatility in mechanics might appear to today's mechanicists as a sign of dilettantism:

“The brief encounters with different areas of mechanics will lead some to call him a dilettante. If he was, then we need more dilettantes to ask the basic questions and give the seminal answers. The accusation shows inter alia a misunderstanding of his applied mathematics, which was not so much a subject as a method, in fact the scientific method for a subject that has reached a certain level of sophistication.” (Ludford 1983, 282)

Von Kármán was at that time anyway almost on his way to American exile, not unaffected by experiences with academic anti-Semitism (Hanle 1982, 122). He wrote to RvM on August 25, 1926 that he had been invited to Pasadena by the American physicist Robert Millikan, “which is quite pleasant considering the beautiful surroundings and stimulating company.”35 In the same letter, von Kármán announced two doctoral theses for possible publication in ZAMM, including Max Knein on stress distribution in a body under pressure (“Spannungsverteilung in einem Druckkörper”). About Knein's work von Kármán said the following, expressing that he felt that his institute in Aachen was in competition with the closely connected Prandtl institute in Göttingen:

“Since I hear similar things are being done in Göttingen, I want to have the results published quickly.”36

Another example where RvM's competence ultimately was decisive is a manuscript on plasticity theory submitted to him by von Kármán on November 28, 1927. Von Kármán wrote:

“Enclosed paper was sent to me by a Mr. Andreas Reuss, Budapest. Frankly speaking, I cannot judge whether the matter has any significance. Since the work is related to your work, I am sending you the same. The address of the gentleman is on the manuscript. Perhaps you could write him a few lines on whether the matter is correct and of value.”37

It is interesting to note that the Hungarian engineer András (sometimes Endre) Reuss (1900–1968), who was to attract attention in the following years with his publications on plasticity theory in ZAMM (Bruhns 2014) and who had probably considered his fellow countryman von Kármán as the natural addressee for his manuscript, was not known to the latter or to RvM at that time. As RvM said in a letter to von Kármán on December 6, 1927, he had written to Reuss, telling him that he had made analogous considerations for single crystals (Einkristalle) “quite some time ago.” RvM further wrote in this letter to Reuss of the same day, which he enclosed as a carbon copy in the letter to von Kármán:

“I will probably publish something about it soon. Then, if you further elaborate on your idea of treating polycrystals, I would be happy to publish it in the journal.”38

Even more important than the 1927/29 work was to become Reuss’ ZAMM article of 1930 (Reuss 1930) which was a generalization of the Lévy – von Mises equations of plasticity. Here, Reuss made allowance for the elastic component of strain, following an earlier suggestion by Prandtl. Bruhns writes:

“Apparently independent from a work by Prandtl [talk at the 1924 Mechanics Congress in Delft], where already elastic deformations have been considered in a plane problem, the Hungarian András (Endre) Reuss … in 1930 connected the de Saint-Venant/Lévy approach with the description of an (incremental) elastic behavior. For this purpose, like Hencky, he emanated from the v. Mises yield condition [1913].”40

About his two works in ZAMM 1924, which are devoted to his “Motor Calculus” (Motorrechnung)47 and which he classifies under “I. Geometry (Statics, Vector Theory, Geometrical Optics)”, RvM remarks in his Overview in 1940:

“In the comprehensive treatise … following the geometrical concept of the ‘Motor’ (= dyname, screw [Schraube]) created by E. Study, a new ‘motor calculus’ is developed, which takes its place alongside the three-dimensional vector and tensor calculus. The new definitions of the motor products and the motor tensor make it possible to treat all tasks of spatial statics, kinematics and dynamics in a form in which no coordinate system, not even the starting point [Anfangspunkt] of one (reference point of moments), is used. The new calculus also proves fruitful in its application to certain questions of elasticity theory (general frameworks) and hydrodynamics (rigid bodies in fluids). … The main results have been included in some [einzelnen] textbooks and supplemented by some Russian authors.” (Mises 1940, xvi)

In 1969, there was a correspondence between Walter Humbach, professor at the Institute for Reactor Technology in Darmstadt, and Hilda Geiringer in Cambridge/Boston about this. Humbach wrote on February 7, 1969:

“For several years I have been repeatedly preoccupied with the motor calculus developed by your late husband on the basis of the work of Klein and Study, with which I became acquainted – albeit only in hints and without realizing the implications – already in 1939 at the beginning of my studies in a mechanics lecture. … I don't really understand why this has not been further developed, not even by the specialists directly concerned. The only deeper explanation for this seems to me to be that your husband here – as in many other places of theoretical physics – was far ahead of his time and simply for this reason could not find any understanding.”48

Geiringer replied on the 11th of the same month:

“Of course I know my husband's work on the motor calculus very well. I think, like you, that they have not received enough attention. But that's the case with a lot of Mises’ work.”49

In the 1990s a mechanics professor from the Austrian Technical University of Graz found the Motorrechnung of his former country man worth another trial – after introducing “consistent notation” – and wrote in the abstract of the paper (Wohlhart 1995):

“This paper reviews the motor calculus as it was presented by Richard von Mises and extends it to a general motor tensor calculus on the basis of unit motors. R. v. Mises defined a scalar and a motorial product of two motors without using Clifford's duality unit ε (ε² = 0) and introduced motor dyads. … A consistent notation for motor and motor dyads, which are used in the forthcoming English translation of v. Mises’ motor calculus, facilitates the algebra.” (Wohlhart 1995, 93)

Within his comments for the publication field III. (Theory of Elasticity and Strength) RvM first has remarks about a Marburg lecture, published as “About the stability problems of elasticity theory” (Mises 1923a):

“Interest in the stability problems of elasticity theory continued unabated throughout time. In 1923 it led to the discovery of the stability limits within the classical theory of trusses [Fachwerke] – astonishing enough that these were not already known long ago, given the great practical importance of many individual cases. The treatise… contains, in addition to the theory of ‘pure’ truss buckling [Fachwerkknickung] and ‘frame buckling’ [Rahmenknickung], a much more comprehensive approach which includes all types of connections of originally straight, elastic rods [Stäbe]. However, this theory is only applied to the case of two dimensions.”51

RvM then discusses the two papers written jointly with Ratzersdorfer in ZAMM [Mises/Ratzersdorfer 1925/1926] on the buckling safety of trusses which connect to this publication of 1923:

“More detailed information on the special problem of trusses as well as on general arbitrary bar connections can be found in the two publications [1925] and [1926], the final editing of which was carried out by J. Ratzersdorfer on the basis of a draft I had written. In [(Mises 1923a), see above], however, several fundamental questions of stability theory were also touched upon – in a certain programmatic form – which seemed to me to be very important and still seem to be so, such as the question of Kirchhoff's uniqueness theorem [of 1859, RS] and the definitive characterization of the various load cases as unstable and stable, etc. The envisaged detailed elaboration of these questions did not come about any more, mainly probably due to increasing distraction by the occupation with other things. Some of this is communicated in the beautiful book by J. Ratzersdorfer.”52

These two works (Mises/Ratzersdorfer 1925/26) have been honored in a book that has been published in several editions, where the authors also use the term “Mises truss” throughout:

“The flexibility coefficients were introduced in stability analysis of frames by von Mises and Ratzersdorfer (1926).”53

A work by RvM in ZAMM on plasticity theory (Mises 1928a) has already been briefly discussed above in connection with von Kármán's mediation of a work by Reuss. RvM himself writes in his “Overview” with reference to several works by himself and by Hencky which were published in ZAMM:

“The study of the basic equations of the mechanics of plastically deformable bodies goes back to the Brünn period (1906–1909). Outwardly prompted by the somewhat fantastic approach of Haar and v. Kármán, I [(Mises 1913)] tried to establish a system of equations which, within the framework provided by classical mechanics, is determined by common facts of experience. Later it was found that M. Lévy had given a similar approach in an unnoticed work of 1871, with a different justification and without the decisive addition of the ‘plasticity condition’.54 My condition of plasticity later proved to be in best agreement with the observations and it is still often used today.

When in 1923 Hencky had found the beautiful differential geometric properties of the stress lines in the two-dimensional case of plastic deformation [(Hencky 1923) in ZAMM], I was able to take the theory for this case much further. In [(Mises 1925a)] the differential equation of streamlines of plane deformation of the plastic body is given for the first time, as well as a number of examples and general theorems.55 In these two works it was exclusively about the isotropic plastic body. In the meantime, various experiments had been carried out on the flow of single crystals and this gave rise to the larger theoretical investigation [(Mises 1928a)] which was published in 1928. Here the most general forms of the plasticity condition are discussed, which correspond to the invariance conditions of the different crystal systems. Two types stand out in particular, the shear stress condition corresponding to Mohr's56 theory and the generalization of my approach for the isotropic case. The main result of the work is the introduction of the term flow potential [Fließpotential, today mostly “yield potential,” RS] which establishes a relationship between the yield condition [here RvM uses “Fließbedingung,” instead like before “Plastizitätsbedingung,” RS] and the deformation laws. I also attach importance to the clarification of the term ‘internal slip’ [innere Gleitung], which is much used by experimenters but never sufficiently defined. The results of this work were later often used in connection with experimental investigations, but do not seem to me to have been sufficiently exhausted.” (Mises 1940, xix/xx)

Knowing RvM's ambition and hyperresponsiveness, and his willingness to enter into dialogue with the authors of ZAMM, it seems to me beyond doubt that RvM overlooked the mention of Huber's priority in the corrections (proofs) of [Hencky 1924/2020, 4], where it was inserted by Hencky at the last minute.57 RvM used the first opportunity in ZAMM, namely a 1926 publication by F. Schleicher, where Huber is also mentioned, to suggest in a “Note from the Editor” (ZAMM 6: 199) the differences between his and Huber's “plasticity conditions.” In his 1928 work mentioned in the “Overview” RvM goes into more detail:

“Especially for the pure tensile tests that are mainly considered in the following, Huber's point of view would lead to completely different results. Recently, one often finds confusion between my 1913 yield condition and Huber's condition.” (Mises 1928a, 170)

Huber himself later published in German in ZAMM and drew attention to his early Polish publications in another field.58 As far as the condition of plasticity is concerned, we follow Bruhns:

“In recognition of the contributions of the three persons Huber, v. Mises and Hencky to its present form, we should call this condition HMH-yield condition.”59

Some of the particularly influential among RvM's overall not very numerous papers in numerical analysis have been published in ZAMM. His student Collatz honored them in 1983 in ZAMM's special issue for RvM's one hundredth birthday. About a Short Communication of RvM in ZAMM of 1924 Collatz wrote:

“In his numerous works on mechanics, he very often uses numerical methods and calculates, for example, the non-linear problem of buckling a rod [(Mises 1924)], whereby he also gains the branches of the branching diagram belonging to higher eigenvalues and is far ahead of his time.” (Collatz 1983, 279)

In connection with RvM's 1930 work on the Adams difference method (Mises 1930), which has been discussed in [RS-Mises-2020, 13], Collatz said in the same article:

“Now it is typical of RvM not to be satisfied with good numerical results, but to carry out a precise error analysis, to examine the ‘quadrature error’ and its influence on the further calculation (ZAMM 10 (1930), 81–92).” (Collatz 1983, 278).

On RvM's last paper in ZAMM (Mises 1954) which appeared posthumously in 1954, Collatz wrote in the commemorative article for his teacher in 1983:

“There has been extensive literature for centuries on approximate calculation of integrals, e.g. Kepler's barrel rule, trapezoidal rule, Gaussian quadrature and many others. From time to time, von Mises turned his attention to the task of establishing a uniform theory of quadrature and cubature formulae and estimating their errors (1953, 1936). In the work ZAMM 34 (1954), 201–210 he examines the numerical calculation of multidimensional integrals. These error estimates also had a stimulating effect in the following period, and many generalizations were made (J. Albrecht et al.).” (Collatz 1983, 279)

Collatz also referred to the two-part joint work with Geiringer, published in ZAMM in 1929, which is based on lectures by RvM (Mises/Pollaczek-Geiringer 1929):

“In two fundamental works, ‘Practical methods for solving equations’ (ZAMM 9 (1929), 58–77, 152–164), Mises and his student Hilda Pollaczek-Geiringer (his later wife) gave a well-rounded theory with convergence proof and error estimation for iteration procedures to obtain approximate solutions.” (Collatz 1983, 278)

About this work, which appeared in ZAMM under “Summary Reports” and which RvM himself included in his above-mentioned bibliography of original publications, Collatz later also said:

“He also did not shy away from doing extensive numerical calculations himself. The ‘v. Mises method’ for the iterative determination of the eigenvalues of matrices was developed by him.” (Collatz 1990, 281)

Modern numerical analysts wrote recently in 2018:

“Chaim Müntz presented [1913] both the power method and the inverse power method for the symmetric and nonsymmetric matrix eigenvalue problem, as well as for the generalized eigenvalue problem with symmetric matrices. … In modern textbooks it is known as orthogonal or subspace iteration and can be shown to be equivalent to the basic QR algorithm … Although it was presented in von Mises's 1929 survey paper [(Mises/Pollaczek-Geiringer 1929), part II], the method is far too tedious for hand computation and was taken up again with the availability of computers in the 1960s.” (Tapia/Dennis/Schäfermeyer 2018, 8/9)

As noted above, RvM's co-worker at ZAMM Gumbel was at the same time closely associated with Ladislaus von Bortkiewicz. RvM held the latter, his colleague from the state science faculty of Berlin University in high esteem. Close collaboration between the two is not documented, but RvM's important work published outside ZAMM on rare events and extreme value distributions was influenced by Bortkiewicz (Mises 1923b). In 1931 RvM dedicated a short obituary to his colleague in ZAMM, referring to the publication (Bortkiewicz 1922). The obituary is noteworthy especially because of the clear recognition of Bortkiewicz's leading role in mathematical statistics in Germany, at a time when much of economic statistics still remained of a descriptive kind:

“On July 16, Mr. Ladislaus v. Bortkiewicz, professor of mathematical statistics and economics at the University of Berlin, died of a heart attack. He was the most important researcher in the field of mathematical statistics in Germany, and was known far beyond its borders for his work. Our journal owes him an article dealing with an interesting question of error theory, which was published in the second volume.” (ZAMM 11: 340)

As for the second exception: In his book of 1928 RvM commented particularly positively (Mises 1928b, 109/186) on the theory of chained events (verkettete Ereignisse) as developed by Georg Pólya together with a practical statistician, and published in ZAMM (Eggenberger/Pólya 1923). This is today known as the “Pólya-Eggenberger urn scheme” and is counted among the most important of Pólya's probabilistic work (Chung 1987). The coming about of this publication is also an example of RvM's constructive collaboration with authors, which in this case led to the change of title. He wrote to Pólya on December 15, 1922 among others:

“Dear Colleague.

With best thanks I confirm the receipt of your Ms. ‘About the increase of chances by success.’ [,Über die Chancenvermehrung durch Erfolg‘]. I will gladly publish the work in one of the next issues. You will allow me to change the language in some places. … As to the title I would suggest saying something like, ‘On the statistics of chained processes’ [‘Über die Statistik verketteter Vorgänge’] which I would also like to see because it sounds more ‘applied’.”60

The fact that the above mentioned second part of Geiringer's habilitation thesis was not published in ZAMM is also related to the marginal position of mathematical statistics in Germany as a whole and in ZAMM in particular. In 1932 Geiringer wrote in ZAMM, certainly with the approval of RvM, in a review of the German translation of an American Handbook of Statistics (H. L. Rietz) which had been published with an introduction by RvM:

“Compared to other countries, the cultivation of mathematical statistics in our country is rather poor: just think of Scandinavia with its interesting and leading ‘Aktuarietidskrift’ and of Pearson's inexhaustible English ‘Biometrika’.” (ZAMM 12: 126)

The latter had not mentioned geometrical optics in his “Tasks and Goals” in ZAMM (Mises 1921). In an exchange of letters RvM advised Herzberger several times scientifically and also personally regarding his professional activities. On October 11, 1929, RvM recommended, among other things,

“working with line coordinates instead of vectors or, what is even better, using the Study dual numbers or my motor calculus.”62

Herzberger wanted to gain a foothold at the university in Jena as well, in addition to his industrial work. He tried to submit his twenty-page article “About the vicinity of a ray in optical systems” (“Über die Umgebung eines Strahls in optischen Systemen”) (ZAMM 10: 476–486) as a habilitation thesis. In a letter to RvM on October 2, 1930 Herzberger, who was later expelled from Germany as a “Jew”, reported on the failure of his academic aspirations due to the early role of the Nazis in the regional government63 and anti-Semitism also at the university. RvM tried to help him also later during emigration. Although Herzberger had not quite followed his advice for using the motor calculus, RvM provided him with an expert opinion written 1934 in Turkish emigration RvM, after Herzberger had also been dismissed from his industrial position at Zeiss:

“Dr. Herzberger has succeeded in achieving many remarkable new results by going into the line geometric principles of optics, which deserve great interest both from a theoretical point of view and for applications in industrial optics. It is no exaggeration to say that Herzberger's work opened up a new fruitful period of research in the field of geometric optics.”64

In an otherwise very positive review of the book Foundational Notions of Mechanics (Grundbegriffe der Mechanik, 1921) by Hamel, RvM says in the first volume of his journal, at a time when the theory of relativity was still struggling for recognition even among scientists:

“For the wider circle of readers, for whom the book is intended, the assertion that one of the main achievements of Einstein's theory is the ‘fixing of the unshakable idea of absolute space and absolute time’ can only be confusing. This also applies to what is said in support of this strange sentence.” (ZAMM 1: 224)

In 1929, RvM wrote about Walther's Introduction to the Mathematical Treatment of Scientific Problems (Einführung in die mathematische Behandlung naturwissenschaftlicher Fragen), among other things:

“In general, the main focus of the author seems to be the desire to appear original. One is tempted to advise German publishers, who often complain about the excessive overproduction of books, not to publish a new introduction to higher mathematics for ten years. We have enough books, some of them excellent, and really fruitful new ideas are not to be expected in this field in the near future.” (ZAMM 9: 253)

About an encyclopedia of mechanics published in Vienna in 1923 by a professor at his former alma mater, the TH, RvM says without mercy:

“After these samples, anyone who already knows the elements of hydromechanics will probably come to the conclusion that the author, instead of writing a textbook, should still go to school himself.” (ZAMM 4: 272)

Although RvM was mainly an applied mathematician, as a reviewer he sometimes assumed the role of the pure and rigorous mathematician, probably also in order to mute still existing reservations against applied mathematics. RvM objected to a book on the foundations of probability theory:

“The author probably only knows mathematical set theory from hearsay. He defines probability as the quotient of the powers [Mächtigkeiten] of two sets.” (ZAMM 4: 445)

But RvM also occasionally pointed out the ambivalent position of the applied mathematician vis-à-vis modern mathematics, for instance, when he said the following about the very successful Introduction to Set Theory (Einleitung in die Mengenlehre 1928) by Adolf Fraenkel:

“Even if set theory, according to the current state of affairs, must be considered rather distant from applied mathematics, a review of this book seems to me to be very appropriate … Incidentally, perhaps the time when questions of set theory can become important for the applications of mathematics is not very far off.” (ZAMM 9: 252)

Elsewhere RvM emphasized the specificity of applied mathematics compared to physics. In the review of a Handbook of Physics (Springer 1927/28) he said:

“In a series of final chapters, K. Mader acquaints physicists with numerical and graphical methods that have long been common in technology and certainly deserve to be included in mathematical physics.” (ZAMM 8: 500)

In his 1926 review of an English book on the history of mathematics RvM wrote, probably critical of the conditions in Germany:

“As is the natural view in England, there is no separation between pure and applied mathematics in the presentation.” (ZAMM 6: 335)

Elsewhere RvM dealt with the methodological and historical aspects of applied mathematics. In his review of Julius Bauschinger's The Determination of the Orbits of the Celestial Bodies (Die Bahnbestimmung der Himmelskörper, 1928) RvM wrote:

“Calculating astronomy [rechnende Astronomie] is the ancestor of applied mathematics. … If one wants to draw conclusions from the experiences of astronomers for the development of other parts of applied mathematics, one will have to recognize above all that in the long run only the simplest procedures will hold their ground, but that these, in order to become really useful, require a very thorough elaboration through to the smallest details.” (ZAMM 9: 82)

RvM emphasized useful works on little developed areas of applied mathematics when he said in the review of Ballistics (Ballistik, 1922) by the Greifswald mathematician Theodor Vahlen:

“It is a great merit to have not only found out the essentials from the almost unexplorable semi-scientific literature in this field, but also to have created a clear classification of material based on new aspects.” (ZAMM 3: 69)

RvM also used book reviews to represent his philosophical positions in a German environment largely averse to empirical philosophy. About the fifth edition of the Popular Science Lectures (Populär-wissenschaftliche Vorlesungen 1923) by Ernst Mach, who died in 1916, RvM said:

“The scientific literature of Germany and other nations has very few books that can be compared to this popular work of the great physicist and philosopher.” (ZAMM 4: 528/29)

RvM often showed benevolence even towards non-established scientists or academic outsiders. He attested the Berlin school teacher Erich Mosch an unusually high quality of his Physics Textbook (Lehrbuch der Physik) published in 1925:

“One finds clear and reasonable formulations everywhere, which are far above what is offered in most university textbooks. I hardly know of any German textbook of mechanics, including the most famous ones, in which something as understandable and intelligible would be said about the law of inertia as here in the second chapter on p. 32.” (ZAMM 6: 82)

RvM also tried to meet outsiders of contemporary technology with objectivity. In a thoroughly benevolent but also critical review of the book by the rocket pioneer Hermann Oberth Paths to Space Travel (Wege zur Raumschiffahrt 1929), RvM said:

“The real difficulties of space travel, i.e. the ascent to spaces far from the earth's surface, lie in the technical and, as far as the ascent of living beings is considered, in the physiological field. …

And that is why it is a useful beginning that through books like this one, attention is drawn to the rocket problem, even if this is done here in a way that appeals at least as much to the sensationalist need as to the scientific research urge.” (ZAMM 9: 517)

In the “News” section, RvM frequently reported – often anonymously – about scientific events and organizations, appointments, deaths, or he had them reported. Among them were of course reports about his own institute. He let his student Fritz Rehbock report about the study program of the institute (Rehbock 1926). Under the title “Utilization of scientific research for the industry” RvM wrote anonymously in 1932:

“The representatives of applied mathematics and mechanics in Göttingen have founded an organisation called ‘Göttingen office for the mediation of engineering research’ [Göttinger Vermittlungsstelle für ingenieurwissenschaftliche Untersuchungen, Göttingen, Böttingerstraße 8], which is to carry out scientific-technical work on a broad basis in the interest of industry at the request of interested parties and with the involvement of several research institutions. On this occasion, it should be pointed out that the Institute for Applied Mathematics at the University of Berlin, which is headed by Prof. v. Mises, also carries out work of a mathematical nature for the purposes of industry or other public and private enterprises at their request.” (ZAMM 12: 191/92)

In 1924 and 1925 there were discussions on ministerial proposals to reduce the teaching of mathematics from 4 to 3 hours a week at some types of higher secondary schools (grammar schools etc.).67 The “Reich Mathematical Associations” (“Reichsverband deutscher mathematischer Gesellschaften und Vereine”), led by RvM's former head in Brünn (Brno), Georg Hamel, was the main protest against this. RvM found these protests too agitated and exaggerated. Being anyway critical of in his opinion too abstract mathematical teaching at schools RvM doubted above all the claim that by reducing the teaching of mathematics the understanding of the pupils for technology would necessarily suffer. RvM summarized his views in the second of two notes in ZAMM:

“The relationship between the purely mathematical school subject matter and technology is sparse and remains on the surface anyway. Anyone who sincerely wishes that a certain understanding of the meaning and cultural significance of modern technology be conveyed to pupils at school must make every effort to ensure that this circle of thoughts and ideas gradually penetrates the cultural studies subjects,68 which will always have the strongest and most penetrating effect on the growing youth.” (Mises 1925b, 181)

Perhaps RvM himself realized that he had gone one step too far with his individualism in this discussion. When Erich Trefftz in Dresden, who was later to become his successor as editor of ZAMM, told him about his dissenting opinion, RvM asked him to publish it in ZAMM:

“In any case, it is very important to me not to give the impression that in the journal no one can express a different opinion than mine.”69

A second example for RvM's individualism are various, mostly anonymous statements by RvM in the matter of the International Congress of Mathematicians planned for 1928 in Bologna (ZAMM 8: 159, 248, 340). Together with Bieberbach and Erhard Schmidt from Berlin, and the prominent Dutch mathematician L.E.J. Brouwer, and in contrast to the majority of German mathematicians under the leadership of David Hilbert in Göttingen, RvM opposed the participation of German mathematicians in Bologna. He was not convinced that the congress, which was mainly devoted to pure mathematics, would be independent of the International Mathematical Union (IMU) which had coordinated the boycott of Germany and Austria after the Great War (1914–1918). In his opinion he found some support from Prandtl, but none from von Kármán who attended Bologna.70 When, after the congress had been held, four applied mathematicians and members of GAMM led by Otto Blumenthal in Aachen (Hilbert's longtime confidant) submitted a “short note on the course of the congress”71 for publication in ZAMM, RvM, in a four-page letter to Blumenthal dated October 23, 1928, rather brusquely refused to publish it:

“In any case, you will understand that I cannot publish in my journal a communication that completely evades the essential question [‘Relationship of the Congress to the Union’] and instead uses textbook phrases like ‘landmark in history’, ‘memorable reception’, etc. It would also be highly inappropriate to assure our readers that a new era of international relations has now dawned. For, as you know, two international mechanics congresses have already taken place with the active participation of the journal and its editor (cf. e.g. manifestation vol. 4, p. 85)72 which were completely free of ‘misunderstandings’ … at which the cooperation of Germans, French, Englishmen, etc. was so peaceful that it occurs to no one to speak of it or even to praise it in opening speeches or later reports. It is only necessary to clearly and unambiguously exclude from the outset the participation of that questionable organization, which was created for the sole purpose of preventing the international cooperation which we have been cultivating with constant success for a long time.”73

It is not surprising that the short note from Blumenthal and colleagues was not printed in ZAMM. Instead, RvM published there anonymously a note on the German contributions to the applied sections in Bologna. The following remark in it was probably intended to underline the fruitlessness of the congress at least for international cooperation in the field of applied mathematics:

“In the opening session of the IV Section, Mr. Gini-Padua presented for discussion the plan for the establishment of an International Institute for Applied Mathematics, suggested by Mr. B. Lagunoff - Kieff. The Assembly voted against the plan.” (ZAMM 8: 504)

There is no doubt that in the discussion with Blumenthal and colleagues, RvM on the one hand glossed over the political situation around the international mechanics congresses [RS-Mises-2020, 18], and on the other hand underestimated the attempts at relaxation among the pure mathematicians represented by David Hilbert in Göttingen.74 The subliminal institutional conflict between Berlin and Göttingen played into this. RvM's positioning against Bologna was surprising for people like the Göttingen physicist Max Born, who wrote to his friend Einstein on November 20, 1928:

“I can understand this in Erhard Schmidt's case, for he always did lean to the right in politics, as a result of his basic emotions. For Mises and Bieberbach, however, it is a rather deplorable symptom.” (Born 1971, 98)

Hitler was appointed Reich Chancellor on January 30, 1933. The terrorist rule of the Nazis and their backers was established step by step, through Reichstag fire and the Enabling Act (Ermächtigungsgesetz). The first major state-organized pogrom was the so-called “Judenboykott” (“Boycott of the Jews”) of April 1, 1933; on April 7, the infamous “Law for the Restoration of the Professional Civil Service” (“Berufsbeamtengesetz”) was passed, which, with a few exceptions, expelled all state employees who had at least one grandparent who belonged to the Jewish religion. Although RvM was covered by the exceptions as a World War I participant and pre-war civil servant, he saw the signs of the times and sought employment abroad, eventually finding it in Istanbul. RvM's pupil Lothar Collatz, to whom he gave advice for his future scientific work the day before his departure, correctly described more than half a century later the impact of Nazi rule on German applied mathematics:

“The journal ‘Deutsche Mathematik’ was published and authors were advised not to quote Jewish mathematicians whenever possible. Many important scientists, especially mathematicians close to numerics, and also many representatives of mechanics and physics left Germany. Richard von Mises left Berlin in November 1933 for Istanbul and later for the USA, together with Hilda Pollaczek-Geiringer.” (Collatz 1990, 286)

The dismissals by the Nazis had to be reflected in various ways on the pages of ZAMM, which continued to be published by RvM until the end of 1933. A moving document in ZAMM is the obituary of the engineer Franz Eisner (1895–1933), who was a part-time lecturer at the TH (Technische Hochschule) Charlottenburg and is mentioned several times in the correspondence between RvM and von Kármán as a promising young mechanicist. The obituary by Georg Weinblum, who also mentions Eisner's precarious health, leaves no doubt that Eisner's suicide in June 1933 was a direct consequence of his dismissal from the TH:75

“Eisner was a born teacher and as such had great success in his university activities, which gave him much joy; the resonance of his audience was almost a condition of life for him. … When strong emotional upheavals – there were no reasons for material concern – approached him, he no longer felt up to them and, after previous heavy battles, voluntarily left life without bitterness.” (ZAMM 13: 330)

RvM had his 50th birthday on April 19, 1933, and for this occasion his colleagues prepared a special issue of the journal (ZAMM 13: 65–170). In the first part of this article, I have already referred to the greeting address in the special issue, which emphasized the unchanged importance of the more classical fields of mechanics promoted by ZAMM [RS-Mises-2020, 20]. The special issue contained 24 contributions from 25 colleagues, with the high number of 12 foreigners being conspicuous,76 although according to the ZAMM tradition German was used as language with two exceptions (Hadamard/Fréchet and Taylor). Compared to ZAMM, the topics in this issue were shifted somewhat more towards mathematics, which corresponds to the breadth of RvM's interests. Bieberbach, who soon defected to the Nazis, opened the birthday issue with a short article on nomography (ZAMM 13: 66). In two entries in his diary, RvM expressed surprise about the project and joy about the quality of the work when he heard about the preparations in March 1933:

“7. [III.33]

I learn through Reissner from a planned birthday issue of Zamm [sic]. Get more detailed explanations from Hilda. All in all quite pleasing.

8. [III.33]

In the morning Reissner and Hellmich are with me, bringing me the proofs of the birthday issue, which contains surprisingly great contributions. I am quite pleased about that. Especially Hilda's contribution rather pleasing.”77

One of them was the 33-year-old Walter Tollmien (1900–1968), a student of Prandtl's, who at the time was working at von Kármán's Caltech in California without a permanent position or long-term perspective. In 1926 Tollmien had made a major contribution to the mathematical foundation of Prandtl's turbulence theory with a paper in ZAMM.78 The “Tollmien-Schlichting waves” are also named after him. In 1933 RvM felt that Tollmien, presumably being an “Aryan”, had good chances of obtaining a position in Germany. On June 10, 1933, RvM wrote to von Kármán:

“I'd like to return to the matter of Dr. Tollmien. I do not know if he still desires to come to Germany under the present circumstances. In any case, I have to tell you [Dir] that the irrevocable prerequisite for any kind of employment or scholarship or suchlike is to make a statement on his honor [ehrenwörtliche Erklärung] that his four grandparents are of ‘Aryan, in particular non-Jewish descent.’ As long as I do not know whether Mr. Tollmien can or will make such a statement, it is impossible for me to do anything. Besides I believe that in the positive case the prospects are not bad as indeed a large part of all the previous candidates has to be disregarded now. I ask you to give me the relevant information as soon as possible.”

Von Kármán wrote on the reverse side of this letter:

“Dear Mr. Tollmien, enclosed a letter from H. v. Mises. Indeed a ‘document of our time.’ Please let me know if I should transmit the written evidence of your racial purity to Berlin or whether you want to write to Mises yourself. Please return the letter after having enjoyed it.”79

In a letter dated August 18, 1933, which Hilda Geiringer, who had already been dismissed, wrote to RvM's mother Adele von Mises in Vienna, it is indicated that in RvM the hope for a future in Germany had largely disappeared. However, Geiringer and RvM feared less for the continued existence of ZAMM:

“The journal has not perished at all. He [RvM] once had a conversation with Matschoß and Hellmich [from the VDI, RS], where he asked them if they didn't want a change. At first they didn't understand what he wanted, but after he had made it clear to them, they said that this wasn't an official matter and didn't concern anybody. In most similar cases the previous managers and employees had been thrown out by the fact that some ‘immaculate’ person who wanted the job in question had intrigued against them and declared them ‘unacceptable’. Since, however, obviously nobody wanted to edit the ZAMM, and therefore nobody there was stirring up trouble, they would be more than satisfied if everything remained as it was. By the way, it is a big question whether Matschoß will stay, because although perfectly Aryan, he is not close enough to the Party. … If ZAMM perishes or is taken over by someone else, your son intends to found an international journal for applied mathematics or the like, or especially for statistics, as soon as he is outside and can act. I can only say that he takes all this absolutely calmly and without emotional moments. Incidentally, as you will know better than I do, the Herr Professor is such that most things make him especially happy at the beginning, when you are setting them up, when you have to deal with difficulties.”80

In a letter to his colleague in the faculty in Berlin Erhard Schmidt on October 21, 1933, RvM even recommended the 64-year-old Nazi mathematician Theodor Vahlen as his successor, because he obviously hoped this move would provide political stability for his former institute:

“As far as the final arrangement is concerned, the only successor who can be taken into consideration is Prof. Erich Trefftz in Dresden. . . . However it appears possible and beneficial to find an interim solution for the coming years, i.e., to find someone who would be capable of safeguarding the existence of the Institute and this even in a direction which conforms with the prevailing trends [heutige Zeitströmung]. I suggest that Prof. Th. Vahlen, who is active for the time being in the ministry for education, but who is evidently not happy there, should take over the chair and the Institute for Applied Mathematics.” (Siegmund-Schultze 2009, 171)

Two years later, however, when it came to Vahlen's succession at the Berlin Institute for Applied Mathematics, it became clear that the political situation had by no means calmed down. Even in 1935, Trefftz had no chance to take over the institute. The leader of the NS-loyal lecturers of Berlin University (NS-Dozentenschaftsführer) von Gleispach declared on February 22 in an internal political review:

“Prof. Trefftz is politically opposed to National Socialism and belongs to the type of intellectuals whose caustic mind disparagingly criticizes everything that has its origin and carrier in something other than the purely spiritual. He gave Jewish students special treatment not only in class, but also after they left the university.” (Siegmund-Schultze 1984, 55)

The excerpts mean in English translation:

“Mises would let the journal perish. Reduced volume makes a proper selection impossible. … For the time being no Aryan paragraph. Decline in production due to emigration of Jews not to be expected. Jews publish little with us [in our journal] V.D.I. pays 100.- Marks [apparently monthly, RS] for a secretary. Stamps and materials provided extra, honorarium M. 720.- per year.”

After taking over the editorial office, Trefftz wrote to Prandtl on December 1, 1933:

“Regarding the Z.A.M.M., I count on your approval of the following measure, which I have taken after consultation with Matschoss and Nägel. In the future, the title page will read: edited by E. Trefftz, Dresden, with the collaboration of renowned colleagues. Therefore, the names of the co-editors will no longer be explicitly mentioned on the title page. You can guess why. I wanted to avoid being forced to delete the non-Aryan names.” (Gericke 1972, 13)

On October 28, 1933, RvM sent a report for Stefan Bergmann to his British colleague and applied mathematician Richard V. Southwell, who forwarded it to the Academic Assistance Council (later Society for the Protection of Science and Learning, SPSL):

“One owes to him a beautiful method for the numerical treatment of elastic problems (by means of developments according to special orthogonal functions).”83

RvM wrote to Herzberger from Istanbul on October 9, 1934, after he had heard of his dismissal by the Zeiss company in Jena:

“I am firmly convinced that you will find something suitable and something good, since the rest of the world is certainly not so unreasonable to dispense with services that are in many ways as useful as yours..”84

RvM then recommended Herzberger to contact various refugee organizations, provided him with addresses, and wrote further:

“I am in the process of recommending to the Zurich Notgemeinschaft85 some scientists for lectureships, partly in South Africa, partly in Ecuador, and I would like to take this opportunity to name you as well. However, it is my opinion that the right place for you would be in the western countries of Europe or in North America, at least in a country where there is already an advanced optical industry. … You will be interested to know that from this semester onwards Prof. Geiringer is here, who sends warm greetings. Best regards from me, too. Yours Mises.”86

RvM contributed to a memorial issue of ZAMM for Trefftz, which appeared in February 1938 as the first issue that year. RvM's contribution begins with the following words:

“I do not want to evade the participation in the honoring of the memory of my longtime friend, former student and later successor Erich Trefftz. It is now almost exactly 27 years since an advanced student first took the floor in the Strasbourg mathematics seminar, which was headed by Heinrich Weber, and immediately attracted the attention of all the lecturers. Shortly afterwards, Trefftz began his doctoral thesis, which later became very famous, and which he quickly completed. Since those days we have never been out of contact, and I have found in him, who in 1921 became my successor in the Dresden chair and in 1933, at my request, took over the management of this journal, a faithful and sincere88 friend. … I will add just two words here: ‘He was a clear head and a reliable man.’” (Mises 1938, 74)

Four months after appearance of the Trefftz-memorial-issue, in a letter to Prandtl dated June 9, 1938, Dr. Dames from the Nazi Education Ministry complained that among the contributors had been several “non-Aryans,” and he asked whether Prandtl had been informed before about this fact. Prandtl replied on June 15, 1938 in a three-page letter in which he insisted that foreign scientists had no understanding of the exclusion of Jews in Germany. In particular, he wrote:

“As to the non-Aryans mentioned by you, von Mises was Trefftz's doctoral advisor and, in addition, predecessor in his [Dresden] chair and could hardly be excluded on such an occasion. . . . Von Kármán, however, is due to his absolutely fundamental achievements so much above any critique, that his exclusion could not come to the mind of anybody who knows the facts.” (Siegmund-Schultze 2018, 516/17)

Prandtl ended the letter to Dames with an argument that referred to economic aspects (need for foreign currency) and was typical of the often tactical and indirect defense of scientific communication in the Third Reich:

“I would also like to add that the Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) is an internationally read journal. As far as I hear, 70% of the circulation goes abroad. This is another reason why a journal serving international cooperation in this way cannot be judged according to the principles that would apply to purely German journals.”89

It also seems remarkable that the former student of RvM, Fritz Rehbock (1896–1989), published an obituary of Trefftz even in the mathematical journal with racist overtones “Deutsche Mathematik” edited by Ludwig Bieberbach. Rehbock, who had not been a student of Trefftz, had never worked in Dresden and had just joined the Nazi party NSDAP in 1937 (Tobies 2006, 268/69) did not include any racist or otherwise nationalistic feelings in his obituary of Trefftz. The editor Bieberbach may have been reminiscent of his friendship with RvM in the 1920s, when he accepted passages as the following in Rehbock's obituary:

“His love of the practical methods of mathematics he owed to his teacher and uncle Carl Runge, … his love of mechanics and its neighboring fields to his teacher Richard von Mises with whom he obtained his doctorate in Strasbourg in 1913.”(Rehbock 1937, 582)

Friedrich Adolf Willers (1883–1959), who was the same age as RvM but was “racially acceptable”90 to the Nazis, had made a name for himself through work in numerics, in particular through his internationally acclaimed German textbook Methoden der Praktischen Analysis (Methods of Practical Analysis) of 1928. From 1928 he was full professor at the Bergakademie Freiberg near Dresden, where Alexander von Humboldt had once studied in 1791/92. His “retirement” with a political background at the age of only 51 years is described in an obituary in ZAMM of 1960, co-authored by his successor as editor since 1959, Helmut Heinrich:

“Unfortunately, Willers’ activity in Freiberg came to an untimely and unpleasant end in 1934. (He) saw himself forced to work energetically on an increase of the strongly decreased level of performance of the students. This led to a sharp contrast between him and the student body, which was exploited by the then ruling NSDAP. Due to the Party's influence Willers had to apply for his retirement against the will of the professorial collegiate. In this extremely difficult and delicate situation for him, he found a reliable and helpful friend in Trefftz in Dresden. With him, beyond human relations, a lively scientific exchange of ideas took place, which led to a whole series of remarkable works in the field of elasticity theory.” (Sauer/Heinrich 1960, 3)

Willers’ anxiety to quote Jewish authors becomes grotesquely clear in a review he published in ZAMM in 1939. It was about an “unaltered reprint” of the third edition (1882) of Bernhard Riemann's Partielle Differentialgleichungen und ihre Anwendungen auf physikalische Fragen, which had just appeared in Braunschweig in 1938. After pointing out the multiple editions of Riemann's work by Karl Hattendorff and then by Heinrich Weber, RvM's boss in Strasbourg who died in 1916, Willers said in his short review:

“After his [Weber's] death, an unaltered print of the Riemann-Weber was published, and about ten years ago the work was completely redesigned with the help of a large number of authors. This, however, completely changed the character of the book, turning it from a textbook into a Handbook [Nachschlagewerk].” (ZAMM 19: 60)

Other book reviews in ZAMM were more political in nature. Right after Trefftz's death, Willers had published Trefftz's rather dismissive review of the book Deutsche Physik (1936) by the elderly Nobel Prize winner and Nazi physicist Philipp Lenard (1862–1947). There it says:

“Anyone who is used to approach the problems of mechanics from the side of its technical applications should not expect to find in this volume the mental tools for the work of the day. The choice of material and presentation are strongly influenced by the author's pronounced aversion to theoretical physics and mathematics.” (ZAMM 17: 58)

There is no doubt that the enormous expansion of engineering research institutes and armament factories after 1933 could only increase the importance of ZAMM for the regime as a whole. As Willers’ editorial at the re-launch of ZAMM in the Russian sector of Berlin in 1947 shows, the topics published by ZAMM had shifted strongly in recent years towards “practical analysis and mechanics of solid and deformable bodies” (see below). This did not mean that the theoretical development of mechanics came to a standstill under wartime conditions. In a review of the book Theoretische Einführung in die Gasdynamik (Theoretical Introduction to Gas Dynamics) by Robert Sauer (1943), for example, Adolf Busemann wrote:

“While German books on gas dynamics have so far been written by mechanical engineers, this is the first time that an applied mathematician has had his say. He has worked through, compiled and supplemented the original literature in accordance with his competence in the theoretical-mathematical treatment of the subject matter, dispensing with the physical and metrological questions.” (ZAMM 23: 299)

Of course, during the war years, the “pride in the German armed forces” and the role of science in the war occasionally had to be reflected in ZAMM. In a review of the reprint of the book by Carl Cranz and O. von Eberhard Die neuzeitliche Entwicklung der Schusswaffen (The modern development of firearms, 1939), the Berlin TH Professor Rudolf Rothe wrote in 1941:

“When we read in an army report today that our long-range guns shot an enemy ship out of a convoy from the Flemish coast, a good deal of such precision can be attributed to both the exact methods of today's ballistics and the technical level of our firearms.” (ZAMM 21: 61)

In the review of the small 51-page book by Claus Hinrich Tietjen Space or number (vol. 6 of School in Reconstruction based on National Reality)93 with an introduction by Ministerialdirektor Prof. Dr. Vahlen,94 Leipzig 1936 (ZAMM 18: 145/146), Mosch criticizes several mathematical definitions as “more emotional-illustrative than logical-correct.” (ZAMM 18: 146). Mosch then lets the text speak for itself in its absurdity:

“Using the example of the air raid, the author again develops the thesis that ‘the power of the sense of space, and this is the elementary power of the Nordic man, which is shattered by the power of number’ (i.e. by the Jewish influence) ‘is awakened to new life, for this is the question of the fate of the German people’.”

To leave no doubt about his irony, Mosch ends the review with the words:

“In his review, the reviewer was only able to highlight some of the most important ideas of the work.” (ZAMM 18: 146)

About the German written book Einführung in die mathematische Logik und die Methodologie der Mathematik (Introduction to mathematical logic and the methodology of mathematics, Vienna 1937) by the famous logician Alfred Tarski – twice stigmatized as a Pole and Jew in the Nazi Empire – wrote Mosch in 1938:

“The book wants to give those educated people who are interested in the questions of the foundation and structure of mathematics without having any closer relationship to mathematics an idea of that ‘development of mathematics in its depths’ [Entwicklung der Mathematik in die Tiefe] which began about a century ago and has already reached a high degree of perfection.” (ZAMM 18: 256)

One year later, in April 1939, the year the war broke out, ZAMM published a review by Mosch of a book by an emeritus professor at the TH Stuttgart, W. Häbich, entitled Organisationselemente einer Funktionstechnik (Organisational Elements of a Functional Technology) of 1938 (ZAMM 19: 122/123). There it says at first:

“The starting point and cause of the investigation were the disturbances that afflict our culture [Kulturkreis] today.”

These were different from previous disturbances in that they

“give the impression of a world epidemic of persecution mania [Verfolgungswahnsinn], which appears as technical madness (excessive increase of the speed of production), as economic madness (mutual sealing of borders) and as armament madness (in the form of active and passive persecution mania).” (ZAMM 19: 122)

Mosch supported Häbich's analysis, which also reflected obvious phenomena of Nazi society in the pre-war phase, with the following concluding words:

“The clarity with which the author sees the problems, the heartiness with which he tackles them, the individuality of the presentation make the reading of the book enjoyable and profitable even for the non-technician.” (ZAMM 19: 123)

About the book Das Hauptproblem der Mathematik (The Main problem of Mathematics) by Max Steck, published in the middle of the war in 1942, Mosch says at first:

“In the opinion of the author, the mathematical research of our time is on the wrong track. It has devoted itself to formalism and logicism. The way of thinking of what he called the ‘German line’, which has its origin in Plato, has had to give way to the ‘Western line’ due to the influence of mainly Jewish researchers … The main mathematical directions of this Western line are empiricism (Pasch), formalism (Hilbert) and logistics [Logistik] (Husserl - Whitehead - Scholz), whereby he attacks the Hilbert point of view particularly vehemently … The tone of his explanations is often excessively sharp [reichlich scharf].” (ZAMM 22: 301)

Indirectly alluding to the fact that David Hilbert could in no way be suspected by the Nazis of being of “Jewish origin”, Mosch then makes clear the absurdity of Steck's argumentation when saying at the end of the review:

“The author concludes his work with the admonition to faithfully administer and multiply, also in mathematics, the heritage that the great Germans and the Aryan researchers thoughtfully gained.” (ZAMM 22: 301)

The APC program of course only concerned the reprinting of European publications, generally in original languages. But there were also initiatives for new, American publication projects. Already since February 1940 there had been contacts between RvM and von Kármán about a new journal for applied mathematics. As reported above, von Kármán had been working on the other side of the American continent at the California Institute of Technology for over 10 years. RvM told von Kármán on February 10, 1940, among other things, that a publisher had suggested to him that he publish, together with von Kármán, an American successor to ZAMM:

“1) the eventual new foundation should be international, not purely American; 2) it should include applied mathematics (like the ZAMM), for which there is no organ in America; 3) it should be intended for longer work with mathematical derivations that are not included in Applied Mechanics [the existing American journal, RS]. …Incidentally, I am by no means ‘eager’ and have been completely passive in this matter so far.”99

Von Kármán reacted somewhat skeptically in his English reply letter of February 19, probably also alluding to RvM's rather short experience in the U.S.:100

“As far as the project is concerned, I am somewhat worried about the future of a journal published by a newly Americanized publisher and editors of such outspoken European direction. If you want to do something in this direction, I believe the most important thing would be to get a young American scientist who could act as managing director and would do the work. If you have someone who is really good and is willing to devote his time to this task, we could talk over the chances of such a venture.” (Kármán Papers, 20.37).

For reasons that have not yet been fully clarified, RvM and von Kármán were unable or unwilling to pursue their plans to found a journal in 1940/41. A letter from RvM to von Kármán dated September 2, 1942, speaks of “endless intrigues that have been playing at this matter for a year” and of the intention of some Americans “not to let either of us become too powerful.”101 The project of an American ZAMM was instead actively pursued at Brown University in Rhode Island, especially by the former longtime Secretary of the AMS R.G.D. Richardson. This eventually led to the founding of the Quarterly of Applied Mathematics in 1943. A letter to Richardson from John L. Synge, an applied mathematician from Ireland and working in Toronto, dated August 1942, was part of these preparations, and shows the role of ZAMM in the background, not least in the naming of the Quarterly:

“The ZAMM is taken as model, but do not the initials QAMM make that a little too obvious? I don't see the necessity for putting Mechanics as well as Mathematics in the title, unless the idea is to include experimental results in Mechanics. I would think Applied Mathematics Quarterly or Quarterly of Applied Mathematics would fill the bill.”102

Richardson wrote to Warren Weaver, the head of the American “Applied Mathematics Panel” (APM), on September 24, 1942:

“We found that von Kármán is willing to serve as an editor, if we start the journal and that he is entirely independent of von Mises.”103

Richardson tried in vain to persuade RvM to join the board of editors. In a letter to RvM, dated September 14, 1942, he reacted to a previous letter in which RvM had apparently complained about the very large board of editors for the planned journal Quarterly of Applied Mathematics, fearing lack of opportunities for individual editors to influence decisions. In order to convince RvM, Richardson stressed the national and patriotic importance of the planned journal and pointed to differences in attitudes between Europeans and Americans:

“I believe that there is a considerable difference between the situation here and in Europe and that policies which would be successful in one country might easily be failures in others. Here in America we manage things by cooperation . . . general policies are laid down by a group and not by an individual. . . . My own desire is to make it possible to use all the talent we have in America in this terrible struggle for the existence of civilization.” (Siegmund-Schultze 2009, 246)

RvM wrote a rather critical and detailed review of the first issue of the journal in the widely distributed American journal Science (Mises 1944), . This document, which cannot be analyzed in detail here, is important for a biography of RvM, and contains, among other things, interesting historical comparisons between German and American applied mathematics. Although the title of the Quarterly of Applied Mathematics deliberately – at the suggestion of Synge and others – did not mention mechanics, RvM found that

“the whole program is focused on ‘tooling up mathematics for engineering.’ Papers on probability, statistics, economy, biology seem practically excluded.” (Mises 1944, 81)

RvM alluded to the brilliant article by von Kármán with which the new Quarterly opened (Kármán 1943), which, however, cannot be compared either in content or in scope with RvM's introductory article for ZAMM 22 years earlier (Mises 1921). RvM does not mention that von Kármán was the author of this article, but then clearly recognizes his old friend and competitor as a specialist in aerodynamics, not an applied mathematician in RvM's broad understanding:

“In the board of editors, which includes Th. von Kármán, leading man in aeronautical research, none of the country's representative mathematicians is listed.” (Mises 1944, 81/82)

As the “most interesting contribution so far” in the Quarterly, RvM does not coincidentally consider an article by two students of his former student Stefan Bergmann, “L. Bers and A. Gelbart, on certain differential equations in mechanics” (Mises 1944, 82). RvM felt a certain degree of over-organization in the Quarterly and said:

“History has taught that the best, if not the only, way to promote scientific achievements is to leave people who are able to do creative work to themselves and to protect them as far as possible against all kinds of organizers and inciters.” (Mises 1944, 82)

In April 1947, 2 years after the war, ZAMM reappeared as the first German mathematical journal in Berlin with a license from the Soviet military administration. RvM's former university, soon to be called Humboldt University, was now located in the Russian sector of Berlin. Willers, the now already 64-year-old editor, said in an editorial, among other things, alluding to the until recently prevailing conditions of armament war (see figure 16):

“In the future, the journal will be published monthly in 32-page issues. In the new volumes the journal will not only, as it was the case in the last years, publish articles mainly from the fields of practical analysis and the mechanics of solid and deformable bodies, but also from other fields, e.g. electrical engineering, thermodynamics, optics, geodesy, statistics etc., if they contain mathematically interesting ideas. The journal is to become as comprehensive as the first volumes were. In the last years the emphasis was on mechanics. In the future the applications of mathematics shall be the main focus.” (ZAMM 27: 1)

In 1956, after another scant decade in which the volume of the journal had gradually risen to pre-war levels,104 Willers described the transition from war to post-war as follows:

“During the Second World War, due to the lack of paper, the issues gradually became thinner, and finally the journal had to cease publication altogether. The last issue was volume 24, issue 5 / 6, which was dedicated to Prof. L. Prandtl on his seventieth birthday. The two previous issues had been destroyed by aerial bombs during transport from the printing house to the publishing house and could therefore not be delivered. The remainder of the remaining issues also burned up during the fights around Berlin." (Willers 1956, 121)

Willers then added that the intention of thematic breadth announced in 1947, which may in part have reflected the political limitations of mechanical research in the immediate post-war period,105 could not quite be realized – probably due to the increasing specialization in scientific journals:

“Since, as mentioned above, special journals had been created for some of the areas previously covered by the journal, ZAMM now mostly published only papers from the fields of practical analysis, mathematical statistics, and the mechanics of solid, liquid, elastic, and plastic bodies. These are still the main areas of publication. Recently, papers on the computational technology of calculating machines and their construction have been added. …Most of the issues are sent to non-German-speaking countries.” (Willers 1956, 122/123)

Stefan Bergman, the former co-worker of RvM at ZAMM, now working in America and written with only one n, had spoken of his political concerns in a letter to Geiringer on December 30, 1951:

“Concerning the tribute to Mises, the idea of arranging an issue of ZAMM does not seem to me to be very recommendable: ZAMM appears in the Russian zone109 and it may well happen that as a result of some political incident the whole thing would be prevented and all the preparatory work would be in vain. And besides, articles about pure mathematics and probability theory cannot be published in ZAMM. I personally think that a special volume would actually be preferable. … Would you agree that we form a kind of committee where you are the driving force?110

Bergman's political concerns were finally shared by Geiringer. She wrote to Günter Schulz on October 12, 1952, her colleague at Berlin University in the 1920s:

“I am indeed quite sad, because just now, after everything is finished, after a long time of work, when I wanted to send the ms. to Mr. Willers, it occurred to me with horror that a paper on Mendel's biology might be ‘intolerable’ in the Russian zone. Since I do not want Mr. W. to have any difficulties under any circumstances, I take the liberty of involving you again. …. Do you think that the publication is possible (possibly after omitting the name ‘Mendel’ in all places)?”111

While RvM still lived to see the ZAMM issue of April 1953, he and Geiringer were disappointed with it. In addition to Geiringer's, it contained only eight articles by exclusively German authors, including Collatz, Iglisch and Schmieden, the former students, and RvM's former boss Hamel, with whom he had some controversy in the 1920s and whose behavior under the NS RvM disapproved. Geiringer wrote on February 10, 1953 to her colleague and former acquaintance Alfred Basch in Vienna, who had contributed to the extensive anniversary volume but not to the ZAMM issue, and said that she had hoped for Austrian contributions. On the same day she wrote again to Schulz, this time because of the small number of German contributions:

“I can't explain it, because when we were in Germany [in 1951, RS] it seemed as if many of the former students were still very devoted to Mises. Here in the U.S. there is much talk of a new and strong awakening of Nazi ideology in Germany. I hope this is all exaggerated.”112