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“The joy that engineers and mathematicians have come together.” 1

2020; Wiley; Volume: 100; Issue: 2 Linguagem: Inglês

10.1002/zamm.202002017

1521-4001

Reinhard Siegmund‐Schultze,

Benford’s Law and Fraud Detection

“Richard von Mises’ merits for ZAMM have already been acknowledged. While formerly (before 1920) ‘applied mathematics’ at best was considered an appendage of ‘pure mathematics’ and occasionally used in journals and during meetings as an ‘advertising sign’ [Aushängeschild], the foundation of GAMM and ZAMM stressed both the independence of applied mathematics and its close connection to mechanics.” (Collatz 1983, 279) Although Collatz's article and the two articles by Garrett Birkhoff and G.S. Ludford (Ludford 1983) in the same issue of ZAMM provide valuable, albeit fragmentary, information on von Mises' scientific work, there is – contrary to Collatz's remark – no thorough evaluation in the literature on von Mises’ work for ZAMM so far. This remains a task for the present article, which will, however, only fulfill part of the task by limiting the discussion mainly to the founding years of ZAMM, namely 1919–1921. Von Mises’ 13 years of activity for ZAMM until his emigration from Nazi Germany in 1933, especially the broader scientific impact of ZAMM under his editorship can only be indicated in section 5 and will have to be discussed later and separately. The journal itself, which is now published in English under the name “Journal of Applied Mathematics and Mechanics” (ZAMM), has – in addition to the 1983 issue for von Mises – already made some efforts to explore its own history. As examples of the scientific impact, two main areas that were flourishing at ZAMM at the time can be mentioned here: fluid dynamics and plasticity theory.2 In fluid mechanics at that time, the inviscid flow was calculated with potential-flow theory, and the flow in the boundary layer with the new integral method for solving Prandtl's boundary layer equations, derived by Theodor von Kármán in ZAMM.3 In plasticity theory, Hencky introduced – after some suggestions by Prandtl [1921] and Nádai [1921] – the “slip line theory” (Hencky 1923), which became generally accepted in engineering practice, e.g. of forming processes, almost three decades later. Prandtl [1923] as well as Carathéodory and Schmidt [1923] supplemented these ideas with graphical solution methods and numerous other statements. Hilda Geiringer and William Prager [1934] contributed to the dissemination of this theory and contributed own ideas as well.4 Von Mises’ later relationship with ZAMM during his Turkish and American emigration must also remain outside the scope of this article. Von Mises’ journal became a model for international journals of applied mathematics. In 1932/33 the journal of the same name Prikladnaya Matematika i Mekhanika was founded in the Soviet Union. Richard von Mises had many followers there among physicists, engineers and mathematicians, not least because of the success of his Handbook on Differential and Integral Equations, the so-called “Frank-Mises” (1925/27),5 edited with his friend, the Austrian-Czech physicist Philip Frank. The American Quarterly of Applied Mathematics, which was founded in 1943 during the emigration of von Mises, also followed the example of ZAMM. Von Mises himself discussed this foundation somewhat critically in (Mises 1944). The following section 2 gives some basic biographical information on von Mises and attempts to describe briefly the main developments in the institutionalization of applied mathematics first in Göttingen and later, after World War I, in Berlin. The role of Felix Klein (1849–1925), the great reformer of mathematical and technical education in Germany and mentor of Richard von Mises, will be an important point in this section (see also Appendix B). The next section 3 focusses on unknown and unpublished archival material concerning von Mises’ activities mostly in 1919 and 1920 which led to the foundation of ZAMM. A major and hitherto unknown document is von Mises’ handwritten “program of a journal of applied mathematics and mechanics” (Programm einer „Zeitschrift für Angewandte Mathematik und Mechanik“). Von Mises’ “program” is preserved as a clearly legible handwritten draft in the Von Mises Papers at the Harvard University Archives. It was written for the Association of German Engineers (Verein Deutscher Ingenieure, VDI) and its publishing department, from 1923 officially the “V.D.I .Verlag.” The document shows von Mises’ versatility and his commitment to all aspects of producing6 and running the prospective journal. Although von Mises proposed in it the nomination of a “scientific commission” to advise the editor (mentioned then on the title pages as “under participation” – “unter Mitwirkung”), the entire program shows that von Mises has ensured his own dominant role within ZAMM. Most of the proposals from von Mises’ “program” were realized in ZAMM, for instance the “Summary Reports” (Zusammenfassende Berichte) and the “Short Excerpts” (Kurze Auszüge), the latter essentially being reviews of articles. Von Mises himself wrote many of the reviews of articles and books published in ZAMM, although Goldstein's claim that “he did practically all the reviewing” (Goldstein 1963, xii) seems exaggerated. The “Program” is published below as Appendix A, both in the German original and in an English translation. Von Mises’ “program” must not be confused with his introductory 15-page article to the first issue of ZAMM in 1921, the “Tasks and goals of applied mathematics.” This article has often been quoted but never completely translated into English. For reasons of space I cannot do this within the present article either and will restrict my efforts to characteristic quotes with brief commentary. This will form section 4. It remains for the future to systematically compare the introductory article by von Mises with the actual work and results of ZAMM during the 13 years of von Mises’ editorial work. In such a future investigation the contribution and assistance of Richard von Mises’ student and future wife Hilda Geiringer (1893–1973) – a well-known applied mathematician of independent significance, the creator of the Geiringer equations in plasticity theory – would also have to play a major role. Without jumping too hasty to conclusions we can state that in the publications of ZAMM there was much realized of what von Mises had planned and promised both in the “program” and in “Tasks and Goals”. This concerned for example the central role of mechanics, in particular fluid dynamics and plasticity, in the new journal (see above). Also, the still important role of graphical methods in ZAMM corresponds to von Mises’ “tasks and goals” while numerical methods gradually assumed a bigger share than von Mises had anticipated in 1920. Some areas such as mathematical optics were not mentioned (but not excluded either) in von Mises’ plans but appeared nevertheless on the pages of ZAMM (especially by Max Herzberger). Experimental works played a somewhat controversial role in the publications. They were considered underrepresented by some engineers like Ludwig Prandtl. Some insights into von Mises’ editorial policy during his editorial tenure from 1921 to 1933 are given in the last, fifth section of this article. I will try to show the high degree of independence of von Mises in his role as editor. Von Mises did not even shy away from some attacks against “coworkers” like Ludwig Prandtl and their schools (see below). Of particular relevance is von Mises’ view of the different, partly coinciding, partly contradicting interests of German engineers, physicists, pure and applied mathematicians and the institutions to which they belonged. The international context and von Mises’ somewhat unclear relationship to internationalism are also discussed in part. Throughout the discussion, especially of the “Tasks and Goals”, the reader must be aware of the drastically changed character of applied mathematics today compared to the 1920s, not least because of the computer development in the rather recent past. Von Mises and ZAMM were active in the pre-computer age, even before analog computers like V. Bush's Differential Analyzer appeared around 1930. In particular, modelling, statistical methods, numerical analysis (a name that apparently first appeared in the title of a 1930 book by James B. Scarborough)7 and, of course, computers and algorithms have now acquired a much broader role within applied mathematics than in the 1920s and 1930s. As far as the individual contribution and impact of von Mises is concerned, the paper will hopefully be able to show that, through his versatility and energy, he represented exactly the kind of personality needed to combine the efforts of various interest groups into a joint, groundbreaking and far-reaching effort in science, mathematics and technology. This allows us to draw conclusions at the individual, biographical level about what was typical in a broader historical process. Finally, a few remarks on the sources used and on the technical aspects of this paper. The two main sources are publications in the journal ZAMM itself and von Mises’ estate in the archives of Harvard University, his final institution in American exile. Another archival source is the Ludwig-Prandtl papers in the archives of the Max Planck Society (MPG) in Berlin. Smaller sources are mentioned separately in footnotes. All non-English citations are given in English translation, usually by the author. The German original is added in cases where the source has not yet been published. For example, the German is not added to excerpts from the ZAMM. Within the quotations, notes by the author, e.g. original words to some translated words, are added in brackets. For the sake of brevity, I refer to shorter excerpts from the ZAMM directly by “ZAMM, Volume No.: Page No.” without including the source at the end of the article in the references. Before we go into the prehistory of ZAMM and its foundation in 1919/20, a few brief remarks on the biography of Richard von Mises8 and on the rise of applied mathematics in Göttingen and later in Berlin are necessary. Göttingen was the traditional center with which the Berlin School, von Mises, his institute and his journal cooperated and competed (see also Section 5). Richard von Mises was born in 1883 in Lemberg (Galicia) under the Habsburg Monarchy; the city is today's Lvív (Ukraine). He received his school education in Vienna and studied engineering at the Technical University there from 1901 to 1905. In addition to his keen interest in technology, von Mises developed an early interest in purely mathematical subjects such as geometry (to which his first publication (Mises 1905) belonged even before his doctorate), and he attended lectures by the then leading probabilist Emanuel Czuber. Subsequently von Mises became assistant to the former student of David Hilbert in Göttingen and professor of mechanics at the Technical University in Brno (Moravia), Georg Hamel. Von Mises wrote his habilitation thesis on water turbines in 1908. One year later he was appointed associate professor of applied mathematics at the university of the German occupied city of Strasbourg. Here he had good relations with the versatile algebraist and analyst Heinrich Weber (1842–1913) and his family. Weber had published revisions of Karl Hattendorff's edition of Bernhard Riemann's Lectures on partial differential equations and their applications in physics in 1900 and 1901. The “Riemann-Weber” was later (1925/27) revised again by von Mises and Philipp Frank, which, as mentioned above, became the “Frank-Mises”. In Strasbourg von Mises became advisor to, among others, Erich Trefftz (1888–1937), later his successor as editor of ZAMM. Trefftz’ doctoral thesis on circular fluid jets of 1913 belonged to von Mises’ main research area, hydrodynamics. In the following year von Mises published a book on the technical aspects of the subject with the Teubner Verlag in Berlin/Leipzig. In 1913, the first full professor of applied mathematics in Germany, Carl Runge (1856–1927) of Göttingen, incidentally Trefftz’ uncle and the latter's former professor in Göttingen, presented von Mises’ most important paper on plasticity theory to the Göttingen Academy of Sciences (Mises 1913). It contains the Mises yield condition that has subsequently been used in engineering practice on a daily basis and is known to practically all mechanical engineering students. The paper shows von Mises’ full awareness of experimental findings which he combined with his rather simple and elegant mathematical model. Although the latter could not be interpreted directly in terms of physics, it proved to be well suited to making predictions for practical applications. The Mises condition therefore made his name better known and more durable among engineers than among mathematicians. Among mathematicians as a whole, von Mises is probably best known for creating ZAMM and – with often uninformed disapproval – for his failure to find the “right” foundations for probability theory. Since the relationship between the Göttingen and the Berlin schools of applied mathematics is an important background to von Mises’ work for ZAMM during the 1920s and 1930s, a short look at the older school in Göttingen is necessary. “We must be very careful to ignore the pseudo-authorities in the subject – albeit with the utmost caution – as they deserve. The picture of mechanical engineering in its current state will thus become much clearer. … Every progress in the teaching of mechanics and its recognition and evaluation at the technical universities makes it easier to work in this direction and contributes to the gradual development of genuine scientific activity by the technician, as we see in England with Osborne Reynolds. We want to create a picture of the tools of mechanics that have been ignored until now.”9 In the course of his collaboration with Klein von Mises met Prandtl's protégé and his and Prandtl's future rival Theodor von Kármán (1881–1963), who was only two years older than von Mises (Hanle 1982). Later von Kármán became a leading aerodynamicist both in Germany (from 1912 chair in Aachen) and in the United States (from 1929 mainly at Caltech in Pasadena). Early patterns of competition and cooperation between the three men, von Mises, von Kármán and Prandtl, emerged. For example, when von Mises, supported by Klein, criticized von Kármán's article on strength of materials for the encyclopedia, or when von Kármán, supported by Prandtl, was awarded the chair of aerodynamics in Aachen in 1912, while von Mises was unsuccessful (Siegmund-Schultze 2018, 493). During World War I von Mises was an officer in the Austrian Air Force in Vienna. In 1916 he designed a “large aircraft” (Großflugzeug), which was conceived as a bomber, but never went into service due to engine problems. He gave lectures to air force officers in Vienna, which resulted in von Mises’ “Theory of Flight” (“Fluglehre”) for a wide readership of engineers, and which was published by Springer in Berlin in 1918, when the war was still going on. A more theoretical result was von Mises’ two-dimensional theory of the aerofoil, published in two parts in 1917 and 1920, which even had implications for future work on the reversibility theory in fluid dynamics by von Mises’ Harvard colleague Garrett Birkhoff after World War II, as the latter testifies in (Birkhoff 1983, 283). These few biographical facts should suffice to indicate that von Mises was very familiar with the works of the Göttingen school and with the leading figures there, both mathematicians and engineers. He had a boundless admiration for Felix Klein, as evidenced by his contributions to ZAMM, both on Klein's 75th birthday in 1924 and on Klein's death a year later in 1925 (Mises-anon 1925). Klein, for his part, was impressed by von Mises and in 1908 called him “one of the most successful examples to date of a crossbreed between mathematics and technology” (Siegmund-Schultze 2018, 486). In von Mises’ relationship with Runge (born 1856) and Prandtl (born 1875) the difference in age played a role, especially in relation to the former. In fact, no publication by Runge appeared in ZAMM, and only a few of Runge's students, such as E. Trefftz and F.A. Willers, published there before 1933. When Trefftz died in 1937, Willers became his successor as editor of ZAMM. World War I and especially the defeat of Germany created new appreciation and new conditions for applied mathematics in Germany, but also in many other European countries and in the United States. “The increasing penetration of practice with mathematical methods due to the development of technology in the last pre-war years and, above all, the unexpectedly clear need during the war for practically and theoretically trained mathematicians –in the General Staff for questions of cartography, topography, imaging, in the Artillery Proving Commission for ballistic tasks, in the Air Force for static and aerodynamic calculations, etc. – require that applied mathematics is adequately represented at the largest university in the state [Prussia]. This is all the more so as the new examination regulations for candidates for the higher teaching profession, in contrast to the old ones, require from every candidate for the first level teaching qualification in mathematics experience in mathematical calculation and drawing.”10 Despite his age of 62 at the time, it was Runge (a good friend of the Berlin physicist Max Planck) who was originally considered by the faculty as a candidate, although it was unlikely that he would accept. In any case, the faculty's application to create the professorship was rejected by the Ministry in January 1919 for financial reasons. “Applied mathematics can be practiced and taught in so many different ways that one cannot demand that one single person takes all possible points of view into account. On the contrary, in order to achieve a worthy representation of this science at a large university, one must strive to ensure that the scholar to be appointed gives a personal touch to his teaching, without of course neglecting the elementary main lectures in the field of applied mathematics. This applies to each of the three men mentioned. For Runge, numerical and graphic calculation would predominate, for Hessenberg the purely geometric methods of drawing, and for von Mises the interest and understanding of technical issues.”11 The Ministry did not agree and only allowed the use of a vacancy as an associate professor (Extraordinariat) for the purposes of applied mathematics. Consequently, the two older candidates declined the offer. Eventually von Mises was appointed to the University of Berlin, officially only as an associate professor, but with acceptances which he obtained through negotiations and found satisfactory.12 “As you know I am decided to settle in Berlin around Easter and take over a large-scale scientific enterprise [wissenschaftlicher Grossbetrieb].” (Siegmund-Schultze 2018, 500) One is probably not mistaken in assuming that von Mises tried to subliminally compensate for the defeat against von Kármán in the competition for the chair in Aachen in 1912. However, a comparison of his rather small institute in Berlin (Bernhardt 1980) with Aachen, let alone Göttingen, was out of place from the outset, if only because of the much larger personnel required to operate the experimental facilities (wind tunnels) there. It soon became apparent that the research grants granted by the “Notgemeinschaft” (Emergency association), the predecessor organisation of the German Research Foundation, in the early years of the Weimar Republic went mainly to the centers in Göttingen, Aachen, and partly Karlsruhe, while applications by von Mises for the expansion of his institute and for support for teaching were rejected (Tobies 1982, 19/20). In fact, ZAMM was to become much more of a “large scientific enterprise” than the small von Mises Institute at the university. “It can be regarded as a peculiarity of German science that the boundaries between the disciplines are much more sharply drawn here than elsewhere. There is hardly any other country, for example, where such a clear distinction is made between pure ‘university’ mathematics on the one hand and ‘applications’ of mathematical theories, especially in the engineering sciences, on the other. …. Efforts to achieve a mutual rapprochement have been made over several decades, especially under the influence of the Göttingen movement under Felix Klein, especially in the Zeitschrift für Mathematik und Physik. The latter, however, never found full contact with the circle of scientific engineers.” (Mises 1921b, 268) This section will show that the separation described by von Mises was felt by various influential mathematicians, engineers, associations and publishers. But it took the peculiar and energetic personality of von Mises to change the situation and create a much-needed meeting place. “The plan you mentioned for a ‘Zeitschrift für angewandte Mathematik’ interests me very much. However, I have serious doubts about the publishing.”13 Two months later, on 17 March, Prandtl wrote to von Mises that Springer had told him about von Mises’ attempt when he himself came to Springer with “very similar” plans. However, the “poor economic situation, especially in the publishing industry” made such plans seem unrealistic.14 In any case, at that time Springer was still considering taking over the existing German journal for applied mathematics Zeitschrift für Mathematik und Physik from Teubner Verlag, which had been discontinued during the war.15 As is well known (Remmert, Schneider 2010), Springer developed broad activities for publications in the natural sciences and mathematics after the war, while Teubner scaled back his efforts in these areas. Springer took over Teubner's traditional Mathematische Annalen and, among other things, founded a new journal for pure mathematics in 1918, the Mathematische Zeitschrift, edited by Leon Lichtenstein. There von Mises published his two fundamental articles on probability theory in 1919. “As far as the question of the Zeitschrift für Mathematik und Physik is concerned, I have spoken to both Runge and Klein. Runge is confident that a redesign of the journal in your publishing house will succeed with new life in the editorial department. He attributes the decline of the journal to, among other things, his and Mehmke's low activity. He thinks a lot of Mises as editor-in-chief, but what I can't hide is that Klein had a personal objection to Mises, that he often insults people by showing signs of arrogance.16 I'll let you have the verdict in confidence, of course. I can't confirm it, but I would ask you to discuss it again with Lichtenstein. Mises is definitely the right man for the job.”17 “Negotiations with Gieseke at Teubner. For hydromechanics, second volume, for strength theory. Finally, for the “Zeitschrift für angewandte Mathematik”. The plan for this is becoming more and more decisive for me.”19 “Discussion in the House of Engineers with Matschoss and Meyer concerning the founding of a journal for applied mathematics. Pretty good impression, the cause has been substantially promoted.”20 “It seems remarkable that they not only talked about the necessity of such an outlet in general, but immediately created it. The VDI publishing house was strong enough to make this possible even in difficult times – after all, this was shortly before the hyperinflation of 1923.” (Gericke 1972, 6) Already on May 29, von Mises had written in his diary: “This morning the program for the Zeitschrift completed.” During a stay in Münster, von Mises wrote a note in his diary on September 10th about a “draft for the editorial in the journal (Entwurf für den Leitaufsatz in der Zeitschrift). The “program” already mentioned in the introduction above and the “editorial” (Leitaufsatz) were two different things. The latter was the very first article to be published in ZAMM 1 (1921) and comprises 15 printed pages. Its translation into English is still a desideratum, because – according to many in the field – it has more than just historical value. It is partially commented on in section 4. It is interesting that the “Program of a ‘Journal of Applied Mathematics and Mechanics’” (Appendix A) shows the complete title of ZAMM for the first time. After failing in negotiations with the scientific publishers Springer and Teubner with his proposal for a “Journal of Applied Mathematics”, von Mises apparently had to add “mechanics” for the VDI. The publishing house was to remain the same in the 1930s and 1940s until ZAMM was reissued after the war by Akademie-Verlag in East Berlin in 1947. “As for the title of the journal, as you know, I myself am not satisfied with what we have so far. But to say ‘Angewandte Mechanik’ seems to me to be incorrect, because I do not understand by it anymore – though in contrast to the Göttingen usage – a theory of mechanics, but rather the applied subjects like mechanical engineering or bridge building. It would probably be the right thing to say ‘Mechanics and Applied Mathematics’, but that again does not sound very good. From the circles of the V.D.I. ‘Z. f[ür] wissenschaftliche Technik’ or for ‘Grundwissenschaften der Technik’ have been suggested, but the publisher also considers the title as it is now to be the best one. I believe that your concerns are best addressed by the name of the publisher, which is always mentioned in a journal. The V.D.I. will not easily be expected to be too theoretical, and perhaps even a slight emphasis on mathematics as a counterweight is not undesirable if the journal is not to be limited to engineers alone.”21 “The applied mathematicians, i.e. those who want to do useful mathematics in the spirit of the main task of the society, should be very welcome. What I want to avoid is, however, the dominance of mathematics and the mathematizing treatment of problems. I believe that the experiment has to be stressed as least as much as the theory.” (Gericke 1972, p.8) Finally, the fact that ZAMM and its name already existed and were successful also seems to have influenced the decision for the name GAMM. From the beginning there were plans for a cooperation between the journal and the society, which further suggested the identity of the names. In fact, this cooperation was to be reflected, for example, in the regular reports on the GAMM meetings printed in ZAMM, including the publication of abstracts of the lectures. “Many plans for the immediate future, some things clearer now: focus on fewer topics in my own writings, thereby consideration for my health. Working first for organizational aspects, later returning to science, in the long run not ruling out political activity.”22 This seems to me a key quote for understanding the man and the scientist von Mises, including his entire activity for ZAMM and his many other efforts for the organization of science and engineering, combined with a tinge of hypochondria. “I also have to tell you that I will have to develop a new activity from next time on: I have founded a ‘Zeitschrift für Angewandte Mathematik und Mechanik’, which will be published by the Verein Deutscher Ingenieure from 1921 on. It cannot be changed that this will again be a great strain on my time and work. But objectively it was absolutely necessary to do so and I could not evade this task. I am the sole editor and have a very favorable contract with the publisher, who pays me a fixed sum of 3000 M and for each contribution 400 M per sheet [comprising 16 pages], moreover I am reimbursed for all costs of my management. In any case I will hire a secretary for the afternoon hours.”23 Two months later, on December 1, 1920 von Mises reports in his diary about his visit to the printing office (Druckerei Schade) and the delivery of the first manuscripts. “Your journal completely realizes what I once had in mind, but which I could only prepare organizationally, no longer through my own production. It is a special satisfaction for me that the many suggestions made in the Encyclopedia of Mathematical Sciences, which were hardly followed at the time, are now being realized.”24 In alluding to their close collaboration in the Encyclopedia, Klein adopts a personal tone towards von Mises and acknowledges – despite any reservations he may have had about his aggressive personality – that the latter acted in the spirit of his own unfulfilled ambitions. Not quite as personal was Felix Klein's more official letter to the VDI at about the same time, after he had seen the first issue of the journal in February 1921. This letter is reproduced in translation in Appendix B. But even there Klein expresses his “joy … that engineers and mathematicians have come together”. The two letters from Klein close the circle to von Mises’ advertisement for ZAMM in the Naturwissenschaften (above), which among other things expressed the mood in defeated Germany at the time to develop “science as a substitute for power”. “For myself, as a significant progress compared to the previous year: the journal and the securing of the financial situation. But little or no scientific return.”25 External delineation (Abgrenzung nach außen) Inner characterization (Innere Kennzeichnung) Problems from Analysis (Probleme aus der Analysis) Geometrical themes (Geometrische Fragen) The field of mechanical problems (Der Aufgabenkreis der Mechanik) Other Problems. Conclusion (Weitere Probleme. Schlussbemerkung) Von Mises started the very first page of his new journal ZAMM in late February 1921 with a 15 page article “Zur Einführung. Über die Aufgaben und Ziele der angewandten Mathematik,“ which can be translated as „As an introduction. On the tasks (problems) and goals of applied mathematics“ with the German word “Aufgaben” having both a general (tasks) and a more specific (problems) meaning. What strikes the reader immediately is that von Mises reduces the title of the journal ZAMM (