A Private Man in a Public Context

Wilhelm Martin Kutta (fig. 6.1) was born in Pitschen in Upper Silesia in 1867. He lost both parents at an early age and was brought up in the household of an uncle in Breslau. After attending the university in Breslau from 1885 to 1889, he went to the University of Munich, where he studied from 1891 to 1894. Kutta went on to achieve a lasting place in the history of applied

figure 6.i. Martin Wilhelm Kutta (1867-1941). In 1910 and 1911 Kutta published and extended an analysis of the flow of air around the wing of Lilienthal’s glider that he had worked out in 1902 in a dis­sertation at the technische Hochschule in Munich. Kutta assumed that the flow contained a circulation and showed how to link the flow around the wing to the simpler and already solved problem of the flow around a circular cylinder. He was then able to make a plausible prediction of the lift of the wing. After these pioneering papers, Kutta published nothing more. (By permission of the Universitatsarchiv Stuttgart) mathematics for two reasons. First, in his doctoral work of 1900, he developed a numerical method for solving ordinary differential equations. This has be­come known as the Kutta-Runge method and is to be found in all textbooks on the subject.2 Second, he produced a pioneering paper on aerodynamics which appeared in 1910,3 with further developments published in 1911. These papers were based on methods he had developed in his Habilitationschrift of 1902, which he wrote at the technische Hochschule in Munich.4 (This institu­tion is often referred to by its initials as the THM and, for brevity, I follow this practice.) Unfortunately no copies of the Habilitationschrift appear to have survived.5 From the brief summary that was published in 1902, however, it seems to have been the first, mathematical analysis of lift that was based on the circulation theory.6

Kutta was a conscientious teacher who, over the years, introduced hun­dreds of engineering students to the methods of applied mathematics. His mathematical knowledge was said to be of enormous scope and his help was frequently requested by colleagues. He had a deep knowledge of history, literature, and music, a command of languages, including Arabic, and was widely traveled. He never married, however, and was something of a recluse. A colleague of long-standing, Friedrich Pfeiffer, who had been a student un­der Kutta at the THM, wrote an obituary for Kutta after the Second World War.7 In the article, Pfeiffer recalls that Kutta would typically sit alone in the most remote corner of the Mathematical Institute at Munich. After Kutta’s retirement, said Pfeiffer, he and other colleagues would sometimes encounter Kutta, though this happened infrequently. The lack of contact was put down to Kutta’s reticence. When they did meet, Pfeiffer was unhappy with what he found. In later years, he said, Kutta obviously lacked a loving and caring hand (“wie sehr ihm eine liebende und sorgende Hand fehlte”). He went on:

Oft habe ich Kuttas Leben reich und beneidenswert gefunden wegen seiner Aufgeschlossenheit fur so viele Seiten menschlichen Geisteslebens, oft aber fand ich es auch arm und bedauernswert in seiner Einsamkeit und Zuruck – gezogenheit. (56)

I have often found Kutta’s life rich and enviable because of his openness to so many aspects of human cultural life, but I have also often found it poor and rather sad in its solitariness and seclusion.

How were things really, asked Pfeiffer, and did not know the answer. But if Kutta’s inner life was closed to his colleagues, and must be closed to us, his work is open to inspection. Seclusion notwithstanding, he published work that bore the stamp of a time and a place. It was the product of a specific, professional milieu.

Kutta’s career as an academic began in 1894 when he became a teaching assistant in higher mathematics at the THM. Like all the technische Hoch – schulen, the THM had experienced long-standing tensions over the role to be played by mathematics in the training of engineers. How much mathematics should be on the syllabus? What sort of mathematics should be offered, at what level, and who should teach it? These tensions have now been the subject of close, historical study, and thanks to this work there is much about the overall structure of the situation, as well as the particular circumstances in Munich, that can be sketched with some confidence. It is thus possible to form a pic­ture of the context in which Kutta came to do his work on aerodynamics.

Three points must stand out in any general overview. First, the technische Hochschulen (or THs) tended to recruit their mathematics teachers from the universities and, when they were good, lose them again to the universi­ties. This mixture of policy and necessity carried with it certain problems. From the mid-1850s, university mathematics in Germany had been increas­ingly dominated by a concern with rigor and so-called pure mathematics.8 Although the THs provided jobs for mathematicians, those who took the jobs often had their eyes focused on matters that fell outside the concerns of the THs. Their teaching, like their research, was abstract and lacked relevance to engineering. Justifiably, this caused resentment among the engineers, with the result that mathematics appointments often turned into a struggle be­tween different factions in the TH.9

Second, and predictably, engineers were not a homogeneous group. Some engineers wanted to use mathematics as the model on which to construct a “science” of engineering and the nature of machines. The aim was to create a body of knowledge that was general, abstract, and deductive. This movement, which was designed to improve the status of engineering, was associated par­ticularly with the names of Franz Reuleaux and Franz Grashof and achieved considerable influence during the 1870s and 1880s.10 These tendencies in the direction of purity and rigor by one part of the profession provoked an angry reaction in the 1890s from some other parts of the profession. The reaction took the form of an antimathematical movement (Anti-mathematische Be – wegung) led by Alois Riedler at the TH in Charlottenburg. Riedler presented the issue as one of the very survival of Germany in a world where technologi­cal effort must go hand-in-hand with commercial activity and efficient social organization. In this struggle for existence (“Kampf ums Dasein”) there was no place for the speculations of the unproductive classes, whether they be literary or mathematical. The practical men who backed Riedler (the Prakti – kerfraktion) argued that mathematical teaching should be cut down to what was, in their opinion, immediately useful.11

Third, and finally, in 1899, in a measure backed by Kaiser Wilhelm II, the THs were finally granted the right to issue doctoral degrees, hitherto the prerogative of the universities. As a consequence the status, influence, and size of these technical institutions increased steadily in the years leading up to the First World War. The engineering profession was, in many ways, still a divided and fractious body, but in the course of the expansion, the anti­mathematical movement lost much of its force. The alliance of industry and sophisticated science became increasingly acknowledged as an economic and military necessity. The emergence of aviation and the rapid uptake of this subject in the THs helped to consolidate the position of the applied math­ematician and swing the pendulum back to a less hostile stance toward math­ematically formulated theory.12

In his important study of engineers in German society, New Profession, Old Order, Kees Gispen quotes, and expresses agreement with, “a certain Friedrich Bendemann,” writing in 1907, who commented on this swing back and forth between theory and practice and declared that it was time to redress the present imbalance and reintroduce more theoretical training.13 Though Gispen does not mention it, the Herr Bendemann in question, who had re­ceived his doctorate from the TH in Charlottenburg, was a significant force in the aeronautical world. He was a specialist in aircraft engines and propel­lers. In 1912 he was to become the director of the Deutsche Versuchsanstalt fur Luftfahrt at Adlershof outside Berlin.14 Bendemann’s 1907 comments were a direct, and face-to-face, riposte to Riedler. They suggest the growing con­fidence of the aeronautical community in the THs in the face of old schisms and old campaigns.15 Those involved with airships and airplanes were begin­ning to think of aeronautics as a natural home for what von Parseval called the “gebildete Ingenieure,” that is, the educated or cultivated engineer whose thinking, by definition, combined both theory and practice.16

Kutta’s career thus began amid some of the more acrimonious attacks on mathematicians, but he was fortunate to be sheltered from the worst ex­cesses of the Theorie-Praxis-Streit by the special situation in Munich.17 The mathematicians at the THM had long made efforts (though with varying de­grees of determination and success) to accommodate the needs of engineers. They had cultivated a geometrical, visual, and concrete mode of teaching. The trend had started when Felix Klein held a chair at the THM and was continued by his successor Walther von Dyck, who was appointed in 1884 at the age of twenty-seven.18 Von Dyck had been Klein’s pupil and remained a friend and confidant. It has been said that von Dyck played an analogous role in South Germany to Klein’s role in North Germany.19 Von Dyck wanted the THM to be an institution of high scientific merit as well as being tech­nologically oriented. He was able to call upon the support of mathematically sophisticated members of the more technical departments at Munich, such as August Foppl, who likewise had no time for the simple Praktikers.

Kutta was von Dyck’s teaching assistant and frequently took on his classes when von Dyck became involved, as he increasingly did, with running the THM. Kutta also worked with Sebastian Finsterwalder (1862-1951), who held a mathematics chair at the THM. Finsterwalder was significantly more ori­ented to applied work than von Dyck and has been called “der Prototyp des ‘Technik-Mathematikers’”—the prototype of the technologically oriented mathematician.20 As early as 1893 Finsterwalder was giving lecture courses on the application of differential equations to the problems of technology. He was also an aeronautical enthusiast and a member of the local ballooning club.21 It was Finsterwalder who suggested that the topic of Kutta’s Habili – tationschrift should be the mathematical analysis of the flow of air over an aircraft wing. This may be guessed from Kutta’s thanks to Finsterwalder, but the colleague who wrote Kutta’s obituary endorsed the point.22 He said that the stimulus for the chosen topic would, in any case, be clear:

das ist aber fur denjenigen auch klar, der die Jahre kurz nach 1900 im Ma – thematischen Intitut der T. H. Munchen miterlebte. Von Finsterwalders re­gem Interesse an den aerodynamischen Grundlagen der damals in den ersten Anfangen stehenden Luftfahrt wurden auch die jungeren Krafte am Institut angesteckt. Ich denke noch daran, mit welchem Interesse Photographien der ersten Fluge—heute wurde man bescheidener sagen: Sprunge—die Farmen mit seinem Aeroplan bei Paris ausfuhrte, studiert und ausgemessen wurden, Photographien, die Finsterwalder mitbrachte: es wird so 1906 oder 1907 ge – wesen sein. (50)

quite clear to anyone who had been at the Mathematical Institute at the TH Munich in the years after 1900. Finsterwalder’s avid interest in the aerody­namic basis of the first beginnings of aviation at that time also infected the younger people at the institute. I think of the interest with which the pho­tographs of the first flights—today one would more modestly say jumps— were studied and measured. These photographs of Farman with his airplane in Paris, which Finsterwalder brought back with him, would have been in 1906 or 1907.

Finsterwalder’s suggestion to Kutta must have been made some four or five years before the episode with the photographs recalled by Pfeiffer, and thus before the first powered flights had been made. At this earlier date Fin – sterwalder would have been preparing his chapter on aerodynamics for Felix Klein’s encyclopedia of the mathematical sciences.23 The aeronautical adven­tures that were attracting attention at that time were the experiments with hang gliders of the kind pioneered by the engineer Otto Lilienthal. Lilienthal had been killed in a flying accident in 1896 but had left a legacy of both en­thusiasm and information. The information was in his book Der Vogelflug als Grundlage der Fliegerkunst published in 1889.24 Kutta was explicit about the connection between his work and Lilienthal’s machines in both the 1902 account and the 1910 paper.25 The link is clearly evident in the circular arc that Kutta took as his representation of a wing profile. This was not only a mathematical simplification; it also corresponded to the profile used by Lilienthal.26

After his successful Habilitationschrift Kutta continued as teaching assis­tant in the TH Munich until 1907. He then became an extra-ordinary profes­sor (that is, an associate professor) in the same institution. In 1909 he moved on to become an extra-ordinary professor at the University of Jena, and in 1910 was appointed as an ordinary professor (a full professor) at the TH in Aachen. Finally in 1911, the year of his second paper on the circulation theory, he settled down as an ordinary professor at the TH in Stuttgart, where he stayed until his retirement. After his two papers on aerodynamics, in 1910 and 1911, he published nothing more, although he did not retire until 1935 and lived until 1944.