Reinhard Siegmund-Schultze

The late arrival of academic applied mathematics in the United States: a paradox, theses, and literature

The article discusses the “paradox of the late (around 1940) arrival of academic applied mathematics in the U.S.” as compared to Europe, in particular Germany. A short description of both the indigenous traditions in the U.S. and (in some more detail) of the transfer of scientific ideas, persons, and ideals originating in Europe, particularly in Germany, is given, and some theses, relevant literature, and a tentative solution of the “paradox” are provided.

Military Work in Mathematics 1914–1945: an Attempt at an International Perspective

After discussing some general methodological points this paper investigates in some detail the use of mathematics (not necessarily confined to academic mathematicians) in military work in the German and American cases, where as of now most knowledge is available. With respect to five other countries (Soviet Union, Great Britain, Italy, France, Japan) the discussion has to be restricted to a rough outline of problems and a collection of the rather scattered sources available. A case study is presented of mathematical war work in ballistics (Wolfgang Haack) which illustrates the complexity of the problems involved and the short distance between basic academic research and applied work for the military. The paper is concluded by appendices (tables) giving condensed information on mathematical war work in the seven countries considered.

Dealing with the political past of East German mathematics

ConclusionsIncomplete though my remarks may be, I hope I have been able to show the following:Looking at the early political history of mathematics in the GDR, it is pointless to differentiate between “good mathematicians” and “bad politicians.” Mathematicians sometimes quite unexpectedly find that circumstances compel them to act politically to make mathematics. Their moral judgments, therefore, have always to consider both domains, mathematics and society as a whole. A reliable picture of the history of mathematics in East Germany has to combine domestic political constraints, international relations, and, last but not least, the individual and collective interests of mathematicians. The political history of mathematics in the GDR#x2014;yet to be written—will be a new occasion to discuss the political and social responsibility of mathematicians in the modern society.

From “Mixed” to “Applied” Mathematics: Tracing an important dimension of mathematics and its history

The workshop investigated historical variations of the ways in which historically boundaries were drawn between ‘pure’ mathematics on the one hand and ‘mixed’ or ‘applied’ mathematics on the other from about 1500 until today. It brought together historians and philosophers of mathematics as well as several mathematicians working on applications. Emphasis was laid upon the clarification of the relation between the historical use and the historiographical usefulness and philosophical soundness of the various cate-

Emigration of Mathematicians and Transmission of Mathematics: Historical Lessons and Consequences of the Third Reich

This conference provided a focused venue to explore the intellectual migration of mathematicians and mathematics spurred by the Nazis and still influential today. The week of talks and discussions (both formal and informal) created a rich opportunity for the cross-fertilization of ideas among almost 50 mathematicians, historians of mathematics, general historians, and curators. Mathematics Subject Classification (2000): 01A60. Introduction by the Organisers The talks at this conference tended to fall into the two categories of lists of sources and historical arguments built from collections of sources. This combination yielded an unexpected richness as new archival materials and new angles of investigation of those archival materials came together to forge a deeper understanding of the migration of mathematicians and mathematics during the Nazi era. The idea of measurement, for example, emerged as a critical idea of the conference. The conference called attention to and, in fact, relied on, the seemingly standard approach to measuring emigration and immigration by counting emigrants and/or immigrants and their host or departing countries. Looking further than this numerical approach, however, the conference participants learned the value of measuring emigration/immigration via other less obvious forms of measurement. 2892 Oberwolfach Report 51/2011 Forms completed by individuals on religious beliefs and other personal attributes provided an interesting cartography of Italian society in the 1930s and early 1940s. Observing the length of time a Minister of Education in Spain remained in office over three-quarters of a century provided a unique assessment of the educational and scholarly values (or lack thereof) in Spain before, during and after World War II. Mapping the geographical paths followed by refugees on a single globe and looking for patterns offered still further insight into how mathematicians and mathematics traveled. For all these proactive forms of measurement, one speaker urged participants to use caution when measuring emigration and immigration in terms of gain and loss. Measuring the anguish of physical emigration in the form of a painting, such as Frans Henriques’ “Travel to Sweden. October 1943,” provided a distinctly human evaluation of this moment in history and highlighted another meaningful insight from the conference. As one speaker put it, “this was an intensely personal moment in history.” In the words of a Jewish mathematician of the time, “sudden and arbitrary unemployment was the first step to serious personal catastrophe.” At this “moment in history,” personal and professional lives were inextricably linked. The talks and discussions underscored the role of choice in emigration and immigration. Here again, the conference called attention to more obvious forms of choice in the form of, say, the choices of Karl Menger to leave Austria or Emil Artin to leave Germany. Those individual choices, however, depended on institutional choices in the host countries. Other talks pointed out the more subtle choices of Arnold Scholz that ultimately prevented his emigration from Germany or the lingering choices of university officials that resulted in disastrous consequences for mathematicians hoping to immigrate. Economic interests sometimes motivated these administrative choices and yielded their own consequences. From the outset, the conference organizers placed an especial emphasis on gaining a better understanding of refugees from countries other than Germany. A collection of talks on issues related to emigration and immigration in Czechoslovakia, Hungary, Poland, Spain and Denmark (“a temporary refuge”) helped achieve this aim. Even better, many of these talks were prepared and presented by young scholars in the field. The 46 conference participants came mainly from Europe and North America, among them five young researchers who participated as Oberwolfach Leibniz Graduate Students. The organizers are very grateful to the Leibniz-Gemeinschaft for this support. The staff of the Mathematische Forschungsinstitut Oberwolfach was—as always—extremely supportive and helpful. We thank them for providing excellent working conditions. The conference participants especially appreciated the interesting mix of people and talks we enjoyed during our week at the MFO. The last talk of the conference discussed the difference between one grain, one pile, and one heap of rice and raised The Danish title of Henriques’ 1952 painting is “Rejsen til Sverige. Oktober 1943.” The organizers would like to thank Henrik Kragh Sörensen for calling attention to this painting in his talk and for providing a translation of the title. Emigration of Mathematicians and Transmission of Mathematics 2893 the critical question of how one moves from the pile to the heap. This conference allowed participants to add to the pile, but not quite reach the heap, in terms of our understanding of migration and immigration in the Nazi era. Continued conversations and investigations will add to this perpetual progress. Finally, the organizers would like to thank the reporter, Craig Stephenson, for his excellent work with the abstracts which is evident in the coherence of the report and which was much appreciated by the authors. Emigration of Mathematicians and Transmission of Mathematics 2895 Workshop: Emigration of Mathematicians and Transmission of Mathematics: Historical Lessons and Consequences of the Third Reich

Richard von Mises

Von Mises was principally known for his work on the foundations of probability and statistics (randomness) which was rehabilitated in the 1960s. He founded a school of applied mathematics in Berlin and wrote the first textbook on philosophical positivism in 1939.

Emmy Noether – „das Experiment, eine Frau zum Ordinarius zu machen“

Der Artikel legt dar, mit welchen Argumenten Emmy Noethers Kollegen Adolf Fraenkel und Helmut Hasse  ihre mögliche Berufung nach Kiel ausschlossen. Neben teilweise gerechtfertigten aber scheinheiligen Zweifeln an Noethers Eignung für elementarmathematische Vorlesungen waren es anscheinend selbstbezogene Minderwertigkeitsgefühle auf Fraenkels Seite und generelle Vorurteile gegen Frauen im akademischen Bereich bei Hasse.

“Not in Possession of Any Weltanschauung”: Otto Neugebauer’s Flight from Nazi Germany and His Search for Objectivity in Mathematics, in Reviewing, and in History

Two major factors have to be considered to account for Neugebauer’s “Weltanschauung”, in particular his apparent or real rejection of philosophical or political judgments. On the one hand, Neugebauer, as a mathematician and a historian, had to cope, with the double character of mathematics as a science in its continuity and universality, independent of time, and of mathematics as a characteristic and fundamental product of each individual culture. On the other hand emphasis has to be put on Neugebauer being torn between organizational work (institution building, reviewing, editing) and historical research. One has to consider the vicissitudes of Neugebauer’s long and eventful life, which was highlighted by a series of highs and lows and marked by many contradictory, often frustrating and sobering political experiences, mainly connected to repeated emigration.

Weierstraß’s Approximation Theorem (1885) and his 1886 lecture course revisited

The paper provides new insight into the origins of Weierstras’s 1886 lecture course on the foundations of function theory and of the mimeographed lecture notes connected to this course which were published by the author in German in 1988. A short overview of the content of the lecture course is given; the central role that Weierstras’s famous approximation theorem of 1885 played in it is emphasized. The paper uses archival material recently discovered at the Institut Mittag-Leffler in Djursholm.

Pulling Harriot Out of Newton’s Shadow: How the Norwegian Outsider Johannes Lohne Came to Contribute to Mainstream History of Mathematics

The focus of this paper is on the peculiarities of Lohne ’s “outsider approach” to the historiography of mathematics and physics. The main thesis is that the circumstances of Lohne ’s outsider position both narrowed down and sharpened the focus of his research, but that he succeeded because he joined the then rising tide of archival based and content oriented internalist research in the history of physics and mathematics and because he was supported by scholars such as D.T. Whiteside and J.E. Hofmann , whose connections to the international community were better than his own. The main conclusions are based on Lohne ’s Nachlass in Oslo and on some other archival sources. In addition Lohne ’s publications are used, which were mostly in English and German, and partly in Norwegian. We do not, however, discuss Lohne ’s contributions to the historiography of mathematics and physics in any detail, because they are published and accessible. We merely sum up two outstanding results of Lohne ’s research on Thomas Harriot (1560–1621), concerning the discovery of the sine law of light refraction and the calculation of the Mercator map, in order to stress the quality of his work and his critical mind and to give some idea about his historical method. Concluding the paper we reflect once again, on the basis of our biographical evidence in the case of Lohne , and with some emphasis on Scandinavia, on the relative notions of the “outsider” and the “main stream” within the process of professionalization of the historiography of mathematics and sciences in the second half of the 20th century.