In developed symbolic algebra, from Viète onward, the handling of several algebraic unknowns was routine. Before Luca Pacioli, on the other hand, the simultaneous manipulation of three algebraic unknowns was absent from European algebra and the use of two unknowns so rare that it has rarely been observed and never analyzed. The present paper analyzes the three occurrences of two algebraic unknowns in Fibonacci’s writings; the gradual unfolding of the idea in Antonio de’ Mazzinghi’s Fioretti; the distorted use in an anonymous Florentine algebra from ca 1400; and finally the regular appearance in the treatises of Benedetto da Firenze. It asks which of these appearances of the technique can be counted as independent rediscoveries of an idea present since long in Sanskrit and Arabic mathematics, and raises the question why the technique once it had been discovered was not cultivated – pointing to the line diagrams used by Fibonacci as a technique that was as efficient as rhetorical algebra handling two unknowns and much less cumbersome, at least until symbolic algebra developed, and as long as the most demanding problems with which algebra was confronted remained the traditional recreational challenges.

This work offers an introduction to the history of scientific thought in the region between Iran and the Atlantic from the beginnings of the Bronze Age until 1900 CE—a “science” that can be understood more or less as a German Wissenschaft: a coherent body of knowledge carried by a socially organized group or profession. It thus deals with the social and human as well as medical and natural sciences and, in earlier times, even such topics as astrology and exorcism. It discusses eight periods or knowledge cultures: Ancient Mesopotamia – classical Antiquity – Islamic Middle Ages – Latin Middle Ages – Western Europe 1400–1600 – 17th century – 18th century – 19th century. For each period, a general description of scientific thought is offered, embedded within its social context, together with a number of shorter or longer commented extracts from original works in English translation.

The purpose of this manual is to provide an overview of one of the methods used to classify the books included in the “Sphaera database”: http://db.sphaera.mpiwg-berlin.mpg.de/resource/Start. A method used in libraries to catalogue an inventory of early modern printed texts has been slightly adapted for this purpose. The approach is based specifically on the process outlined in the EDIT16 database: http://edit16.iccu.sbn.it/web_iccu/ihome.htm.

The idea of gravitational collapse can be traced back to the first solution of Einstein’s equations, but in these early stages, compelling evidence to support this idea was lacking. Furthermore, there were many theoretical gaps underlying the conviction that a star could not contract beyond its critical radius. The philosophical views of the early 20th century, especially those of Sir Arthur S. Eddington, imposed equilibrium as an almost unquestionable condition on theoretical models describing stars. This paper is a historical and epistemological account of the theoretical defiance of this equilibrium hypothesis, with a novel reassessment of J.R. Oppenheimer’s work on astrophysics.

This paper presents six cases in ancient Greek cultures of knowledge, which make it possible to posit a connection between certain modes of presentation and institutional context. Among the texts looked at are the Hippocratic Epidemics, Aristotelian discourse, Hellenistic mechanics, and theoretical mathematics. While historical reconstruction of the institutional contexts involved is impossible, each of the cases leaves room for observations concerning an interdependence of knowledge-presentation and ‘setting’, understood as standard social context of reception. The paper describes resulting modes (collective, epideictic, school mode, how-to mode, analytical, and esoteric modes) as responding to and possibly emerging from certain contexts, but also as registers that later became per se possible choices for science writers, each catering to specific functions within the transmission and presentation of knowledge. With respect to Greek science, it remains an open question, whether and how one can separate a style of reasoning from a mode of presentation, that is, separate epistemic from rhetorical structures.

In this paper, the importance of the cosmographical activities of the Vienna astronomical “school” for the reception of the Tractatus de Sphaera is analyzed. First, the biographies of two main representatives of the Vienna mathematical/astronomical circle are presented: the Austrian astronomers, mathematicians, and instrument makers Georg von Peuerbach (1423–1461) and his student Johannes Müller von Königsberg (Regiomontanus, 1436–1476). Their studies influenced the cosmographical teaching at the University of Vienna enormously for the next century and are relevant to understanding what followed; therefore, the prosopographical introductions of these Vienna scholars have been included here, even if neither can be considered a real author of the Sphaera. Moreover, taking the examples of an impressive sixteenth-century miscellany (Austrian National Library, Cod. ser. nov. 4265, including the recently rediscovered cosmography by Sebastian Binderlius, compiled around 1518), the diversity of different cosmographical studies in the capital of the Habsburg Empire at the turning point between the Middle Ages and the early modern period is demonstrated.

Handwritten comments in the Vienna edition of De sphaera (1518) also show how big the influence of Sacrobosco’s work remained as a didactical tool at the universities in the first decades of the sixteenth century—and how cosmographical knowledge was transformed and structured in early modern Europe by the editors and readers of the Sphaera.

Four years prior to receiving the Nobel Prize, Albert Einstein pledged the prize money to his soon to be ex-wife Mileva to ensure her and their sons’ livelihood and to serve as an advance payment of the sons’ inheritance. With this money, Mileva Einstein bought three Zurich apartment houses in 1924 and in 1930. During the Great Depression in the 1930s, this investment plummeted in value. Thanks to Albert Einstein’s persistent financial efforts for over more than ten years, a small sum constituting the rest of the Nobel Prize capital was actually transferred to the sons, following Mileva’s death in 1948.

This paper discusses the origin of technical terminology in everyday language by outlining stages in a long-term history of technical terminology marked by increasing degrees of reflexivity. It uses the examples of spatial terminology in an ancient Chinese theoretical text, in Newtonian mechanics, and in relativity theory, and attempts to explain the increasing distance of the meanings of technical terms from their everyday counterparts by relating it to historical processes of knowledge integration.

The processes of long-term migration of physicians and scholars affect both the academic migrants and their receiving environments in often dramatic ways. On the one side, their encounter confronts two different knowledge traditions and personal values. On the other side, migrating scientists and academics are also confronted with foreign institutional, political, economic, and cultural frameworks when trying to establish their own ways of professional knowledge and cultural adjustments.

The twentieth century has been called the century of war and forced migration: it witnessed two devastating World Wars, which led to an exodus of physicians, scientists, and academics. Nazism and Fascism in the 1930s and 1940s, forced thousands of scientists and physicians away from their home institutions based in Central and Eastern Europe. “Did you ever go half way …” was a central question that all of them had to align with their personal consciousness, their family bonding, and the relationship to their academic peers. No one could leave without finding their individual answers to this existential question that lay at the bottom of their professional and scientific lives.

Following this general theme, the current special issue particularly reflects on the personal stories and institutional narratives of German-speaking scientists and physicians to North America since the 1930s, as a relevant case study from twentieth-century history of medicine and science. By drawing on diaries, questionnaires, institutional histories (including those of the Max Planck Society among others), novels, and personal estates, this special issue as a whole intends to emphasize the impact of forced migration from a North-American perspective by describing the general research topic; showing how the personal lives of many of these individuals were intertwined with their careers and choices of scientific topics, projects, and personal destinies. Moreover, this special issue seeks to explore whether new historiographical approaches can provide a deeper understanding of the impact of European émigré psychiatrists, psychologists, and cognitive scientists on emerging fields of medicine and science, including community and geriatric medicine, developmental neuroscience, and psychiatric traumatology to which the individuals in the respective cohort have strongly contributed in their new host countries.

The resources used for teaching at medieval universities became increasingly enriched by pictorial material, particularly during the fourteenth century. This work explores the epistemic function of pictorial material—images of science—in the context of medieval and early modern medicine, alchemy, and anatomy. The historical context is defined by the expansion in the thirteenth century of the spatial horizons of Western culture and the consequent need for a cultural identity, first expressed through the assimilation of the local European calendric systems. The regulation of time is determined as the first cause of the diffusion of pictorial material as an epistemic means of transcending the boundaries of learned scholarly circles, thereby enabling a broader access to knowledge. Originally based on a seminar delivered at the Cohn Institute for the History and Philosophy of Science and Ideas at the University of Tel Aviv by Matteo Valleriani, this work is the result of a science history exhibition supported by curator Yifat-Sara Pearl, for which students collaborated with artist and designer Liron Ben Arzi to further develop their research activities.

The exploration of Mesopotamian mathematics took its beginning together with thedecipherment of the cuneiform script around 1850. Until the 1920s, “mathematics in use” (number systems, metrology, tables and some practical calculations of areas) was the object of study – only very few texts dealing with more advanced matters were approached before 1929, and with quite limited results. That this situation changed was due to Otto Neugebauer – but even his first steps in 1927–28 were in the prevailing style of the epoch, so to speak “pre-Neugebauer”. They can be seen, however, to have pushed him toward the three initiatives which opened the “Neugebauer era” in 1929: The launching of Quellen und Studien, the organization of a seminar for the study of Babylonian mathematics, and the start of the work on the Mathematische Keilschrift-Texte. After a couple of years François Thureau-Dangin (since the late 1890s the leading figure in the exploration of basic mathematics) joined in. At first Thureau-Dangin supposed Neugebauer to take care of mathematical substance, and he himself to cover the philology of the matter. Very soon, however, both were engaged in substance as well as philology, working in competitive parallel until both stopped this work in 1937–38. Neugebauer then turned to astronomy, while Thureau-Dangin, apart from continuing with other Assyriological matters, undertook to draw the consequences of what was now known about Babylonian mathematics for the history of mathematics in general.

With only Apuleius and Augustine as partial exceptions, Latin Antiquity did not know Archimedes as a mathematician but only as an ingenious engineer and astronomer, serving his city and killed by fatal distraction when in the end it was taken by ruse. The Latin Middle Ages forgot even much of that, and when Archimedean mathematics was translated in the 12th and 13th centuries, almost no integration with the traditional image of the person took place. With the exception of Petrarca, who knew the civically useful engineer and the astrologer (!), fourteenth-century Humanists show no interest in Archimedes. In the 15th century, however, “higher artisans” with Humanist connections or education took interest in Archimedes the technician and started identifying with him. In mid-century, a new translation of most works from the Greek was made by Jacopo remonensis, and Regiomontanus and a few other mathematicians began resurrecting the image of the geometer, yet without emulating him in their own work. Giorgio Valla’s posthumous De expetendis et fugiendis rebus from 1501 marks a watershed. Valla drew knowledge of the person as well as his works from Proclus and Pappus, thus integrating the two. Over the century, a number of editions also appeared, the editio princeps in 1544, and mathematical work following in the footsteps of Archimedes was made by Maurolico, Commandino and others. The Northern Renaissance only discovered Archimedes in the 1530s, and for long only superficially. The first to express a (purely ideological) high appreciation is Ramus in 1569, and the first to make creative use of his mathematics was Viète in the 1590s.

Peter Fulde is not only one of Germany’s leading solid-state physicists but is prominent also due to his outstanding career, his general involvement in science, and the exceptional activities he undertook in organizing science in various circumstances. Fulde grew up in the eastern part of the country and went to the West as a student. He obtained his PhD in the United States and then returned to Germany to become full professor at the University of Frankfurt at the age of 32 and later director in various research institutes. He was a member of the German Science Council (Wissenschaftsrat), the board of the German Physical Society (DPG) and numerous other bodies. After the re-unification of Germany he returned to the East and built up the Max Planck Institute for the Physics of Complex Systems in Dresden. Finally, after his retirement in 2007, he followed a call to South Korea to head a similar institute there and eventually helped to establish a Korean analogue of the German Max Planck Society. The interview presented here follows the steps of his life. It was conducted on the occasion of his 80th birthday in April of 2016 and is supplemented by a curriculum vitae and by two brief accounts of his physics research and of his role in Dresden and Korea in the context of the Max Planck Society.

Around 1801 Louis-Bernard Guyton de Morveau (1737–1816) designed his famous fumigating machine. The machine spread a controlled emission of a specific gas—described as an oxygenated acid—that was supposed to destroy the contagious miasmas in the air, objects, and bodies. During the 1804 outburst of the yellow fever, the Spanish Government ordered that the original design of Guyton’s fumigating machine be adapted to the Spanish market for extensive use in households. This was done against some criticism, as the nature of the contagion was avowedly unknown and the acid fumigation technology polemic. Nonetheless, the machine was pictured as crucial for the health of individuals and for society as a whole.

The essay looks at the fumigating machine as a way of exploring how scientific and political practices pervaded societies and, vice-versa, how ways of interpreting nature and politics became embedded in artifacts. It will show, first, how the machine served to spread the new French chemistry among Spaniards; second, how it embodied a new relationship between the citizens and the state, and third, how this artefact was imported by the Spanish absolutist state, appropriated, and used for political propaganda. By focusing on a chemical artefact, it shows a historically complex and significant interweaving of theory, material culture, and politics.

Erich Kretschmann (1887–1973) was a German theoretical physicist whose work on Einstein’s General Theory of Relativity (1917) offered some interesting insights, but was also critical of Einstein’s semantics. Einstein responded in a paper in 1918 and agreed that Kretschmann’s criticism was valid. Kretschmann wrote his thesis under the supervision of Max Planck and obtained his doctorate in 1914. A psychiatric disease during his adolescence made him permanently unfit for military service and saved him from having to participate in the First World War. From 1920 he lectured in theoretical physics at the University of Königsberg. In 1926 he became an apl. professor, a position which he held until 1945. After his escape from Königsberg in January 1945 he found temporary accommodation at Rendsburg, Schleswig-Holstein. In 1946 he was appointed as a full professor of theoretical physics at the Martin-Luther-Universität Halle.

When the Federation of German Scientists (VDW) was founded as the West German section of Pugwash in the late 1950s, several high-profile scientists from the Max Planck Society (MPG), especially nuclear physicists, were involved. Well into the 1980s, institutional links existed between the MPG, the Federal Republic’s most distinguished scientific research institution, and Pugwash, the transnational peace activist network that was set up in 1957 in the eponymous Nova Scotia village following the Russell-Einstein Manifesto. In the beginning, the two organisations’ relationship was maintained primarily by the physicist and philosopher Carl Friedrich von Weizsäcker. However, it was difficult right from the start, and the distance between them grew during the rise of détente in the 1970s, when the scientific flagship MPG was deployed more and more frequently in matters of foreign cultural policy, not only for the FRG but for the western alliance as a whole. This contribution explores the resources and the risks of transnational political engagement – not only as the individual strategies of top-ranking researchers, but also in terms of policy deliberations within a leading scientific organization at one of the Cold War’s sharpest divisions: the front line between two Germanys.

This paper is the translation by Giampiero Esposito of a paper originally published in French in Acta Mathematica 88, 141-225 (1952) under the title: Théorème d’existence pour certains systèmes d’équations aux dérivées partielles non linéaires. The first three chapters are devoted to the solution of the Cauchy problem, in the nonanalytic case, for a system of nonlinear second-order hyperbolic partial differential equations with n unknown functions and four independent variables. This task is accomplished in chapter III by using the system of integral equations fulfilled by the solutions of partial differential equations that approximate the original nonlinear system. In chapter IV, such results are applied to the vacuum Einstein equations. The resulting Ricci-flatness condition is expressed, in isothermal coordinates, through nonlinear equations of the kind studied here. It is hence proved that the solution of the Cauchy problem, pertaining to such nonlinear equations, satisfies over the whole of its existence domain the isothermal conditions if the same is true for the initial data. One therefore obtains a solution of the vacuum Einstein equations which is unique up to a coordinate change.

According to the topos “Ende der Naturgeschichte” (Foucault, Lepenies) a veritable historical understanding of Nature came into being around 1800. The contribution re-considers this thesis and discusses in particular the historical speculations in deistic cosmologies as well as in the context of the idea of a “Great Chain of Beings.” Finally attention is drawn to the implications of the fact that the then new physiological understanding of development (ontogenesis) as an epigenetic process became a naturalistic model of historical development in general just in this period.