The borrowing registers of university libraries represent ‒ especially for the history of science ‒ a new source genre and thus a new approach. They enable to reconstruct the decisive influences and stimuli on scientists working at the places in question. In this article, this is exemplified by the Göttingen mathematician Bernhard Riemann (1826–1866), who, apart from a few stays abroad, lived and worked almost exclusively in Göttingen. In the first section, the Göttingen University Library borrowing registers are introduced and the most important previous book-historical publications related to them are presented. In the second section, I first describe how and why I came to examine these registers with reference to Riemann, and present in the following some new results regarding the genesis of Riemann’s groundbreaking philosophical as well as mathematical ideas. I conclude with an unaltered photomechanical reproduction of Riemann’s book and journal borrowings from the Göttingen University Library, as I extracted and compiled them quite some time ago without the use of digital tools. The definitive edition of this article will be published in an appropriate journal for the history of science after having been revised and then translated into English in post-Covid times, with further consultation of the originals in Göttingen. For the convenience of English-speaking readers, a work-in-progress English version of this preprint can be obtained from the author.

The remarkable degree of accuracy with which some of the Old Kingdom pyramids are oriented towards the cardinal directions is one of the most challenging problems in the history of science. The progressive deviation of the orientation of the 4th Dynasty pyramids from true north was long understood to be a consequence of the pyramids having been aligned to a star whose celestial position changed due to the effect of the general precession of the rotational axis of the Earth. Instead of a single star, recent proposals considered a possible orientation towards some notable vertical or horizontal stellar configurations. The main idea behind these recent attempts at explanation was to justify the gradual deviation of the pyramid alignments by way of the selected target stellar configuration exhibiting a similar azimuthal trend. Considering conventional Egyptian chronologies of this period to be only relative, and the astronomically determined data to be fully reliable, the researchers tried to make the two trends match perfectly by shifting the conventional Old Kingdom chronologies by some, often significant, number of years. Too little attention, however, was paid to allowing for systematic and random errors in the surveying of stars and in the orientation of pyramids towards the observed asterism, which may obfuscate the real accuracy of the methods and conceal the actual targets of observations. In this text, we consider recent proposals and analyze their errors. We propose and discuss two new solutions whose systematic errors are minimal among all the known proposals: one based upon the horizontal alignment of Alioth and Mizar, and another one upon the vertical alignment of Kochab and ζ UMi. In contrast to other methods, the latter pair has the advantage that it could have been observed at lower altitudes. Both variants show an impressive degree of agreement with the trend in the orientation of the pyramids for von Beckerath’s (lower estimates) as well as for Baines and Malek’s chronologies of the period. It appears to us that the preserved Egyptian astronomical diagrams are fully consistent with our new proposals.

The following collects observations I made during the reading of Fibonacci’s Liber abbaci in connection with a larger project, “abbacus mathematics analyzed and situated historically between Fibonacci and Stifel”. It shows how attention to the details allow us to learn much about Fibonacci’s way of working. In many respects it depends critically upon the critical edition of the Liber abbaci prepared by Enrico Giusti and upon his separate edition of an earlier version of its chapter 12 – not least on the critical apparatus of both. This, and more than three decades of esteem and friendship, explain the dedication.

Vortrag im Rahmen der Ringvorlesung der International Max Planck Research School „Knowledge and Its Resources: Historical Reciprocities“, 17. Februar 2022:
Wenn man Wissen als Ressource bezeichnet oder von den Ressourcen des Wissens spricht, als handele es sich um Stoffe, über die man verfügen kann, übersieht man allzu leicht die komplexen und dynamischen Strukturen, die die Geschichte des Wissens charakterisieren. In meinem Vortrag möchte ich diese Strukturen näher beschreiben, und zugleich die zentrale Rolle deutlich machen, welche die Wissensgeschichte als Teil der Gattungsgeschichte für die kulturelle Evolution und für unsere Zukunft im Anthropozän spielen kann.

This introduction to historical epistemology offers a general overview of the main themes, debates, and currents of this multifaceted field, which has emerged at the intersection of the philosophy of science and the history of science. The authors offer a historical reconstruction of the main debates that forged historical epistemology and assess today’s challenges. Additionally, they provide the reader with the conceptual and methodological tools that are necessary to enter this field and understand its main questions and approaches. This preprint is in Italian and available in print form only.

The pioneering work, Scienza e Industria 1848–1915: Gli sviluppi scientifici connessi alla seconda rivoluzione industriale (Science and Industry 1848–1915: Scientific developments related to the second industrial revolution) by Angelo Baracca, Stefano Ruffo, and Arturo Russo is reproduced in this preprint. Published in Italian by Laterza in 1979, it is an unjustly forgotten treasure of a highly fertile and innovative period of the history of science. The introduction to the preprint describes the historical circumstances in which this book and the approach it proposes emerged. It covers a wide range of subjects, from the different ways in which the Second Industrial Revolution unfolded in Great Britain and in continental Europe to the upheaval in modern science, in particular in chemistry in the latter half of the nineteenth century and in physics at the beginning of the twentieth century. Although each of these themes has meanwhile become the subject of detailed historical investigations, the survey and overall picture that Scienza e Industria provides is still intriguing: it connects the new knowledge economy of the Second Industrial Revolution with the conceptual revolutions in modern physics by pointing to the mediatory role of chemistry.

The present article continues an earlier analysis of occurrences of two algebraic unknowns in the writings of Fibonacci, Antonio de’ Mazzinghi, an anonymous
Florentine abbacus writer from around 1400, Benedetto da Firenze, and another anonymous Florentine writing some five years before Benedetto, and Luca Pacioli.
The following article investigates how Benedetto da Firenze explores in 1463 the use of four or five algebraic unknowns in symbolic calculations, describing it afterwards in rhetorical algebra; in this way he thus provides a complete parallel to what was so far only known from Johannes Buteo’s Logistica from 1559. It also discusses why Benedetto may have seen his innovation as a merely marginal improvement compared to techniques known from Fibonacci’s Liber abbaci, therefore omitting to make explicit that he has created something new.

Die Rolle wissenschaftlicher Expertinnen und Experten in der Corona-Krise ist wiederholt kritisiert worden, insbesondere von geisteswissenschaftlicher Seite.  Ein Hauptvorwurf, der auch an die Adresse der Nationalen Akademie der Wissenschaften Leopoldina gerichtet ist, lautet, wissenschaftliche Experten seien anmaßend, wenn sie als politische Berater mit ihrer wissenschaftlichen Kompetenz und mit Sachzwängen argumentieren. Die Brisanz des Arguments wird noch durch die Behauptung zugespitzt, der wissenschaftliche Experte benötige für seine politische Beraterrolle besondere persönliche Qualitäten, für die ihm die Wissenschaft kein Rüstzeug liefere. Diese Mystifizierung der Figur des Experten dient dann als Rechtfertigung eines vorgefassten, tiefsitzenden Skeptizismus gegenüber naturwissenschaftlichem Spezialistentum und Expertise. Ein Rückblick in die Geschichte entzieht dieser Mystifizierung die empirische Grundlage. Die Geschichte zeigt: Experten oder „Sachverständige“ zeichnen sich vor allem durch praktisch relevantes, empirisches Wissen aus, das im technischen Umgang mit „Sachen“, Experimente eingeschlossen, erworben wurde; diese Sachkompetenz war meist der ausschlaggebende Faktor für ihre Beratertätigkeit. In der anschließenden Diskussion des Begriffs Sachzwang argumentiere ich gegen die weit verbreitete Ansicht, Sachzwänge seien technokratische Totschlagargumente.  Das Argumentieren mit Sachzwängen legt nur offen, welche Konsequenzen und Handlungsoptionen sich aus vorhandenem Sachwissen ergeben, es impliziert jedoch keine Normen und damit auch keine Vorabentscheidung über Handlungsziele.

The role of experts in the recent corona crisis has often been criticized, especially by scholars from the humanities. A major objection is that experts claim their political advice is based on scientific knowledge and that related constraints are presumptuous. The objection—addressed also to the German National Academy of Science—is accompanied by the argument that the advisory role of scientific experts presupposes certain personal qualities of the expert that cannot be acquired in the scientific community. This mystification of the figure of expert then serves as justification for preconceived general skepticism toward scientific expertise. The historical part of this paper shows that experts have long been recognized as persons with outstanding empirical knowledge acquired in technical activities, including experimentation; their role as political advisors is based primarily on the fact that this kind of knowledge is recognized as practically useful knowledge. The historical figure thus does not lend itself to mystifying definitions. The historical part is complemented by a discussion of the concept of natural and technical constraints of actions (Sachzwänge). I argue that this kind of knowledge neither implies norms nor goals of action. Hence it always leaves open different possibilities of action.

Turning everyday ordinary happenings into struggling moments for existence—from breathing to socializing—is how the Covid-19 pandemic will mark history. What we ask here is not how the ordinary becomes abnormal but how it becomes political and diplomatic.  We argue that the spread of the Covid-19 virus, which is measured through virologic and epidemiological models, overlaps with feverous diplomatic and political activities taking place among big geopolitical powers. Yet, this is not new in history of health. The first encounters between diplomats and health professionals were elicited by the social and economic challenges caused, on a global scale, by the cholera epidemics of the nineteenth century. Indeed, health sciences and diplomacy have been historically co-produced. Such a historical perspective on science and health diplomacy facilitates our understanding of international institutions such as the World Health Organization as highly political and diplomatic endeavors. The Diplomatic Studies of Science, a new interdisciplinary research field underpinned by a historical perspective on science diplomacy, sheds light on the multiple factors contributing to the worsening of the global COVID-19 crisis we are facing nowadays.

The Tacuinum sanitatis is a genre of illuminated medical texts from the Late Middle Ages that contains an intriguing and surprising combination of theoretical knowledge and lavish, detailed, and colorful images. By exploring a specific manuscript of this genre, and by comparing it with related practical medical texts and genres, this study wishes to better understand the different aspects of this text and explain this combination. The Late Middle Ages are traditionally thought of as a time of stagnation in the history of science and particularly in the history of medicine. However, in recent decades historians have observed the long-term intellectual and social evolutions of the Middle Ages and have demonstrated the ways in which these changes formed the grounds for the great achievements of the sixteenth century. These evolutions include the translations and dissemination of Greek and Arab knowledge traditions in the Latin West, the establishment of universities, the formation of a medical market and the medicalization of society, and the formation of new audiences for practical and theoretical medical texts. The arts were also heavily influenced by the rise of naturalism and natural study from direct observation, for example. This study demonstrates how a singular text can be linked to major historical evolutions and how a text of this sort can function as a historical source, shedding light on the major intellectual and artistic shift between the Middle Ages and the Renaissance.

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.