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.

Auch in der Wissenschaft wird die politische Rhetorik über- und die Verwaltung unterschätzt. Wissenschaftspolitik kann durch die Art, wie Verwaltung sie umsetzt, ruiniert werden. Der Bologna-Prozess ist ein beredtes Beispiel dafür. Verwalter, die sich, den Methoden des New Public Management folgend, auf  Indikatoren verlassen und so die Wissenschaft steuern, verfehlen ihre Aufgabe. Reflexive Verwaltung dagegen bedenkt die unausgesprochenen Voraussetzungen und unvorhergesehenen Wirkungen ihres Handelns, und kommt so ihrem verfassungsmäßigen Auftrag als vollziehender Gewalt nach, in der Demokratie eingehegt durch Parlament, Regierung und Rechtsprechung. Sie setzt auf eine verantwortungsvolle Haltung der Verwalter und auf deren Urteilskraft. In der Wissenschaft setzt sie auf Serendipity und schützt die Freiheit der Wissenschaftler, auch wenn sie allein ihrer Neugier folgen. Reflexive Verwaltung ist eine anspruchsvolle, erfindungsreiche Tätigkeit, die wesentlich zur wissenschaftsdienlichen Gestaltung öffentlich finanzierter Forschung beiträgt, im Interesse der Wissenschaftler, ihrer Institutionen und des Gemeinwohls.

Verwaltung ist keine Wissenschaft. Sie ist eine Kunstfertigkeit. Verwaltung gewinnt durch Wissen, Bildung, Einsicht, kritisches Denken und Geschmack, wird aber dadurch nicht zur Wissenschaft. Sie bedarf der Erfahrung und der Beispiele gelungener Verwaltung. Das Buch beschreibt solche Beispiele, häufig aus dem Umkreis des Wissenschaftskollegs zu Berlin. Sie zeigen, wie facettenreich diese Tätigkeit ist, insbesondere wenn Verwalter Institutionen gestalten. Sie sollen plausibel machen, dass die perversen Effekte quantifizierender Methoden vermeidbar sind – und dass Wissenschaftsverwaltung zu einer intellektuellen Leidenschaft werden kann.

This preprint is a glossary of uncertainty, closely connected to six specific case studies, which provides an insight into diverse uncertainties and coping methods that were historically discussed and practiced in China and Japan. When people encountered unknowingness or uncertainty in various historical periods, these endeavors were processed in ways that some called predicting, and others thought of as plans or ways to “think ahead”. Still other notions had a very particular character, so not all forms of accounting for and framing the not-yet-known were transferrable beyond an individual example or region. Yet what such forms of explanation often seem to have had in common was a wide range of material formats: in attempts to predict or plan, people may have been less concerned about truthfulness than they were with finding traceable patterns—seeking reliability in repetition.

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.

This article summarizes a historical perspective on the nation’s experience in the development of nuclear physics, with a special emphasis on its relationship with the Cuban Nuclear Program and the scientific and technological achievements attained as well as their social and economic impact. The development of nuclear energy and nuclear facilities requires the creation of specialized institutions, the training of professionals in the field, the structuring of interdisciplinary groups made up of nuclear physicists and specialists in theoretical and experimental physics, and engineers and specialists in other areas. This article also addresses the multiple peaceful applications introduced in Cuba, particularly those related to the scientific nuclear program.

The essay focuses on of the very first incunabulum herbal, printed in Rome by Philippus de Lignamine in 1482/83. It takes this incunabulum as a starting point for further reflections on the status of plant illustrations and their naturalism in herbals of the 15th and 16th centuries. Philippus’ intention was to edit a herbal of the so-called Pseudo-Apuleius tradition. For this, he used the schematized illustrations of a Pseudo-Apuleius manuscript he had previously discovered as patterns for the plant illustrations of his print. Philippus believed the manuscript to be a Roman antique herbal manuscript, but investigations by Hunger (1935) have shown that the manuscript was a ninth-century Pseudo-Apuleius copy. The essay asks for the reason of Philippus’ reuse of schematic plant pictures. It argues that at the end of the 15th century, the belief in the truthfulness of antique herbal texts was still as big as to stimulate Philippus to copy the presumed antique illustrations. There was an intense printing activity of treatises completely or partly dedicated to herbs during the last quarter of the 15th century, in Germany as well as in Italy. At the same time, however, herbal illustrations in manuscripts, during the last third of the 15th and the first third of the 16th century, were becoming far more naturalistic than prints and employed own means of picturing plants. The manuscripts also used pictorial patterns, but were more inventive in iconography during the first third of the 16th century, employing nature prints and dried plants, and therefore employed their own ways to convey knowledge on plants.