# Research projects

Our group hosts a variety of research projects. Click on the titles to read more!

## Big Mathematics? The Classification of Finite Simple Groups, 1950s to 1980

PIs: Volker Remmert and Rebecca Waldecker (Mathematics Dept., University of Halle)

The Classification of Finite Simple Groups (CFSG), also known as the enormous theorem, is a highlight of 20th-century mathematics, both with respect to its mathematical content and to the complex process of proving the result. From a historical perspective, it offers an excellent opportunity to focus on more general developments in the history of 20th-century mathematics, such as changing perceptions of what a mathematical proof is, the character and the many contexts of mathematics as an intergenerational and international collaborative enterprise, the roles that trust and consensus play within this enterprise, and the impact of Cold War research policies on CFSG/pure mathematics. We consider the CFSG as (possibly) the first instant of what we tentatively call big mathematics in this project (a concept to be critically discussed within the framework of the project).

The existing proof of the CFSG is estimated to be spread on somewhere between 10.000 and 15.000 journal pages in ca. 500 separate articles written by more than 100 mathematicians. The unprecedented nature of this enterprise from the 1950s until the 1980s is quite tangible: the extraordinarily large number of mathematicians involved internationally (working as a team), the difficulty and complexity of the problem, the use of computers within the proof, the repercussions for the mathematical community, the effect of the Cold War on CFSG/pure mathematics (e.g. via new funding possibilities by both civil and military agencies).

Our overall long-term goal is to thoroughly analyze the history of the CFSG and use it as a magnifying glass allowing to draw general conclusions not only about the history of mathematics and the mathematical community in the context of the Cold War. In particular the history of CFSG has to be studied as a key example of the impact of politics on research in pure mathematics in the Cold War, namely via new possibilities of funding research in general and of mathematical research in particular, a largely unexplored territory, but crucial for CFSG.

The historical analysis will be guided by three themes: suitability of big mathematics as an analytical concept, the role of self-historicization in CFSG, and the changing nature of proof in mathematics in the second half of the 20th century.

## Political crises and disciplinary development. Mathematics in Germany, 1920-1960

PIs: Volker Remmert and Thomas Heinze (Sociology Dept., Wuppertal)

The project focuses on the history of mathematics in Germany between 1920 and 1960, a period characterized by political crises (Weimar period: 1920-1933, Nazi period, 1933-1945, postwar period: 1945-1960), with special attention to internal disciplinary developments as well as institutional dynamics and human resources. Based on a prosopographic-bibliometric database, which will be provided via an open access website, the project aims at a detailed mapping of mathematics within the German university system from a combined perspective of history of science and sociology of science.

The project will offer answers to questions of who has worked when on what subjects in collaboration with whom in specific research fields. This will allow to map specific subdisciplinary fields as well as the role of mathematics as a transdisciplinary resource. From a theoretical point of view, the project draws on concepts from historical institutionalism which seems particularly suited to exploring gradual-cumulative changes in the context of political crises. In this framework, we will probe several hypotheses, including that during national socialism abstract subfields of mathematics were substituted with “war-related” fields (displacement) and more applied fields were supported with targeted funding (layering). In addition, we will examine whether military patronage during the Cold War has led to a focus on particular research fields within mathematics (drift).

In methodological terms, the project connects a dedicated archive-based prosopographic approach with bibliometric analyses. This double approach will allow both to systematically charter the historical and institutional development of mathematics and to develop and test a research tool that can be transferred to other disciplines and periods. In this way, the project is conceived as a model project, because its open access repository is conceptualized as a generally available tool for future projects.

## Iconography of Early Modern Scientific Instruments

PI: Volker Remmert

During the Scientific Revolution scientific instruments, such as astrolabes, air pumps, microscopes and telescopes became increasingly important for the study of nature. In the early modern period they had not yet reached the status of standardized and impersonal means to study nature. Rather they usually were unique items, which by their function as well as their design could serve the mediation between scholars, social elites and beyond. In this context the iconography on the instruments played a crucial role. In fact, a great number of early modern instruments are adorned with images, that in themselves have no relevance for the use of the instruments, as for instance the depiction of Atlas and Hercules on an astrolabe by Praetorius (1568, Dresden) or the line of tradition in astronomy and geometry on Bürgi’s astronomical clock (1591, Kassel) stretching from the church fathers to Copernicus. As of now such imagery on instruments and its contexts have only sporadically been analysed.

The project Iconography on early modern scientific instruments specifically analyses the imagery on the instruments. It aims for the first time at a systematic analysis of the multifaceted visual material on the instruments asking for its role in the various contexts of the adorned instruments (genesis, function, use) and its importance for setting up or supporting stories/histories of success and relevance within the emerging field of the sciences. The iconography points to quite a few significant topics as, for instance, statements of specific positions in theoretical debates (e.g. Copernican question), mediation and illustration of knowledge, in particular by picturing the usability of the instruments, or the role of instruments as patronage artefacts with specific iconographic programmes.

The analysis of the imagery is likewise highly relevant in order to understand the intellectual, cultural and artistic contexts shaping and determining the production of instruments in the early modern period. It opens a window on the investigation of collaborative processes during the conception, design and construction of instruments in the multi-layered field between instrument makers, artists, artisans, patrons and scholars.

## The Oberwolfach Research Institute for Mathematics, 1944-1963: From „National Institute for Mathematics“ to an international „social infrastructure for research“

PI: Volker Remmert

The Oberwolfach Research Institute for Mathematics (Mathematisches Forschungsinstitut Oberwolfach/MFO) has been a member of the Leibniz Association since 2005 and is internationally highly renowned. Founded in late 1944 by the Freiburg mathematician Wilhelm Süss (1895-1958) as „Reichsinstitut für Mathematik“, in the 1950s and 1960s the MFO developed into an increasingly international conference centre. While the history of its foundation has been analysed the development after 1945 has scarcely been touched on by historians of mathematics/science.

The project aims at filling this gap, namely to analyse the history of the MFO as it institutionally changed from a projected National Institute for Mathematics with a wide, but standard range of responsibilities to an international social infrastructure for research. That was completely new in the framework of German academia. The project focusses on the evolvement of the institutional identity of the MFO between 1944 and the early 1960s, namely the development and importance of the MFO’s scientific programme (workshops, teamwork, Bourbaki) and the instruments of research employed (library, workshops) as well as the corresponding strategies to safeguard the MFO’s existence (for instance under the wings of the MGP). These topics are closely connected to the topic of the perception of mathematics in the public and political realms in the 1950s and 1960s.

The year 1963 marks the end of the project as in 1963 the MFO’s directorship was handed over from Theodor Schneider (1911-1988) to Martin Barner (1921-2020, director 1963-1994). At this point the MFO was basically institutionally secured. In the methodological framework of the analysis of the development of a new and permanent institutional identity of the MFO three aspects will be key to the project, namely the analyses of the historical processes of (1) the development and shaping of theMFO’s workshop activities, (2) the (complex) institutional safeguarding of the MFO, and (3) the role the MFO played for the re-internationalisation of mathematics in Germany. Thus, the project opens a window on topics of more general relevance in the history of science such as the complexity of science funding and the re-internationalisation of the sciences in the early years of the Federal Republic of Germany.

## Putting Invisible Science on Stage. Mathematics Communication in the 19th and 20th Centuries

PI: Maria Remenyi

In the last decades the vivid public discourses on various scientific contents during the 19th and early 20th century have often been discussed and analysed. Although the important role of mathematics as a cross-disciplinary resource for science and technology is widely accepted, historians and sociologist of science until now have scarcely analysed the representations of mathematics in the above-mentioned public discourses. The project fills this gap by exploring and interpreting mathematical contributions on the basis of a representative selection of books and magazines communicating science in the period from about 1880 to 1960. The investigation takes into account three epistemic dimensions, which are the history of media, the history of science and the sociology of science. The projected monograph will argue in four chapters.

Chapter 1 describes the special epistemic status of mathematics as a scientific discipline and discusses advantages and disadvantges of its role as an indispensable cross-disciplinary resource.

Chapter 2 is devoted to some relevant aspects of the history of media. It discusses mathematical authors, publishers and contents in context of the formation and development of science communicating print media.

Chapter 3 stresses the history of science aspect by highlighting contexts of the history of mathematics and associated aims of mathematics communication.

Last but not least, chapter 4 deals with issues of mathematical knowledge transformation related to science communication as a subject of the sociology of science.

Overall, the monograph illuminates the role of the investigated media in shaping longlasting self- and public images of mathematics.

## The History of the Society of Applied Mathematics and Mechanics

PIs: Volker Remmert and Moritz Epple

The project lays the foundations for the exploration of the History of the Society of Applied Mathematics and Mechanics (GAMM) and its Journal of Applied Mathematics and Mechanics (ZAMM). The period under consideration extends from the founding in the early 1920s to the Cold War Era. After the First World War the practical benefits of Applied Science were obvious. The institutionalization of Applied Mathematics and Mechanics, however, was accompanied by scientific and political conflicts: Especially the demarcation from Mathematics turned out to be difficult. Questions concerning the history of its origin, its special transdisciplinary character, and the political and scientific relations in East and West during the Cold War are the focus of interest.