Periodic Reporting for period 1 - ARITHMETIC (German Arithmetical Treatises in Manuscripts of the Late Middle Ages (1400-1522). A Study on Philology, History and Culture based on a Digital Edition of the Treatises.)
Reporting period: 2022-09-01 to 2025-02-28
How was the practice of arithmetic developed and spread during the transition between the Middle Ages and the Modern Period? We know a lot about the evolution of mathematical theory and its diffusion in Latin, but little about the way in which arithmetic knowledge spread in the vernaculars in the 15th and early 16th centuries. Translation and adaptation of arithmetic treatises and manuals provided access to mathematical knowledge for new groups of people, shaped the practices of reckoning, and opened new ways of teaching arithmetic skills to persons without higher education. These efforts also endowed European vernaculars with new linguistic forms of abstraction and thus enhanced their potential to serve as a tool in the modern scientific revolution.
ARITHMETIC will study handwritten German arithmetic treatises from their first appearance around 1400 until the time when printed reckoning-books became easily available at the beginning of the 16th century. These texts have not been studied before, although they are important witnesses of the vernacularization of mathematical knowledge, of the interdependence of vernacular and Latin pragmatic literacy and of the links between mathematics, sciences, and commerce.
German mathematical manuscripts of the Late Middle Ages have hardly been studied yet, neither from a historical nor from a philological perspective: But the first handwritten German mathematical treatises already appeared around 1400. These treatises are not just proof that a vernacular mathematical tradition emerged early, they can also inform us on aspects relevant for several fields of research.
The Project wants to answer the following main questions:
• How does mathematical knowledge emerge, circulate, and change in a vernacular European context and what role do advancements in trade, other sciences, and social changes play?
• How did a mathematical and didactical jargon develop in the vernacular out of a Latin tradition?
• How does the underlying orality of instructive/pragmatic texts shape these treatises?
• What can we learn from the manuscripts as carriers of embodied knowledge in terms of material, agents (writer/recipient), and their movements across Europe?
• How can we adapt current digital methods to edit these heterogenous texts and make them accessible for further research?
The project will uncover 150 years of vernacular intellectual history and the development of scientific thinking. It will explain as well as introduce almost unknown sources to an interdisciplinary audience. It will add to and change our current understanding of a Late Medieval and Early Modern knowledge society by incorporating vernacular and therefore non-academic mathematical treatises as sources of research. Due to the availability of the Latin source material, we will be able to describe the formation process of a specialized mathematical jargon syntactically, semantically and on a lexical level. This study will help researchers to analyze other emerging jargons (trade, religion, other sciences), will contribute to the understanding of German as a language of science, and can be applied to other vernaculars as well. Lastly, this project will set a new standard in editorial practice, especially for complex and heterogenous research corpora, which will result in the creation of a transferable editorial model.
ARITHMETIC will study handwritten German arithmetic treatises from their first appearance around 1400 until the time when printed reckoning-books became easily available at the beginning of the 16th century. These texts have not been studied before, although they are important witnesses of the vernacularization of mathematical knowledge, of the interdependence of vernacular and Latin pragmatic literacy and of the links between mathematics, sciences, and commerce.
German mathematical manuscripts of the Late Middle Ages have hardly been studied yet, neither from a historical nor from a philological perspective: But the first handwritten German mathematical treatises already appeared around 1400. These treatises are not just proof that a vernacular mathematical tradition emerged early, they can also inform us on aspects relevant for several fields of research.
The Project wants to answer the following main questions:
• How does mathematical knowledge emerge, circulate, and change in a vernacular European context and what role do advancements in trade, other sciences, and social changes play?
• How did a mathematical and didactical jargon develop in the vernacular out of a Latin tradition?
• How does the underlying orality of instructive/pragmatic texts shape these treatises?
• What can we learn from the manuscripts as carriers of embodied knowledge in terms of material, agents (writer/recipient), and their movements across Europe?
• How can we adapt current digital methods to edit these heterogenous texts and make them accessible for further research?
The project will uncover 150 years of vernacular intellectual history and the development of scientific thinking. It will explain as well as introduce almost unknown sources to an interdisciplinary audience. It will add to and change our current understanding of a Late Medieval and Early Modern knowledge society by incorporating vernacular and therefore non-academic mathematical treatises as sources of research. Due to the availability of the Latin source material, we will be able to describe the formation process of a specialized mathematical jargon syntactically, semantically and on a lexical level. This study will help researchers to analyze other emerging jargons (trade, religion, other sciences), will contribute to the understanding of German as a language of science, and can be applied to other vernaculars as well. Lastly, this project will set a new standard in editorial practice, especially for complex and heterogenous research corpora, which will result in the creation of a transferable editorial model.
This project is organized in 4 different subprojects which are focussing on different objectives relevant to answer the research questions stated above:
Subproject 1: German arithmetic manuscripts: documentation, context
This Subproject deals with the objective of organizing, cataloguing, and describing the relevant manuscripts of our research corpus. They will be analyzed in relation to their textual environment with a focus on the whole manuscript/miscellany. We will define the textual networks, the learned discourses, and environments of knowledge of which the arithmetical texts were part of. By studying the carriers of embodied knowledge, we will learn about the corresponding agents, their intent, and their educational background. This will lead to an exemplary study of the process of manifestation, transformation, and circulation of vernacular mathematical knowledge.
Subproject 2: German arithmetic manuscripts: Transcription, Encoding, Annotation
This Subproject deals with the objective of building an enriched digital edition of German arithmetical texts and to making them available for further research. We will adhere to the high standards of exact textual scholarship while also making the historic information recorded in the texts easily available. We will accomplish this by transcribing the sources (TEI/XML), encoding them (semantic enrichment), and publishing them digitally in combination with the digitized images of the handwritten texts and extensive commentaries. We also want to further our understanding on how an arithmetic discourse is structured and how it functions by creating an ontology of late medieval and early modern arithmetic, to make connections of knowledge within this discourse visible.
Subproject 3: German arithmetic manuscripts – philological and historical analysis
This Subproject deals with the objective of describing an arithmetical discourse of the Late Middle Ages by analyzing the source material from a philological and historical point of view. We will identify other discourses intertwined with the arithmetical discourse and study the effects of these connections. The goal is to understand the relevance and transforming power of a developing mathematical discourse on the circulation of (mathematical) knowledge and the connected carriers of embodied knowledge.
Subproject 4: Late medieval German arithmetical jargon: development, vocabulary, didactic function
This Subproject deals with the objective of understanding how a German arithmetical jargon in connection with a developing didactic vernacular language was established. This will be accomplished by analyzing the vocabulary, the structure, and the semantics of the source material at hand in relation to the Latin templates. To build a glossary of German late medieval arithmetic terminology upon the established research corpus.
Subproject 1: German arithmetic manuscripts: documentation, context
This Subproject deals with the objective of organizing, cataloguing, and describing the relevant manuscripts of our research corpus. They will be analyzed in relation to their textual environment with a focus on the whole manuscript/miscellany. We will define the textual networks, the learned discourses, and environments of knowledge of which the arithmetical texts were part of. By studying the carriers of embodied knowledge, we will learn about the corresponding agents, their intent, and their educational background. This will lead to an exemplary study of the process of manifestation, transformation, and circulation of vernacular mathematical knowledge.
Subproject 2: German arithmetic manuscripts: Transcription, Encoding, Annotation
This Subproject deals with the objective of building an enriched digital edition of German arithmetical texts and to making them available for further research. We will adhere to the high standards of exact textual scholarship while also making the historic information recorded in the texts easily available. We will accomplish this by transcribing the sources (TEI/XML), encoding them (semantic enrichment), and publishing them digitally in combination with the digitized images of the handwritten texts and extensive commentaries. We also want to further our understanding on how an arithmetic discourse is structured and how it functions by creating an ontology of late medieval and early modern arithmetic, to make connections of knowledge within this discourse visible.
Subproject 3: German arithmetic manuscripts – philological and historical analysis
This Subproject deals with the objective of describing an arithmetical discourse of the Late Middle Ages by analyzing the source material from a philological and historical point of view. We will identify other discourses intertwined with the arithmetical discourse and study the effects of these connections. The goal is to understand the relevance and transforming power of a developing mathematical discourse on the circulation of (mathematical) knowledge and the connected carriers of embodied knowledge.
Subproject 4: Late medieval German arithmetical jargon: development, vocabulary, didactic function
This Subproject deals with the objective of understanding how a German arithmetical jargon in connection with a developing didactic vernacular language was established. This will be accomplished by analyzing the vocabulary, the structure, and the semantics of the source material at hand in relation to the Latin templates. To build a glossary of German late medieval arithmetic terminology upon the established research corpus.
This project will close several research and knowledge gaps: Studying this corpus will introduce a new text type to the philologies with the German tradition being an exemplary study. We will learn about the establishment of practical and theoretical mathematics in the vernacular parallel to a Latin discourse and prior to the reckoning book-tradition. We will also close the research gap on the development of a German mathematical language. The connection to the Latin tradition will be of great interest for linguists and scholars of medieval and new Latin. The edition of these manuscripts will build on and expand the method of the Assertive Edition. Drawing attention to these sources will also change our understanding of the emergence and circulation of knowledge in the late medieval and early modern period. This will impact the field of history of knowledge and their studies on theoretical and practical knowledge.