Figure - available from: Synthese
This content is subject to copyright. Terms and conditions apply.
Source publication
Over the last century, there have been considerable variations in the frequency of use and types of diagrams used in mathematical publications. In order to track these changes, we developed a method enabling large-scale quantitative analysis of mathematical publications to investigate the number and types of diagrams published in three leading math...
Citations
... However, there already exist approaches to creating metataxonomies [54]. As there was almost no diagram research at all between around 1880 and 1990 with the onset of the socalled 'crisis in intuition' [76,101], LLMs can neither draw on a broad data set nor on a uniform classification. Even if there is already a great deal of research on the above example of the two hoops or circles, the definition is still not clear. ...
In the rapidly evolving landscape of multimodal communication research, this follow-up to Gregori et al. (2023) explores the transformative role of machine learning (ML), particularly using multi-modal large language models, in tracking, augmenting, annotating, and analyzing multimodal data. Building upon the foundations laid in our previous work, we explore the capabilities that have emerged over the past years. The integration of ML allows researchers to gain richer insights from multimodal data, enabling a deeper understanding of human (and non-human) communication across modalities. In particular, augmentation methods have become indispensable because they facilitate the synthesis of multimodal data and further increase the diversity and richness of training datasets. In addition, ML-based tools have accelerated annotation processes, reducing human effort while improving accuracy. Continued advances in ML and the proliferation of more powerful models suggest even more sophisticated analyses of multimodal communication, through models like ChatGPT, which can now "understand" images. This makes it all the more important to assess what these models can achieve now or in the near future, and what will remain unattainable beyond that. We also acknowledge the ethical and practical challenges associated with these advancements, emphasizing the importance of responsible AI and data privacy. We must be careful to ensure that benefits are shared equitably and that technology respects individual rights. In this paper, we highlight advances in ML-based multimodal research and discuss what the near future holds. Our goal is to provide insights into this research stream for both the multimodal research community, especially in linguistics, and the broader ML community. In this way, we hope to foster collaboration in an area that is likely to shape the future of technologically mediated human communication.
Recent case studies in the philosophy of mathematical practice have pointed out that certain types of diagrams play epistemic roles in mathematical proofs. To complement such case studies and provide a quantitative basis for further analysis and discussions, we undertake an empirical study based on a large and contemporary corpus of mathematical texts. Following an a priori assumption that diagrams in short proofs carry more epistemic warrant, we focus on 1- or 2-sentence proofs that refer to diagrams, and we build a corpus of such proofs from the arXiv. Based on this corpus we analyze and develop a typology of such proofs in order to conduct selected qualitative close-readings of diagrams in their argumentative contexts. This leads us to discuss tensions between visual and syntactical aspects of diagrams that suggest that hybrid diagrams play distinct roles in mathematical practice.
A recent investigation of the changes in the use of diagrams in published mathematics papers shows that diagrams were frequently used at the end of the 19th century and the beginning of the 20th. They then largely disappeared in the period 1910–1950, whereafter they reappear [1]. Although this story is unsurprising considering the dominance of formalist ideology in the first half of the 20th century, the detailed investigation of the development points out several interesting open questions. Especially, we do not know if the diagrams that disappeared with the advent of formalism are the same as those that are used today. In this paper, we will focus on so-called “resemblance” diagrams, which are one of three general categories of diagrams covered in the investigation in [1]. We will analyze and compare resemblance diagrams used in the late 19th century with those used in the early 20th century to determine if there have been substantial changes. The comparison shows that even though the diagrams can be said to belong to the same general category and share certain general features, the resemblance diagrams used today are very different from those used before the advent of formalism. The criticism raised by the formalist movement of the diagrams used in the late 19th century can be seen as a possible explanation of this change.
