A Typology of Mathematical Diagrams

TY - GEN

T1 - A Typology of Mathematical Diagrams

AU - Johansen, Mikkel Willum

AU - Misfeldt, Morten

AU - Pallavicini, Josefine Lomholt

N1 - Conference code: 10th

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this paper, we develop and discuss a classification scheme that allows us to distinguish between the types of diagrams used in mathematical research based on the cognitive support offered by diagrams. By cognitive support, we refer to the gain that research mathematicians get from using diagrams. This support transcends the specific mathematical topic and diagram type involved and arises from the cognitive strategies mathematicians tend to use. The overall goal of this classification scheme is to facilitate a large-scale quantitative investigation of the norms and values governing the publication style of mathematical research, as well as trends in the kinds of cognitive support used in mathematics. This paper, however, focuses only on the development of the classification scheme. The classification scheme takes its point of departure from case studies known from the literature, but in this paper, we validate the scheme using examples from a preliminary investigation of developments in the use of diagrams. Building on these results, we discuss the potential and pitfalls in using one generic classification scheme, as done in this analysis. This approach is contrasted with attempts that respect and build on individual diagram types, and as part of this discussion, we report the problems we experienced when using that strategy. The paper ends with a description of possible next steps in using text corpora as an empirical approach to understanding the nature of mathematical diagrams and their relation to mathematical culture.

AB - In this paper, we develop and discuss a classification scheme that allows us to distinguish between the types of diagrams used in mathematical research based on the cognitive support offered by diagrams. By cognitive support, we refer to the gain that research mathematicians get from using diagrams. This support transcends the specific mathematical topic and diagram type involved and arises from the cognitive strategies mathematicians tend to use. The overall goal of this classification scheme is to facilitate a large-scale quantitative investigation of the norms and values governing the publication style of mathematical research, as well as trends in the kinds of cognitive support used in mathematics. This paper, however, focuses only on the development of the classification scheme. The classification scheme takes its point of departure from case studies known from the literature, but in this paper, we validate the scheme using examples from a preliminary investigation of developments in the use of diagrams. Building on these results, we discuss the potential and pitfalls in using one generic classification scheme, as done in this analysis. This approach is contrasted with attempts that respect and build on individual diagram types, and as part of this discussion, we report the problems we experienced when using that strategy. The paper ends with a description of possible next steps in using text corpora as an empirical approach to understanding the nature of mathematical diagrams and their relation to mathematical culture.

KW - Classification of diagrams

KW - Corpus analysis

KW - Mathematical cognition

UR - http://www.scopus.com/inward/record.url?scp=85048626587&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-91376-6_13

DO - 10.1007/978-3-319-91376-6_13

M3 - Article in proceedings

SN - 978-3-319-91375-9

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 105

EP - 119

BT - Diagrammatic Representation and Inference - 10th International Conference, Diagrams 2018, Proceedings

A2 - Stapleton, Gem

A2 - Bellucci, Francesco

A2 - Moktefi, Amirouche

A2 - Chapman, Peter

A2 - Perez-Kriz, Sarah

PB - Springer

T2 - 10th International Conference, Diagrams, 2018, Edinburgh

Y2 - 18 June 2018 through 22 June 2018

ER -