Counting Mathematical Diagrams with Machine Learning
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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Counting Mathematical Diagrams with Machine Learning. / Sørensen, Henrik Kragh; Johansen, Mikkel Willum.
Diagrammatic Representation and Inference. ed. / Ahti-Veikko Pietarinen; Peter Chapman; Leoni Bosveld-de Smet; Valeria Giardino; James Corter; Sven Linker. Vol. 12169 Springer, 2020. p. 26-33 (Lecture Notes in Computer Science).Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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TY - GEN
T1 - Counting Mathematical Diagrams with Machine Learning
AU - Sørensen, Henrik Kragh
AU - Johansen, Mikkel Willum
N1 - Conference code: 11
PY - 2020/8
Y1 - 2020/8
N2 - The role and use of diagrams in mathematical research has recently attracted increasing attention within the philosophy of mathematics, leading to a number of in-depth case studies of how diagrams are used in mathematical practice. Though highly interesting, the study of diagrams still largely lack quantitative investigations which can provide vital background information regarding variations e.g. in the frequency or type of diagrams used in mathematics publication over time.A first attempt at providing such quantitative background information has recently been conducted [9], making it clear that the manual labour required to identify and code diagrams constitutes a major limiting factor in large-scale investigations of diagram-use in mathematics.In order to overcome this limiting factor, we have developed a machine learning tool that is able to identify and count mathematical diagrams in large corpora of mathematics texts. In this paper we report on our experiences with this first attempt to bring machine learning tools to the aid of philosophy of mathematics. We describe how we developed the tool, the choices we made along the way, and how reliable the tool is in identifying mathematical diagrams in corpora outside of its training set. On the basis of these experiences we discuss how machine learning tools can be used to inform philosophical discussions, and we provide some ideas to new and valuable research questions that these novel tools may help answer.
AB - The role and use of diagrams in mathematical research has recently attracted increasing attention within the philosophy of mathematics, leading to a number of in-depth case studies of how diagrams are used in mathematical practice. Though highly interesting, the study of diagrams still largely lack quantitative investigations which can provide vital background information regarding variations e.g. in the frequency or type of diagrams used in mathematics publication over time.A first attempt at providing such quantitative background information has recently been conducted [9], making it clear that the manual labour required to identify and code diagrams constitutes a major limiting factor in large-scale investigations of diagram-use in mathematics.In order to overcome this limiting factor, we have developed a machine learning tool that is able to identify and count mathematical diagrams in large corpora of mathematics texts. In this paper we report on our experiences with this first attempt to bring machine learning tools to the aid of philosophy of mathematics. We describe how we developed the tool, the choices we made along the way, and how reliable the tool is in identifying mathematical diagrams in corpora outside of its training set. On the basis of these experiences we discuss how machine learning tools can be used to inform philosophical discussions, and we provide some ideas to new and valuable research questions that these novel tools may help answer.
U2 - 10.1007/978-3-030-54249-8_3
DO - 10.1007/978-3-030-54249-8_3
M3 - Article in proceedings
SN - 978-3-030-54248-1
VL - 12169
T3 - Lecture Notes in Computer Science
SP - 26
EP - 33
BT - Diagrammatic Representation and Inference
A2 - Pietarinen, Ahti-Veikko
A2 - Chapman, Peter
A2 - Bosveld-de Smet, Leoni
A2 - Giardino, Valeria
A2 - Corter, James
A2 - Linker, Sven
PB - Springer
T2 - 11th International Conference, Diagrams 2020
Y2 - 24 August 2020 through 28 August 2020
ER -
ID: 249386737