DH4PMP: Digital Humanities for Philosophy of Mathematical Practice

Project

This project aims to research and develop ways for machine learning and big data digital humanities to assist in posing and answering philosophically interesting questions about mathematical research practice.

The project is led by professor Henrik Kragh Sørensen, Section for History and Philosophy of Science, Department of Science Education, University of Copenhagen. It includes collaborations with colleagues and students at DSE as well as international partners.

Subprojects

We are actively pursuing subprojects on:

Theoretical and methodological aspects of using digital humanities to do philosophy of mathematical practice,
Detection and classification of diagrams,
Mapping of mathematical retractions,
Text-mining mathematical reviews, and
Text- and structure mining mathematical papers in the arXiv.

Group

We encourage friendly collaboration with colleagues, partners from abroad and students.

Henrik Kragh Sørensen, PI, professor, DSE
Mikkel Willum Johansen, associate professor, DSE
Josefine Pallavicini, MA, research assistant, DSE
Anton Kristian Suhr, MSc, research assistant, DSE
Mikkel Tvorup Moseholm, MA, DSE
Chris Søndergaard Gassner Nielsen, MSc student, MATH/DSE
Kristoffer Rank Rasmussen, MSc student, MATH/DSE
Sophie Kjeldbjerg Mathiasen, MSc
Laura Søvsø Thomasen, PhD, Royal Danish Library

Collaborators

We collaborate on international, interdisciplinary projects.

Hester Breman (Maastricht) and Renee Hoekzema (Oxford) on visual thinking in mathematics
Vincent Coumans (Nijmegen) and Ned Wontner (Amsterdam) on evaluations of definitions in mathematics
Irida Altman (Zürich) on evolution of Heegaard diagrams

Data sources

We can integrate data from a large number of sources:

Metadata, pdf-files and LaTeX sources from arXiv
Pdf files of research publications
Threads from lists on StackExchange
Threads in mailing lists such as FOM
Reviews from Mathematical Reviews (MathSciNet)
Public Twitter feeds
Publication networds from Clarivate Web Of Science

Pipelines

We work with a number of corpora with associated pipelines:

A pipeline for detecting and measuring mathematical diagrams in pdf files
A pipeline for extracting context-structured text from arXiv LaTeX sources
A pipeline for accessing metadata and reviews from the Mathematical Reviews
A pipeline for analysing 'threaded corpora' such as MathOverflow, mailing lists, etc.

Tools

We deploy a variety of big-data and ML-tools, including:

Object detection
POS-tagging
Dimension reduction (UMAP, PCA)
Topic modeling
Sentiment analysis

Software

Most of our code is written in python, and we rely on a set of key libraries for LaTeX and XML parsing, NLP, neural networks, statistical analysis, documentation etc.

Upcoming events

Mikkel Willum Johansen and Henrik Kragh Sørensen: What is an experiment in mathematics? New evidence from mining the Mathematical Reviews at Text-Driven Approaches to the Philosophy of Mathematics (TDPhiMa 2) (Online, Invited; 2021-09-01 to 2021-09-03)
Anton Kristian Suhr and Henrik Kragh Sørensen: Explanations in different mathematical contexts at Text-Driven Approaches to the Philosophy of Mathematics (TDPhiMa 2) (Online, Invited; 2021-09-01 to 2021-09-03)
Henrik Kragh Sørensen: Beyond counting: Measuring diagram intensity in mathematical research papers during the past 25 years at Diagrams 2021: 12th International Conference on the Theory and Application of Diagrams (Online, 2021-09-28 to 2021-09-30)
Mikkel Willum Johansen and Josefine Lomholt Pallavicini: The fall and rise of resemblance diagrams at Diagrams 2021: 12th International Conference on the Theory and Application of Diagrams (Online, 2021-09-28 to 2021-09-30)

Recent publications

Sørensen, Henrik Kragh, and Mikkel Willum Johansen. 2020. “Counting Mathematical Diagrams with Machine Learning.” In Diagrammatic Representation and Inference: 11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, edited by Ahti-Veikko Pietarinen, Peter Chapman, Leonie Bosveld-de Smet, Valeria Giardino, James Corter, and Sven Linker, 26–33. Lecture Notes in Computer Science (LNAI) 12169. Springer. https://doi.org/10.1007/978-3-030-54249-8_3.