What is History of Mathematics to 21st-Century Mathematicians?
Insights from Digital History and Philosophy of Mathematics (2024)
In: Mastering the History of Pure and Applied Mathematics. DOI: 10.1515/9783110769968
What do mathematicians today actually think about the history of their own discipline? It's a question that has mostly been answered with anecdote and gut feeling — until now. This article takes a decidedly quantitative approach, using big data and machine learning to mine MathOverflow, the go-to online forum where research mathematicians think out loud, argue, and occasionally wax philosophical about their field.
The numbers come first here. Computational text analysis drives the investigation, with qualitative close reading playing a supporting role — zooming in where the data raises interesting questions rather than the other way around. The result is a rare example of digital humanities methods applied to the sociology and philosophy of mathematical practice, and a demonstration of what these tools can actually deliver when the corpus is rich enough.
The article was published in a volume dedicated to Professor Jesper Lützen (University of Copenhagen), one of Scandinavia's most distinguished historians of mathematics — a fitting home for a piece that is itself very much about the place of history within mathematics.
What is an experiment in mathematical practice?
New evidence from mining the Mathematical Reviews (2024).
In: Synthese. With Sophie Kjeldberg Mathiasen and Mikkel Willum Johansen. DOI:10.1007/s11229-023-04475-x
Can experiments play a role in mathematics — a discipline supposedly built on pure deduction? This article takes a data-driven approach to that question, mining a large corpus of peer reviews from Mathematical Reviews to map how mathematicians themselves talk about experiments in published research. The method moves from quantitative corpus analysis to grounded qualitative coding and back again, and the result is a typology of nine distinct roles that experiments play in mathematical practice — from heuristics and exploration to concept formation and epistemic warrant.
The most striking finding is arguably the negative case: reviewers sometimes explicitly called for experiments that were absent from the papers they evaluated, suggesting that experiments are considered a legitimate — even expected — form of evidence in certain mathematical fields. That finding, combined with the broader typology, pushes back against a purely formalist picture of mathematics as experiment-free by definition.
The article was published in a special issue of Synthese on Linguistically Informed Philosophy of Mathematics — one of the leading journals in philosophy and philosophy of science — and was co-authored with Sophie Kjeldbjerg Mathiasen and Mikkel Willum Johansen.
