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Explanation in mathematical conversations: an empirical investigation
Alison Pease1, Andrew Aberdein2, Ursula Martin3
11 School of Computing , University of Dundee , Dundee , UK.
Mathematicians frequently use explanations in online forums, offering insights into informal conceptualizations of simplicity. This study confirms explanation
Area of Science:
- Philosophy of Mathematics
- Computational Linguistics
- Mathematical Practice
Background:
- Philosophical work has proposed conjectures on the characteristics and occurrence of explanation in mathematics.
- Online mathematics forums represent a rich environment for studying mathematical communication and practice.
Purpose of the Study:
- To investigate the role and prevalence of explanation in online mathematical discussions.
- To test philosophical conjectures about mathematical explanation against empirical data.
- To explore the connection between explanation and informal conceptualizations of simplicity.
Main Methods:
- Extraction of six conjectures from philosophical literature on mathematical explanation.
- Analysis of a corpus of online mathematical discussions.
- Employment of two techniques: indicator term analysis and random sampling of comments.
- Empirical testing of conjectures against the corpus.
Main Results:
- Explanation is a widespread phenomenon in mathematical practice.
- Mathematical explanation occurs in various contexts beyond formal proofs.
- Findings support the utility of empirical methods in addressing philosophical questions about mathematics.
Conclusions:
- Online forums provide valuable data for understanding mathematical explanation.
- The study offers empirical support for philosophical theories on mathematical explanation.
- Mathematical explanation contributes to informal notions of simplicity and understanding.
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