How to Frame Understanding in Mathematics: A Case Study Using Extremal Proofs

Axiomathes 31 (5):649-676 (2021)


The frame concept from linguistics, cognitive science and artificial intelligence is a theoretical tool to model how explicitly given information is combined with expectations deriving from background knowledge. In this paper, we show how the frame concept can be fruitfully applied to analyze the notion of mathematical understanding. Our analysis additionally integrates insights from the hermeneutic tradition of philosophy as well as Schmid’s ideal genetic model of narrative constitution. We illustrate the practical applicability of our theoretical analysis through a case study on extremal proofs. Based on this case study, we compare our analysis of proof understanding to Avigad’s ability-based analysis of proof understanding.

Download options


    Upload a copy of this work     Papers currently archived: 72,766

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library


Added to PP

14 (#738,599)

6 months
4 (#162,711)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Deniz Sarikaya
Vrije Universiteit Brussel

Similar books and articles

Unificatory Understanding and Explanatory Proofs.Joachim Frans - 2021 - Foundations of Science 26 (4):1105-1127.
How to Frame a Mathematician.Bernhard Schröder, Martin Schmitt, Deniz Sarikaya & Bernhard Fisseni - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Springer Verlag.
A Logic Lu for Understanding.Xiaowu Li & Xiangyang Guo - 2010 - Frontiers of Philosophy in China 5 (1):142-153.
Explanation in Mathematical Practice.David Sandborg - 1997 - Dissertation, University of Pittsburgh
Proof Theory in the Abstract.J. M. E. Hyland - 2002 - Annals of Pure and Applied Logic 114 (1-3):43-78.
Kilka uwag o dowodzie w matematyce.Roman Murawski - 2013 - Filozofia Nauki 21 (1).
Plans and Planning in Mathematical Proofs.Yacin Hamami & Rebecca Lea Morris - forthcoming - Review of Symbolic Logic:1-40.
Proofs and Arguments: The Special Case of Mathematics.Jean Paul Van Bendegem - 2005 - Poznan Studies in the Philosophy of the Sciences and the Humanities 84 (1):157-169.