Mathematicians writing for mathematicians

Reading Mathematical Proofs as Narratives

“…But the present account of mathematical understanding seems to suggest that there is a strong connection between the understanding and validation of proofs (in line with Dutilh Novaes 2018; and Mejía-Ramos and Weber 2014). The present account of understanding indicates that mathematicians understand proofs through action pattern recognition, which is the same kind of action pattern recognition that previous studies, based on interviews and a survey with mathematicians, suggest that mathematicians use to validate proofs (Andersen 2020;Andersen, Johansen and Sørensen 2019;Mejía-Ramos and Weber 2014;Weber and Mejía-Ramos 2011). Hence, proof understanding may be a form of proof validation.…”

“…A study by Andersen, Johansen and Sørensen (2019) indicates that the scripts may in part be provided by the main text preceding a proof in an article. The study reports on interviews with a supervisor and his PhD student.…”

“…Note that we would expect that the parts of proofs that follow the scripts are not the parts readers focus attention on, exactly because there are no breaches of the scripts. This is supported by Andersen, Johansen and Sørensen (2019) and Andersen (2020), whose interviews suggest that mathematicians do not thoroughly read the parts of a proof that unfold the way they would expect.…”

On the Contemporary Practice of Philosophy of Mathematics

“…4. Anthropological approaches: e.g., embedding with mathematicians (Kaufman, 2016); longitudinal studies (Andersen et al, 2019); observations of mathematical activity (Barany & MacKenzie, 2014); analysis of internet resources (Martin, 2015); ethnomathematics (François & Vandendriesche, 2016). 5.…”