TY - JOUR

T1 - Paving the cowpath in research within pure mathematics – A medium level model based on text driven variations.

AU - Heuer, Karl

AU - Sarikaya, Deniz

N1 - Funding Information: The first author has been supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (ERC consolidator grant DISTRUCT, agreement No. 648527 ). The second author is thankful for the financial and ideal support of the Studienstiftung des deutschen Volkes and the Claussen-Simon-Stiftung as well as the Research Foundation Flanders (FWO) [grant number FWOAL950 ], the paper was finalized during a visit of the second author in Denmark (University of Copenhagen & Technical University of Denmark) funded by a DAAD-Kurzzeitstipendium with the project “ Theoretical virtues of conjectures and open questions in mathematical practice ”. We furthermore would like to thank Louis Bellmann, Sophie Nagler, Armin Rezaia Nia, José Antonio Perez-Escobar, and Mira Sarikaya for useful comments. The views stated here are not necessarily the views of the supporting organizations and individuals mentioned in this acknowledgement. Publisher Copyright: © 2023 The Author(s) Copyright: Copyright 2023 Elsevier B.V., All rights reserved.

PY - 2023/8

Y1 - 2023/8

N2 - In this paper we show how simple text-driven variations of given statements in mathematics can lead to interesting new problems and push forward a whole theory around simple initial questions. We exemplify this in two cases. Case 1 deals with problem-posing activities suitable for pupils and case 2 is a rational reconstruction of the organisation of mathematical knowledge within problems of graph colorings. Mathematicians learn to systematically look for subsequent problems around a given problem. We argue that this toy-model captures a nontrivial part of professional mathematical research within the pure fields and conjecture that it even grasps high level developments in mathematics. By doing this, we implicitly encourage a very simplistic view on criteria, so to speak a “cowpath” approach to progress in mathematics. The term “cowpath” is borrowed from architecture and software design, where it is commonly used. While we can contemplate which pathways are ideal, we may also just plant grass and see where people choose to walk. Those pathways are also self-enforcing, since we are less hesitant to walk on those rather than criss-cross the landscape.

AB - In this paper we show how simple text-driven variations of given statements in mathematics can lead to interesting new problems and push forward a whole theory around simple initial questions. We exemplify this in two cases. Case 1 deals with problem-posing activities suitable for pupils and case 2 is a rational reconstruction of the organisation of mathematical knowledge within problems of graph colorings. Mathematicians learn to systematically look for subsequent problems around a given problem. We argue that this toy-model captures a nontrivial part of professional mathematical research within the pure fields and conjecture that it even grasps high level developments in mathematics. By doing this, we implicitly encourage a very simplistic view on criteria, so to speak a “cowpath” approach to progress in mathematics. The term “cowpath” is borrowed from architecture and software design, where it is commonly used. While we can contemplate which pathways are ideal, we may also just plant grass and see where people choose to walk. Those pathways are also self-enforcing, since we are less hesitant to walk on those rather than criss-cross the landscape.

U2 - 10.1016/j.shpsa.2023.05.006

DO - 10.1016/j.shpsa.2023.05.006

M3 - Zeitschriftenaufsätze

SN - 0039-3681

VL - 100

SP - 39

EP - 46

JO - Studies in History and Philosophy of Science, Part A

JF - Studies in History and Philosophy of Science, Part A

ER -