Intended and Unintended Mathematics: The Case of the Lagrange Multipliers

  • Daniele MolininiEmail author


We can distinguish between two different ways in which mathematics is applied in science: when mathematics is introduced and developed in the context of a particular scientific application; when mathematics is used in the context of a particular scientific application but it has been developed independently from that application. Nevertheless, there might also exist intermediate cases in which mathematics is developed independently from an application but it is nonetheless introduced in the context of that particular application. In this paper I present a case study, that of the Lagrange multipliers, which concerns such type of intermediate application. I offer a reconstruction of how Lagrange developed the method of multipliers and I argue that the philosophical significance of this case-study analysis is twofold. In the context of the applicability debate, my historically-driven considerations pull towards the reasonable effectiveness of mathematics in science. Secondly, I maintain that the practice of applying the same mathematical result in different scientific settings can be regarded as a form of crosschecking that contributes to the objectivity of a mathematical result.


Mathematical practice Mechanics Applicability of mathematics Objectivity Lagrange Multipliers method 



I would like to thank two anonymous reviewers for their helpful and constructive comments. Their suggestions greatly contributed to improving the final version of the paper. I also wish to thank the organizers of the workshop “Mathematics and Mechanics in the Newtonian Age” and the members of the audience for useful discussion of an earlier version of this paper. This work was supported by the Portuguese Foundation for Science and Technology through the FCT Investigator Programme (Grant Nr. IF/01354/2015) and the project PTDC/FER-HFC/30665/2017.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Centro de Filosofia das Ciências da Universidade de Lisboa (CFCUL)University of LisbonLisbonPortugal

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