The Relationship Between Physics and Mathematics in the XIXth Century: The Disregarded Birth of a Foundational Pluralism

  • Antonino DragoEmail author
Part of the History of Mechanism and Machine Science book series (HMMS, volume 16)


In my previous historical works I suggested that four scientific choices constitute the foundations of Physics. By means of these choices I will interpret the history of the relationship between Mathematics and Theoretical Physics in the nineteenth century. A particular pair of choices shaped the Newtonian relationship between Mathematics and Physics, which was so efficient in producing new theoretical results that it became a paradigm. In the nineteenth century new formulations of mechanics were made according to different basic choices, so that in theoretical Physics three other pairs of choices began to co-exist with the Newtonian relationship. Very few scientists of that time recognised this pluralism; instead, the community of physicists interpreted the new theories as either mere variations of the dominant one, or loose scientific attitudes to be put aside in order to follow the theoretical progress of the dominant paradigm. But just after the mid-century the pluralism of the relationships between Physics and Mathematics came to the fore again, this time the previous alternative choices shaped new physical theories – thermodynamics, electromagnetism – concerning entirely new fields of phenomena. But this novelty was interpreted as simply a conflict – possibly, a contradiction – between the new basic notions and the old ones; in particular, at the end of the nineteenth century there was a great debate about the theoretical role played by the new notion of energy in contrast with the old notion of force. The persistent lack of awareness of the pluralism of relationships is the reason for both the inconclusiveness of this debate and the dramatic crisis occurring in theoretical Physics from the year 1900. This time the crisis was caused above all by two experimental data (both the quantum and the light velocity of light c as the highest possible velocity) which are incompatible with the Newtonian relationship between Mathematics and Physics. Correspondingly, two “revolutionary” theories emerged, again according to the alternative choices to those of this paradigm; both theories required a new relationship with Mathematics, including respectively discrete mathematics and groups.


Theoretical Physic Nineteenth Century Physical Theory Basic Notion Newtonian Mechanic 
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Authors and Affiliations

  1. 1.University of PisaPisaItaly

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