The Relationship Between Physics and Mathematics in the XIXth Century: The Disregarded Birth of a Foundational Pluralism
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 centur
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Abstract 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 midcentury 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 h 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
A. Drago () University of Pisa, Italy e-mail: [email protected] E. Barbin and R. Pisano (eds.), The Dialectic Relation Between Physics and Mathematics in the XIXth Century, History of Mechanism and Machine Science 16, DOI 10.1007/978-94-007-5380-8 8, © Springer ScienceCBusiness Media Dordrecht 2013
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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.
1 Introduction The encyclopaedic study by Grattan-Guinness on both Mathematics and Physics at the time of the French revolution, pointed out a serious problem in the historiography of Physics of the nineteenth century. The origin of the problem can be traced back to the two distinct attitudes of historians of science in writing their accounts [ : : : ] the principal difficulty I have found [is due to the following fact:] Unfortunately, no major synthesising study of French Mathematics of this period has ever been
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