Abstract
On December 10th, 1947, John von Neumann wrote to the Spanish translator of his Mathematical Foundations of Quantum Mechanics: 1
Your questions on the nature of mathematical physics and theoretical physics are interesting but a little difficult to answer with precision in my own mind. I have always drawn a somewhat vague line of demarcation between the two subjects, but it was really more a difference in distribution of emphases. I think that in theoretical physics the main emphasis is on the connection with experimental physics and those methodological processes which lead to new theories and new formulations, whereas mathematical physics deals with the actual solution and mathematical execution of a theory which is assumed to be correct per se, or assumed to be correct for the sake of the discussion. In other words, I would say that theoretical physics deals rather with the formation and mathematical physics rather with the exploitation of physical theories. However, when a new theory has to be evaluated and compared with experience, both aspects mix.
Notes
The author wants to express his thanks to Jeremy Butterfield, Hannes Leitgeb, Ulrich Majer, and Miklós Rédei for inspiring suggestions and critical comments.
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References
If translations of German texts exist, their page numbers are given after those of German originals. In the case of (Neumann, 1932) I have made some modifications to the translation cited here because it is inaccurate in some philosophical passages.
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Stöltzner, M. (2001). Opportunistic Axiomatics — Von Neumann on the Methodology of Mathematical Physics. In: Rédei, M., Stöltzner, M. (eds) John von Neumann and the Foundations of Quantum Physics. Vienna Circle Institute Yearbook [2000], vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2012-0_4
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