I'm interested in physical theories taking the form of precise, unambiguous mathematical statements. What significant work has been done to axiomize physical theories? What is left to be done? The theories I'm referring to are:

  • Newtonian mechanics and its equivalents
  • General relativity
  • Classical electrodynamics (relativistic and otherwise)
  • Whatever big theories of cosmology there are
  • Quantum mechanics (I know von Neumann wrote about this subject)
  • Statistical mechanics (though it might not be a single theory)
  • Thermodynamics (as it might not all have been reducecd to statistical mechanics)
  • The kinetic theory of gases (probably follows from another theory)
  • Quantum mechanics
  • Quantum field theory
  • Quantum electrodynamics
  • Quantum chromodynamics
  • The standard model of particle physics
  • Any big condensed matter theories
  • $\begingroup$ in QFT axiomization gives nothing useful and creates only problems with fields quantization. If you consider "constructive QFT" as the effective description of Nature, all the topics with condensed matter, statistical physics & kinetic theory can be obtained directly from apropriate QFT. $\endgroup$ – Artem Alexandrov Feb 14 '20 at 9:54
  • $\begingroup$ check here ; physics.stackexchange.com/q/388849 $\endgroup$ – Slereah Feb 14 '20 at 10:39
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    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/87239/2451 and links therein. $\endgroup$ – Qmechanic Feb 14 '20 at 10:39