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On person said to me that there is some theory in physics that they have not a good formalization yet, i.e. there is not a mathematical theory that covered them. Is this true? If yes, then without a mathematical theory how they work through such theory? how they compute? thanks.

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    This person probably had [quantum field theory](http://bookstore.ams.org/surv-149) in mind.2017-01-19
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    They compute anyway, throw out "infinities", and if the answer agrees with experiment, who cares if the math is bogus? (except those stuffy mathematicians)2017-01-19
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    Is there any physical theory that has a rigorous mathematical formulation?2017-01-23

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Yes. Of course. There are more phenomenons in physics that are not mathematically described. With a glance search in web, you find many unsolved problems (see: https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics) which have not solved yet. The subjects like fields theory, high-energy physics, particle, cosmology are some of these problems. You might wants to know that physics is not axiomatized yet. This is one of Hilbert problems, that says

Can physics be axiomatized?

In my idea, this is one of the fundamental parts physics which must be discovered. http://mathworld.wolfram.com/HilbertsProblems.html