Mathematical modelling of physical systems is generally what physicists do. Of course you may do more or less of it depending on your subfield, but it is an absolutely essentiall skill for most physicists.
Whatever you call it. Physics is to measure something and put the result into context of other measurements with the goal to deduce a general rule between those measurements. So you have a bunch of numbers representing quantities (variables) and you want to deduce a law (formula) between those quantities.
At school, i.e. in classical physics, those laws are often proportional dependences like ##P\sim T## or ##U\sim R##. In particle physics and cosmology those laws become more complicated and need more framework, but the basic principle is still the same.
What do you think physics is, or how else could it be done?
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