Of necessity, physics had to develop a framework of thinking that would allow understanding counter-intuitive elements of reality. Something like quantum physics is not very intuitive, and in order to make progress, physics essentially evolved a framework of thinking that was very effective for coming to correct answers that are not obvious. And in order to do this, it requires quite a lot of mental exertion. One cannot conduct one’s everyday life reasoning from first principles; it would just require too much mental energy. So I think you have to operate most of your life with reasoning by analogy or essentially copying other people with minor variations. But if you are trying to break new ground and be really innovative, that’s where you have to apply first-principle thinking and try to identify the most fundamental truths in any particular arena and you reason up from there. This requires quite a bit of mental exertion and I can give you some examples of how this helps one in the rocket business.
All of that is very lovely, except that you’re talking about mathematics and not physics. Physics is experimentation and measurement of physical quantities, math and logic are reasoning from first principles. This is basic stuff- I’ve never even read Karl Popper. Why yes, math is quite useful to physicists. That’s why they take all those courses over in the MATH department.
Funny thing? Musk thinks learning physics is supposed to teach people how to think. Well, I’ve known too many physics students to believe that.