Math in physics (at least most of the physics I have done, which covers classical 19th century stuff mostly) is just a tool, if you can take a shortcut, take it! If you can approximate and cheat, do it! What matters in physics is the path from observation to modeling. Math is but a tool.
Now I agree that the math gets rather solid, but it's nothing compared to real math at an equivalent level.
I think my experience is particular because in France where I studied, you study both in parallel very intensively. So the math in physics always kind of seems trivial to you... But still my best physics teacher taught me that it was way more about the "feel and model" than the "exactly prove" that mathematics consists in.
Math in physics (at least most of the physics I have done, which covers classical 19th century stuff mostly) is just a tool, if you can take a shortcut, take it! If you can approximate and cheat, do it! What matters in physics is the path from observation to modeling. Math is but a tool.
Now I agree that the math gets rather solid, but it's nothing compared to real math at an equivalent level.
I think my experience is particular because in France where I studied, you study both in parallel very intensively. So the math in physics always kind of seems trivial to you... But still my best physics teacher taught me that it was way more about the "feel and model" than the "exactly prove" that mathematics consists in.
Gosh I miss those days :)