Theres definitely a lack of rigor math-wise in physics as a rule. It’s not for everyone.

That being said, that lack of rigor is a useful tool sometimes. The dirac delta “function” (functional?) was described in the world of physics first as the only reasonable derivative of a step function/impulse before it was properly defined in the words of mathematics; just because the equational rigor isn’t there yet doesn't mean the argument isn’t solid or the tool is poor.