As someone with a degree in physics and math, I find the line you're trying to draw rather blurry.

> Quantum physics is a theory, as in "as far as we can tell, this is an exact mathematical description of the world".

Is it?

If by "mathematical exactness" you merely mean we have somehow been able to produce some numbers that later on we measured in experiments, then yes. (Though we haven't been able to produce such numbers in all cases, see e.g. [0].)

I my book, though, mathematical exactness means your model is mathematically consistent and is applied with the necessary mathematical rigor.

Quantum mechanics and quantum field theory, as they are commonly taught in universities, are everything but. They are a bunch of concepts and recipes that, albeit successful, are held together loosely with duct tape and lots of hand waving to make you ignore the logical gaps & jumps and the fact that many of the "mathematical" objects physicists refer to don't even exist[1]!

[0]: https://www.scientificamerican.com/article/this-simple-exper...

[1]: Haag's Theorem, Aizenman–Fröhlich Triviality Theorem, etc.