> mathematics is not necessarily a reflection of the physical universe

Nobody knows if it is or not. It could also be that the physical universe is a reflection of mathematical truth.

> It can be, in cases like addition, but it doesn't necessarily need to be. Which was the parent's point.

Again, nobody knows if it what you claim is true or not. What we do know is that all scientific models are based on math, and if there is something wrong at the foundations of math, then all science is pseudoscience. Gödel's theorems are at the foundations of math. You can't just decide that you are skeptical about that part of math being applicable to physical models but addition is fine.

The real problem with Gödel is that it says something that a lot of people don't like to be true.