Whilst some of the replies rebuke large part of your points well, I agree that the argument "mathematics is only good when it's tied to physics" is wrong. I'd

Whilst some of the replies rebuke large part of your points well, I agree that the argument "mathematics is only good when it's tied to physics" is wrong. I'd reformulate his point to: Mathematics, especially when being taught, benefits from intuitive examples that motivate the abstract definitions. A point that is quite obvious. Whilst certainly much intuition concerns physics, that need not be the underlying source of the intuition.