I was not aware of using mathematics that way. Indeed, I am not sure what you mean. Can you give a (simple) example of the difference between mathematical truth and mathematical formalism?
Mathematical truth is more fundamental, because our reality is only one of an infinite number of potential realities, but there is only one set of mathematical truth, and it is common to them all.
That is quite a leap of faith, isn't it? Not that I have anything against faith, you understand. But how can we know that there are infinitely many potential realities but only one mathematical truth? (We seem to have wandered into the thickets of metaphysics, an adventure I am not prepared to undertake.)
I think Physicist is taking what is known as the "intuitionist" position. Loosely, intuitionists regard mathematical concepts as truths rather than as the consequences of logical or formal derivations.
Most mathematicians (and scientists, whether they know it or not) are "formalists." There is no such thing as mathematical truth. There are only theorems derived from a fundamental set of axioms -- we are free to use whatever axioms we want so long as they are consistent. One set of axioms may lead to a theorem that is demonstrably false using another set. Engineers and physicists simply pick axiom sets allowing them to describe their observations, but, fundamentally, all sets are equally valid.
Turns out that, if you take a rigorously intuitionist approach, it's pretty tough to impossible to come up with most of calculus . You can find some interesting links by searching on "axiom of choice," "Godel's Theorem," and "Lowenstein-Skolem Theorem."
Mathematical truth: seven cannot be factored into integers other than itself and one. Mathematical formalism: multiplication is commutative.
That is quite a leap of faith, isn't it? Not that I have anything against faith, you understand. But how can we know that there are infinitely many potential realities but only one mathematical truth?
No, I'm not going all wobbly on you. No Zen here. If you flip a coin, it's either going to be heads or tails. Both outcomes are possible (potential realities) but only one occurs. Avoiding the topic of quantum superposition, there's only one reality. But just about anything you can point to in "our" reality--including, yes, much of what we call the "laws of physics"--could consistently have been otherwise.
Al Gore might have won the election. The Greeks might have been defeated at Thermopylae. The Permo-Triassic impactor might have missed the Earth. The electroweak symmetry might have broken in such a way that photons were as massive as the Z boson. But seven would be prime regardless.