I'm asking this question as a mathematician who is very far removed from the Physics world, and has little to no knowledge of what math goes into it, and what math comes out of it. What I do hear is that people have "physical intuition" about mathematical objects (especially in algebraic geometry), and that they then try to prove it mathematically.

So out of curiousity, my question, then, is this. Which combination of the following is true for why "physical intuition" isn't already rigorous:

1. They assume the existence of objects that they don't construct.

2. Their logic is flawed.

3. They experiment (with particles and such) and assume that if it works enough times then it is true.

4. They assume that "reasonable" mathematical conjectures are true without bothering to be sure.

5. They don't have axiomatized definitions, and rely on vague notions.