Like are we talking about just as well as a mathematician or does he have to know the properties of structure in math that he's studying. Not really the rigour but more like what properties it has and what it can do.
Find a school that offers a program in such an area, and analyze the abundance of math courses that one has to take as part of the degree. Obviously it would help to understand the rigor to do well in these classes, especially upper level.
It really depends on what kind of work you do, I guess. You could be doing for example particle phenomenology and do tedious loop calculations all day without worrying about whether what you do is rigorous, or you could be a mathematical physicist working on rigorous proofs for things that seem to work but haven't been proven yet. Of course having a deep understanding of math should help either way.
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