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mfb comments on How valuable is it to learn math deeply? - Less Wrong
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One of the barriers I run into when I delve into physics is that I have a very rationalist approach to math. I hate terminology and I want as little of it as possible in my reasoning. Physics has rather high barriers in that way in that academic physicists don't really like mathematical rigour, and don't precisely specify, say, the abstract algebraic axioms of the structures they are using. But when I get to a point of being able to specify what structure is behind a physical theory, I can usually intuit it readily.
Physics is domain knowledge compared to mathematical reasoning ability.
If mathematical details matter, they should be specified (or be clear anyway - e.g. you don't define "real numbers" in a physics paper). Physics can need some domain knowledge, but knowledge alone is completely useless - you need the same general reasoning ability as in mathematics to do anything (both for experimental and theoretical physics).
In fact, many physics problems get solved by reducing them to mathematical problems (that is the physics part) and then solving those mathematical problems (still considered as "solving the physical problem", but purely mathematics)