I'll give a perspective, although my specific knowledge of math is not very deep at all, I've thought a lot about concepts and abstractions.
I think the difference here is that math is much more abstract than physics. The concepts backing math are built off of very low level abstractions about the world. For math, over a long period of time more and more relationships and rules were deduced from what had already been induced from reality. And if you CAN deduce, you should likely, as it provides a proof for some idea or concept that induction never could (but only if your previous inductions and deductions were accurate).
Physics on the other hand, cannot deduce as readily. It is primarily based in the realm of gathering more and more data from the world and observing physical relationships firsthand. This cannot be done in abstract math because abstract math does not exist in reality. There is nothing to observe, it is mostly abstractions based on lower level observations in reality. For example, you can measure the effects of gravity firsthand, but you cannot measure infinity, a mathematical abstraction. Infinity does not exist in reality. It is simply a useful abstraction for things that are too large or small for us to meaningfully measure.
I think the difference here is that math is much more abstract than physics. The concepts backing math are built off of very low level abstractions about the world. For math, over a long period of time more and more relationships and rules were deduced from what had already been induced from reality. And if you CAN deduce, you should likely, as it provides a proof for some idea or concept that induction never could (but only if your previous inductions and deductions were accurate).
Physics on the other hand, cannot deduce as readily. It is primarily based in the realm of gathering more and more data from the world and observing physical relationships firsthand. This cannot be done in abstract math because abstract math does not exist in reality. There is nothing to observe, it is mostly abstractions based on lower level observations in reality. For example, you can measure the effects of gravity firsthand, but you cannot measure infinity, a mathematical abstraction. Infinity does not exist in reality. It is simply a useful abstraction for things that are too large or small for us to meaningfully measure.