Math is about given the definition and understand the results through consistency. For example, given the set of Maxwell's equation and a set of boundary condit

Math is about given the definition and understand the results through consistency. For example, given the set of Maxwell's equation and a set of boundary condition, figuring out or understanding the solution -- that is mathematics. So as a mathematician, you would like to have the definition (assumption) and equation, which provides the clear (mathematical) picture. But physics is different. Physics is about the question whether those assumption (including many hidden assumption) can be wrong and how to interpret the mathematical equation even when the equation gives confirmed results. So Maxwell's equations is not a clear picture on what the light is. Maxwell's equation just describes one aspect of how light behave under one set of assumptions. There are other aspects of light and there are different set of maths that physicists tried to describe them. There are physics intuition on what light is, but that is subjectively dependent on which physicist you are asking. In physics, there is simply no mathematically equivalent of "clear picture" where you simply just accept what is given and go from there. In physics, it is "what is given" in question.