Feynman:

The physicist needs a facility in looking at problems from several points of view. The exact analysis of real physical problems is usually quite complicated, and any particular physical situation may be too complicated to analyze directly by solving the differential equation. But one can still get a very good idea of the behavior of a system if one has some feel for the character of the solution in different circumstances. Ideas such as the field lines, capacitance, resistance, and inductance are, for such purposes, very useful. ... On the other hand, none of the heuristic models, such as field lines, is really adequate and accurate for all situations. There is only one precise way of presenting the laws, and that is by means of differential equations. They have the advantage of being fundamental and, so far as we know, precise. If you have learned the differential equations you can always go back to them. There is nothing to unlearn.

Feynman again:

It requires a much higher degree of imagination to understand the electromagnetic field than to understand invisible angels. ... I speak of the E and B fields and wave my arms and you may imagine that I can see them ... [but] I cannot really make a picture that is even nearly like the true waves.

Feynman again:

Dirac discovered the correct laws for relativity quantum mechanics simply by guessing the equation. The method of guessing the equation seems to be a pretty effective way of guessing new laws. This shows again that mathematics is a deep way of expressing nature, and any attempt to express nature in philosophical principles, or in seat-of-the-pants mechanical feelings, is not an efficient way.

Feynman again:

To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature. ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.

I think the last quote is the most telling. One can't understand the deep beauty of nature without a lot of math.

BTW, I was a big Twin Peaks fan. When asked by Bob to tell him his deepest fear, Major Briggs responded "The possibility that love is not enough." In confirmation, Agent Cooper failed even though he had enough love. His heart was pure, but he just didn't do enough work.

I think that story line elevates Twin Peaks to the level of Shakespeare: Love is not enough. You have to do the work.

Language is not enough. You have to do the math.