As soon as Galileo began to apply mathematics to the study of the world, complications arose. Actually, the complications had always been there - but now scientists and mathematicians came face to face with them. The way that scientists and mathematicians deal with nature's complications is generally simple - they ignore them. Right away, scientists realized that the systems that they study need to be simple systems, because often very complicated and sophisticated mathematics is needed to model even a very simple system. To accurately model a car accelerating away from a stop light, the motion of a pendulum, or the fall of a raindrop, for instance, involves calculus and differential equations - at least. Scientists need to reduce a situation to points, straight lines and smooth curves in order to bring the power of mathematics to bear on it - the problem being that nature prefers blobs to points, and random-looking zigzags to straight lines and smooth curves. Simple mathematics will only deal with the most trivial of problems - therefore, it must take enormously powerful and abstract mathematics, far beyond our current human capabilities, to deal with the complexity of nature.
A bit pessimistic at the end. It should be restated like this:
therefore, it must take enormously powerful EM, far beyond our current methods, to deal with the complexity of nature.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.