Is Math the Language of the Universe?
To call math the language of the universe sounds great for mathematicians and propagates it to being sort of a divine subject. If God made the university with math we mathematicians become untouchable priests. That is nice and feels good. But is it really the right way to perceive our subject?
Assume you are living as a small animal on a flat surface moving just a few meters in each direction. You will, e.g., discover that walking 10 steps into one direction, turning right at a rectangular angle (that is the angle that splits the straight angle into two equal parts), then walking another 10 steps and continuing like this brings you back to were you have been. If you are a really clever animal you will discover the Pythagoras and all of the beauty of plane geometry. Why would you want to do this? The simple answer is that a mathematical model of your world is the only way to describe what you see and predict what you expect to happen. It will be enormously useful. It does not „explain“ your world, nor „is it“ your world. It is just your model of the world, accurate enough to do science that you cannot do in any other way.
As soon as we as men look up and a bit further to the horizon, we discover how ships vanish behind the horizon. So the surface we live on does not stretch straight in all directions when we define „straight“ as the way a ray of light propagates. The surface bends somehow. Doing more accurate observations will yield a more accurate model where we live on a ball instead of a flat surface. With just a little effort we can even come up with a rather precise measurement of the diameter of this ball. And we can now predict that walking along a square as above will not exactly bring us back to our starting point. To test this will take some effort, however, as well as to test the prediction that the angles in a triangle no longer add to 180 degrees if the triangle sides follow the surface. We might even predict that we are not capable of reaching India from Spain with the resources of our sailing ships unless we are lucky to find land in between. It is an aesthetically pleasing and useful „explanation“ of our world, but as we now know it is not accurate. Moreover, we cannot „see“ the ball that we live on and have only indirect proof of that fact, such as the shadow of the earth on the moon among a lot of other phenomena. So it is just another model which helps us describe and predict.
The same happens to the planets, the moon and the sun. The first model with the earth in the center had to be made too complicated to explain what we really see in the sky. It turns out that there is a far more simple way to describe and predict the skies. We only have to put the sun into the center and the planets in circles around them. But wait! More accurate measurements show that this is again not a precise way to describe what we see. Indeed, the planets seem to be moving on ellipses with the sun in one focal point. How can this be? The genius that found a simple „explanation“ valid for centuries was Newton. He gave us a model with an interaction called gravity between bodies that decreases with the inverse square of the distance. Using mathematical tools, he showed that the result was just what we see.
Again, this model had flaws. E.g., the movements of Mercury are not exactly explained. This fact was known for a long time. But it took another update of the model by another genius, Einstein, to explain this effect. We always encounter new phenomena that do not fit with our model. Currently, we have a problem with invisible mass and energy in the large universe, and also with awkward behavior in the tiny things.
The history of this goes on and on. E.g., the special theory of relativity is just a model to explain why we do not measure a different speed of light when we move relative to the light source. The combination of time and space into a four-dimensional mathematical model yields very pleasing formulas to describe and predict this. Without these formulas, modern technology would not work. But I would strongly argue against stating that our world „is“ a four-dimensional space-time. This is just a model that helps us to describe the phenomena we see and predict the outcome of new experiments and observations. One of the most striking predictions was the curvature of light around stars by Einstein. He just found a more accurate way to model the straight lines that light rays follow, and to model our measurement of time.
In conclusion, our mathematical models are useful, but they are not identical to the world. Why then are they so elegant? An explanation for this may be that they smoothen statistical facts that we are incapable of seeing. E.g., we describe air by pressure and flow, or even chaotic turbulence, with simple formulas while in fact air is formed by movements of zillions of individual particles. On a more elementary level, we „neglect“ the resistance of air. But even if we find the one world formula like in the „standard“ model I bet it will only yield an approximation of the world, and we will soon discover that it does not represent the complete truth.
However, I could be wrong with this bet. We might be able to model the world as far as is forever possible to us humans. As useful as such a model might be, it will fail to „explain“ the world on a grand scale. We will have to be contempt with our approximate math models which served us so well over the centuries.