Mathematics is a language that is used to represent the universe. It speaks as a language in the same way that a linguistic language speaks, however it is purely logical and strictly represents functions and amounts rather than a more general range of concepts. A language such as English or French will use sounds and symbols to represent abstract constructs which can be used as mental tools in order to understand the world and the processes of it. These constructs are used in conjunction with each other to form large ideas which result in information being passed from one to another. Mathematics uses symbols and sounds to represent amounts and functions, and the logic of the language means that it can be used to describe the universe precisely.
It is not simply made up, although it has been invented, because the logic of mathematics can be accurately used to apply knowledge. The laws of physics are utilised every day in almost every aspect of life as technology becomes ever more prominent in our lives. Because mathematics works, so does the technology. So even though it is an abstract construct which is used to describe something that is represented only in a mental environment, the wisdom of it holds true when applied to reality.
However, if a new discovery forced physics to denounce all of its laws as bogus, the world would not fall apart. Likewise, if a new discovery showed that all in the universe including us and our behaviour was totally governed by a formulaic function that could be proven, we would still remain conscious and aware of our own choices. So in the light of reality, the description of it has no real power over it, it only allows us to use what is already there to do what it already does.
This mental realm of reality that exists as pure number and function is often respected as a real phenomenon. Perhaps the only explanation as to why mathematics works so well in this scheme of reality, is that there actually exists a realm or dimension in which pure logic dictates everything. This reality is often thought of above our own, a realm of pure function and logic that everything follows from. Many physicists believe the nature of reality to be like this.
There is another aspect of reality that exists on the opposite side of this realm. The area of chaos, in which nothing is fixed and all is in transition. The order that we find in the universe due to our own abstract mental constructs is sometimes thought of as just that, i.e. a mental analogy that allows us to make some kind of sense from what is actually a realm of chaos. Why chaos? The answer is because of infinite possibility. Mathematics describes chaos in a set of principles which gives way to rapid change and alterations in process. It can be shown that from the very beginning of reality, the processes which brought it about can be like this. According to logic, everything must be balanced and accounted for. But in the universe, everything is in a continual process of change and it also had to start somewhere.
The laws of physics are simple mathematical principles which describe abstract principle that in turn provide useful mental constructs which allow us to predict and use nature to our advantage. But nature is not uniform and mathematical, it exists as an evolving and changing presence which demonstrates tendencies and behaviours. Even physics itself is now known to be a lot less logical than originally thought, with the onset of quantum theory and phenomena such as spooky action at a distance. Mathematicians create new mathematics and new tools for looking at and ordering number in order to accommodate what is seen in the universe, and only in this way can any logical sense be made out of new observations. The equations that are used to describe quantum processes rely on long chains of principle, each based on abstract notions of amounts and time, which in turn rely on the basic principles of mathematics.
For someone like me, the language of mathematics is beyond my mental landscape and when shown formula, I do not see something that can be mentalised and made sense from. I do however appreciate the nature of infinite possibility and chaos, I see the truth in the fact that all is possible in the universe and that we can look at it in any number of useful ways. If we take away the perspective and just see what is around us without the attachment of any thought, we find infinite possibility, we discover chaos. The flow and flux of all around us, if appreciated without thought or way to look, we find an abundant array of experience.
Mathematics looks at infinity as a concept, and studies it with various functions which has allowed physicists to find ways of looking at the expanding universe. Including the methodology for studying the principles of chaos within mathematics, it seems that we have gone a full cycle in the way we can see the world. The reality we are in, what we see and perceive is not made up of numbers, but information. We can study this with the tools of number or linguistic. For me it feels that number reaches into the pure real of logic, and linguistic reaches into the realm of chaos and infinite possibility. Both of these forms of describing the universe are based on abstract mental principles, which asks the question of if any of these mental constructs represent reality, have reality, or are simply illusions created by us in order to make sense of the inherently senseless