Mathematics invented or discovered

There is a debate about mathematics. It asks whether mathematics is invented or discovered.

Some are of the view that the universe is a purely mathematical entity. This idea is strengthened by the fact that the deeper the scientists and mathematicians try to go into the quantum realm, they find that the subatomic realm is more about abstract mathematical ideas rather than any concreate objective entities. Physicist Max Tegmark believes that any definitive universal theory cannot include concepts such as "subatomic particles", "vibrating strings", "space-time deformation" or other man-made constructs. Because when we go that deep, it is the mathematics that is guiding our imagination towards such possible constructs as the electrons or protons or the springs of the Spring Theory, and not the other way round.

This takes us to the idea if the whole universe, with all its diversity, is made up of, at the very core, abstract ideas and formulas and not anything material. Does the deconstruction of reality down to the quantum realm bring us to a structure of mere ideas - intuitions contemplated in a language we humans can verse in, if we try hard enough. And out of this abstract framework of ideas of structure and movement, does matter just emerge, like fruit emerges from the seed! Or like an act emerges from the mere thought of a thinking agent!

In such case, the universe is reduced into a set of abstract concepts, but fantastically so, this abstraction can be symbolically written down in the language of mathematics. And more so, this same language is possessed by another species in the universe that can think of abstract things, find them in its surroundings and write them down in symbols of that same language. The universe is made up of a blueprint of ideas - God knows who thought of them - but they are completely independent of human perception, yet the fact remains that humans are the only ones in the universe that can perceive them.

So, this leads us to the idea that humans 'discover' the mathematics underlying the grand reality of the universe. That is, it is a language written in the core of the universe and for some unknown reason, humans 'discover' that language as they progressively inquire into its secrets. Again, this is possible only because humans possess the same abstractions in their thoughts that are used in the core structure of the universe. But there is an opposing school of thought that insists that mathematics is 'invented'.

This line of thought says that humans possess a natural faculty of languages, coupled with the ability to perceive thing both objective and imaginary. Language is a set of symbols that humans use to describe their thoughts about the world around them. And with experience, these symbol-structures become richer and richer. One of these symbol-structures is mathematics, which humans have invented to describe certain properties of the world around them.

The problem is that if this language of mathematics has been invented by humans, it is a tool coming out of the human mind and limited by the limitations of human perception. Just like a map drawn to describe a terrain is certainly nothing close to the real terrain, it is just a rough imagination of the real. So, if math is a crude, purely mind-dependent tool of discursive aggregation, how can then it provide the deepest insight of the reality of the universe, unless the abstractions underlying the grand, abstract universal blueprint of idea is in some mysterious way the same blueprint that rests in the a priori framework of the abstractions of the erring human thought!

Erring, because every time the mind comes up with better theories supported by models of mathematical abstractions to describe phenomenon observed around us, soon enough it is found by another struggling mind that there is a better theory that describes the phenomenon rather more precisely, and the older theory is discarded. This gives a sense that all coming theories are better aggregates of reality, and considering the wide gap between what we have found and what we haven't, our understanding of reality must be extremely crude at best. How then can we propound that the universe - which stands with an un-falling grand balance that constantly evens out all dynamics within the grand stasis, with all its vastness, diversity and depth - be explainable with the crude tool of math invented by the human mind, basically upon the simple ideas of counting, adding and subtracting.

It is true that mathematics has become much more complicated than just counting, adding and subtracting. It has collected numerous structures based on different axiomatic models, but at the core it is a kind of story-telling. A story-telling with its own plots, characters and events; of axioms, symbols, operations and solutions of derived formulas. Even though this story begins with the simplest characters like 1,2,3 and operations like adding and subtracting which are very relatable to real life, the advanced models and theorems are far from relatable. Famously, physicists Feynman in his lectures explained that mathematicians play a game of axioms and extend them with logic, but all the while they have no concern what their formulas really mean in real life, it is the physicist who need to relate mathematical sentences with meaning.

How then does a story - written or formed just for the sake of telling that story, without any meaning or practical usefulness in mind - turn out to be exactly the tools needed to describe the real physical world!

And more so, how is it that a bunch of these stories - which have fitted in the theories of Physics, all the while when a whole bunch of other such stories that have not fitted in, that physicist and mathematicians have come to the belief that perhaps not only does mathematics describes reality with precision, but that reality itself is a mathematical entity - not a physical one!

The debate however remains whether mathematics is everywhere in the universe and the mind discovers it or mathematics is the invented tools of the minds with which the mind aims to measure reality and it succeeds to an astounding degree. In both cases one is forced towards the question of the primacy of the 'thought' - the same thought that resonates in the grand structures of the universe and in the neural space of a very tiny, very insignificant entity within it.