Mathematics: Invention or Discovery?

Can we know if mathematics is invented or discovered?

In history, archeologists dig up artifacts and sweep off the dust of prehistoric skulls that uncover new civilizations. In science, medicines are found and improved every day that find cures to fatal diseases. In English we decode symbols in classic literature crafted by amazing writers and in art we decipher the meaning of seemingly ambiguous pieces created by the hands of artists. All of our subject areas seem to have been created, and later analyzed, by humans. Artisans, craftsmen, rulers, writers, doctors, scholars, etc. All of them clearly create their craft. But what about mathematicians and this clean, error-free subject of mathematics. Math seems to be the only subject that hasn't been created, it was discovered, through historical tracing, in ancient civilizations such as the Ancient Egyptians and Greeks. But how do we actually know If math was actually there before humans started to use it. Is math a natural thing, and how can we find out if it is? Unfortunately, this is one of the hardest questions to ask because first of all, we cannot go back thousands of years in a time travel device and simply ask civilizations where they first came upon math and second, if math existed before humans, who can we ask? Furthermore, if mathematics was discovered, this means that it was a natural process of the Earth. It means that even before life forms existed, math was there. 

If we look at how math could have been invented, especially in western culture, it would explain the way children and adults use their numbers as opposed to babies. Babies seem to count in logarithms and so for them, exactly half of 9 would be 3 instead of our 5. It is quite interesting to note that our conventional schools teach  us how to count in a base ten system, teach us the man made concept of decimals and whatnot and then later, after our brains have been rewired to think of numbers in a certain way, we are taught logarithms once again. Furthermore, the concept of counting. In my opinion, counting is something that is somewhat vital in all civilizations. Humans use a base of 10 because we have 10 fingers, and of course, 10 toes. But, this base is only a product of human creation. If we were all created with 6 fingers on each hand, maybe we would use base 12. Also, if we look even further, numbers themselves are a human creation. If I placed two pencils in front of me, there would not be two pencils in front of me. There would just be pencils that represented the concept of twoness. Numbers didn't exist until we made them exist. 

Now, if mathematics was discovered, we would have to look back to the origins of the universe. For example, the Big Bang theory that proposes the creation of the Milky Way Galaxy. Was math used to create this phenomenon, or do we just use math to describe it? My assumption is the latter. If math was used to created everything in our universe, wouldn't everything just be perfectly symmetrical, orderly and structured? I just can't see how something as organic and ambiguous as space being mathematically calculated, and if it was, I can't see it being naturally configured. However, there is math in nature. For instance, we can see golden rations in plants and mathematical explanations for hurricanes and other natural disasters. Also, we can see nature colliding with math with Fibonacci's numbers, originally studied on the how fast bunnies could breed in an ideal circumstance. And so, we can see math as a natural thing that occurs within natural environments, but still, humans created math out of these circumstances. There is no way of really knowing that mathematicians did not create math to fit these natural situations. I think this is where I stand at the moment. Although I try to see the argument that math was discovered, it keeps coming back to me seeing how humans created this math. It is actually quite a shocking realization because if math was created, it makes the whole subject so subjective. It is almost like a religion. There are rules that people have made up because those are their morals and values and then people follow them because they also believe these rules are right. The problem is that if these rules are wrong, does that mean that all of the math we have ever done, since the beginning of time, is wrong? How can we justify a system that was created by the people who use it. What if mathematicians really had no idea what they were doing and just made equations because they sounded right and it made all of the puzzle pieces fit together. Honestly, this is a scary thought; to realize that everything you thought was concrete, suddenly isn't; to realize that a subject that is seemingly so full of certainty and so empty of errors may be complete nonsense. 

I believe in math like a religion. I follow the rules because if I didn't my math would not make sense to anyone else. I have realized that it is more of a subjective concept rater than a concrete subject. Math may have been there when the universe was created and maybe the universe has its own mathematical calculation about everything that goes on inside of it. Maybe humans discovered this math, decoded it and built upon it. But maybe, mathematics is just like faith, with rules and concepts mathematicians made up because they seemed to make sense in their own heads. Maybe math is purely conceptual. Maybe, just maybe we are all just following a system of nonsensical numbers.