Math: Invented or Discovered? 


        It isn’t necessary to have a Ph.D in Mathematics to have the ability to reflect on whether Math was discovered or invented. Basic math gives you tools such as logic that allow you to shape an opinion on the matter. Many support the platonic mathematical theory, where numbers and concepts exist abstractly and humans simply assign symbols to them or use reasoning to find them. However, how can we be sure that a simple mathematical concept like unity exists in all living organisms? What if a completely different organism, who isn’t even powered by oxygen but by chemical reactions, has the same notion of unity? If you put this living organisms in front of two trees, and ask it to count them, will it instinctively count: “One, two”? What if he hasn’t developed the area of our brain that gives unity to objects? Such theory could explain how children have a hard time materializing infinity or uncertainties. We work from what our senses perceive, we see two trees therefore our brain has the necessity to convert our vision into information: “Two trees”. But if this imaginary living organism hasn’t got any vision cones, how could he convert an information which he is unable to retrieve into a concrete information? From this premise, to some extent math is not discovered, as numbers and concepts aren’t set in stone like planets or matter in the universe. Math is subject to the intelligent being that is perceiving it. But is this sufficient evidence to conclude that math was invented?

        Let’s try to ignore Platonic, Empiricism, Formalism and other mathematical theories to avoid any intersection from their and our schema. Therefore it’s more pragmatic to use the tools that Math itself offers us to access the possibility of math being invented. Logic is a fundamental concept that serves as fuel for math. But would it be logical to use a product of an object to prove the own existence of such object? If math is presumed to have been invented, who invented it and when? Ancient civilizations like the Mayas, Chinese or the Greeks had a vast range of astrological and arithmetic knowledge. But their bases would vary, as the Babylonians used a base 70 and our modern mathematical system works on a base 10. Could math be the same kind of solution like Andrew’s proof for Fermat? Could there be different ways to reach a solution for math? It looks like it’s highly probable, but it still can’t prove the invention of math. Like already mentioned, math could be a way for the brain to translate vision into information, so the first apparition of math could be linked to our ancestors, it could be a way for us to preserve our identity. We could used symmetry of the body to recognize other humans and stay in groups. We could also use the number of steps to communicate with the members of our group. Since we have ten fingers on our hands, it’s highly probable that we could count until 10, and when we passed the barrier of the dozen, it’s probably one of the biggest discoveries in math since we could talk about abstract numbers, and we had now an infinite series of possible numbers. So to some extent we started using what was at our disposal to come up with a system that could explain phenomenons around us, could such system be math at its early stages? 

All of this evidence seems to be pointing towards Math being invented along the years. It may look like Math was in some sort invented to explain phenomenas who we have discovered through math. But again, if we do find an extraterrestrial form of intelligence, and they do have a notion of mathematics, my theory would collapse like the Tanayama/Shimura conjecture if you disprove the pillar it is being supported by. Many high school students think Math is completely objective and is perfect with no flaws. But we have seen that our arithmetic is flawed, as infinite causes a problem for us to solve some problems. Uncertainties also are a blind spot in this respected field. Like any other way of knowing, it’s not perfect, you do encounter flaws, which then supports the theory that it might have been created by us humans. 

As a junior high school student, I should embrace Math as a way of knowing, but also when looking at different theorems, it looks so perfect that we tend to argue that it was discovered. We do know that there are some flaws in our algebra and uncertainties, but if decide to change the pillars of math, which is algebra to some extent, we would have to take a completely different approach, and re-learn with different premises. So I advocate for no change until my college graduation. If it were to be changed, only the new generation should learn it as they will have more plasticity.