Otázka: Was math discovered or invented
Přidal(a): Mikuláš Benda
Mathematics is a tool used to depict our reality and any system, based on quantifiable objects. It can be seen anywhere around us and we use it every day. This includes everyday human actions like shopping, but it can be also seen in nature. Humans, upon discovering or inventing this tool, started to realize that it might have been here before the existence of humanity, or on the other hand that we created such powerful tool. This formed various discussions on this topic and it has been centre of discussion in the past centuries. There are various theories against the statement that we have discovered mathematics, but also quite a few that say otherwise. Both sides of the arguments are supported by many studies and theories, but we cannot say for sure which one of them is correct. In my opinion we have discovered mathematics, as there is so much evidence supporting the fact that we have indeed discovered mathematics instead of inventing it. Even though I believe that mathematics was discovered and not invented I will also mention theories against, to give objective view on the topic.
One side of the dispute is that mathematics was discovered through life. Even though there are many theorems and mathematics discovered every day, they are linked to real world and by creating new links and theories; we are only discovering what already existed before we thought of it. There were many mathematicians in past that tried confirming this theory by supporting it with evidence and theories, including Riemann, Einstein Plato and Appolonius of Perga. Even though some might argue that we have created mathematics to understand everything around us, it is actually not true, as we have only described reality around us and things that would exist even without humanity. This means that if humans died and some foreign civilization came to Earth, or different species that would undergo similar development like us emerged, they would perceive mathematics the same way, and even though it would be written differently, it would ultimately have the same rules and principles, because mathematics was, is, and will always be the same.
Theory that tries to prove that mathematics exist around us and have always existed is mathematical realism. Firstly, realism is a philosophy and belief of existence of certain things. If you believe in subatomic particles, you are a science realist and if you believe in existence of numbers, you are a mathematical realist. Even though people cannot see or observe actual numbers in this world, or for example throw number 8 out of the window, these numbers still exist and they are indispensable for science. Realists say that the only math known to humans is the math knowable by humans. This means that in objective mathematical universe, beyond the math we currently know, there might be more complex math that we might or might not one day discover. This means that mathematical realism focuses on the fact that there are certain mathematical entities “out there in the universe” waiting to be discovered, which would exist regardless of their discovery by humans, proving that mathematics was discovered, not invented. Some might say that new mathematical concepts and theorems are like undiscovered species. We just need to find them and in doing so, add them to our set of mathematical knowledge and we uncover them and bring them to practical use
Second argument is that we have invented mathematics in order to ease our lives. This tool is said to come from our brain, but nowhere else. It is said to be completely artificial, with no history before humans, thus stating that nothing around us is actually based on mathematics, but we made mathematics work with our surroundings in order to better understand the world. We have come up with axioms and theories, which are actually only concepts that we apply in our lives. This means that when humans came up with definition of perfect circle or right angle, it was already known that there could never be completely perfect circle or right angle in real life, but it helped to define things around us. Some mathematicians tend to call mathematics a metaphor or a language we use to describe our world, which is correct to some extent. Gideon Rosen came up with the theory of factionalism which states that mathematics is a fiction and everything in mathematics is element of a story of math. For example “10/2 = 5” makes perfect sense, but outside this story, none of it is not correct whatsoever. Fictionalists say that they use the story of math which is complete and perfect to describe real things which themselves do not contain nor perform math. Alain Badiou states that mathematic is a rigorous aesthetic, which means that it does not tell us anything of real being, but forges a fiction of intelligible consistency. All these arguments can be summed up by saying that mathematics was created by our brain only and it is merely a concept of perfection that helps us every day.
Upon describing both points of view, it is also important to define the difference between mathematics being discovered and invented. In my opinion, mathematics remains the same even if it was discovered or invented, as we still use it the same way. Furthermore, if we think about mathematics as something invented, it might not actually be true, as someone could have invented it before, without us knowing about it, which also applies to the future and actually makes our finding a discovery without us knowing about it. Imagine an author publishing a book, which seems to be an original masterpiece, but if translated to sequence of numbers in mathematics, such sequence might have already existed, for example in Pi, which would mean that the book is no longer invented, but discovered. This plays not only a large role in the decision whether mathematics was discovered or invented, but also in our perception of it.
After analyzing all the aspects of mathematics, it really is not easy to decide whether it really was invented or only discovered. I still believe that mathematics was always there even before we evolved from unicellular organisms. On the other hand, there is some evidence that confirms theory of mathematics being invented. I personally do not believe that we could possibly invent something so powerful as mathematics without it being here before us as well as after we leave this planet. Nonetheless, mathematics is incredibly powerful tool of great use, despite its origin.