When asked this question in class, it really made me consider not only my own personal views on the topic, but what else other people had to say about it. This war has been happening on and off again since the Pythagoreans. I’m pretty certain of my own opinion, but wanted to take a look into other’s and see if it would sway my decision at all.
There was one article in particular that gave a question to each side of the debate:
- For those who believe mathematics was discovered – where are you looking?
- For those who believe mathematics was invented – why can’t a mathematician announce to the world that he has invented 2+2 to equal 5?
Plato agreed with the side of mathematics being discovered, which is also known as the Platonic Theory. He described it as a “discoverable system that underlines the structure of the universe”. The more we understand numbers, the more we can understand nature and the world we live in. Math is here regardless if we are or not, it has and will always be a part of the universe. Another article suggested, “the structures of mathematics are intrinsic to nature”. We find things in nature that explain some mathematics and help us put meaning to it. These patterns in nature surround us and help us to create what we call mathematics.
The opposing view questions, well where are these ground of finding such mathematics? Math isn’t just sitting out there waiting to be discovered, we invent it and develop it over time. The only reason math describes the physical world is because we invented it do so and help us with purposes we needed it for. Many non-Platonic views argue that our mathematical models are simply approximations of reality. These models often fail us, or aren’t exact, and we invent new mathematics in order to improve this.
My personal opinion hasn’t really changed, but I can definitely see both sides of the argument. I definitely think mathematics is discovered. Mathematics describes our universe. I see it as almost embedded there and by exploration and connections, we discover patterns that lead to what our mathematics looks like today. Obviously we didn’t just pull the quadratic equation out of no where. It begins with small building blocks and when looking at those foundations, we notice more and more patterns that occur and we continue to break them down to discover new mathematical ideas. Looking at the opposing side, I can understand that it seems a little far-fetched that we could just discover some ideas. I also can see the argument for the idea that someone had to invent numbers at some point. They needed numbers in order to count things they needed, so they named 1, 2, 3, and so on. But, I also don’t think you can just invent something that works out so perfectly in our world and that everyone just agrees on. It’s like the question asked, how could you just invent something? You cannot invent that 2+2=5, it just doesn’t work. I think that when you think about all of the patterns in the world, that is really what it all boils down to.
When I think about this question it really helps me to try and understand what mathematics is all about and I think that as a future educator, it would be a cool idea to do some sort of activity with my students, asking them this same question. There’s obviously no right or wrong answer and I think it can be very valuable to hear other’s opinions and realize your own because it may change how your perceive mathematics.