Is math created or discovered?

Is math created or discovered?

Once again, I will respond this question by saying that to a certain extent, math is both created and discovered. Many will say that it is completely ridiculous to even suggest that math is created because math is completely factual. However, in many ways, math is theoretical and it has its faults.

Mathematicians, for example, spend their lives trying to prove theories or come up with theories. A good example of this is Andrew Wiles. Ever since he was a child, Andrew had been trying to solve Fermat’s last theorem, which was considered to be the greatest mathematical problem because of its simplicity and complexity.  The problem was this: the problem aⁿ + bⁿ = cⁿ  cannot be solved with a value for n that is greater than two. This simple mathematical statement that even young children could understand had created a huge mathematical problem because no one had been able to prove or disprove it. However, ever since Andrew Wiles stumbled upon it as a child, he has dedicated a large part of his life to solving this problem. He finally proved it by using many strategies that he had learned over the years when working on other projects. These strategies were very much 21^st century strategies. So, when Fermat wrote that his proof would not fit in a page, he probably found a different way of solving it because Fermat could not have possibly done it Andrew’s way because he used knowledge that was only discovered way after Fermat passed away. Therefore, although they both came to the same conclusion, they created different ways of solving it. If they found different ways of solving the same problem, doesn’t this mean that they both just created ways of solving it? If they had discovered how to solve it, wouldn’t they have found the same way of solving it? Therefore, does this mean that this kind of math is created? Maybe not. It could be argued that they both just discovered two different ways of solving it. The math itself was always there, it just needed to be discovered.

These series of confusing questions open up another problem when attempting to answer this question. How do we define “create” and “discover”? How do we ever really know if something is created?

I used to think that math was very concrete and factual. However, the image above shows that even simple everyday algebra can be disproved. This is math that we learn at a young age and use for the rest of our lives, can our math just be faulty? Also, who created or discovered math? What about in an alternative universe? If they use the concept of math in a different way, does this mean that we created our own math and so did they? Also, counting in different bases is something I never even knew existed but has been used by many and is still used and taught in some places. Counting in a different base was created to count in a different way. Again, it was created. Also, who decides what the definition of a straight line will be? Will anything ever be perfectly straight? There are many still unanswered questions waiting that may remain as questions forever. We just might have to learn to be happy with the question itself. This includes the question I have been attempting to answer through out this whole argument.

I came into this topic with a clear and certain idea in my head: math is discovered. I thought this because math is what our world runs on and something as important and concrete as that can’t be created. Although I am not great at math, I love how it works. For example, when completing a math test I know that I whatever grade I get will be inarguable because I either got the answer right or wrong. In subjects like English however, my grade depends on rubric and it is subjective depending on who reads it. Unlike math, English can’t be right or wrong.  However, now that I have seen all the evidence and arguments, I realize that, just like many of the other systems in our society, math is subjective in a way. As I have shown, our math can be disproved, and proofs can be created in order to prove something. Therefore, math is both created and discovered. However, I don’t think anyone will ever be able to fully answer this question. But then again, that’s what mathematicians said about Fermat’s last theorem.