Math Blog

Prompt: Can we know if mathematics is invented or discovered?

Renato Curiati

Block 4

Mathematics is a subject we learn in school as it being “set in stone”, this is, we assume that it was invented. The teacher goes to the board, explains the rules with examples, and we have homework for the next class. Every single math class is the same. We use variables, symbols, numbers, syntax, and various other forms to solve a problem or expression. And most importantly, we use math to communicate with each other, and it is considered a language. The social interaction is key to the understanding of mathematics, which is an interesting thing.

On the other hand, one might argue that mathematics is discovered. In our number system, we use base ten, which is what we learn in school. But according to the presentation Mr. Fertig showed us, there are numerous ways we can count. If we use base 4, 3x3 is 21, since there are two two’s and one four, which becomes 21. Now, when we see that we think: “No way! 3x3 is 9!”. But that’s what we learned, but not necessarily what is the only correct answer. Also, when we say: 1 + 1= 2, there are other ways to use 1 +1. In binary numbers (computer numbers), 1 + 1= 10. And again, our brain sees it and completely rejects it.  We learn since we are little that 1 + 1 is always true. But as Mr. Fertig told us, 1 + 1 is not always true, and this makes us insane! We see it as something incorrect, but other societies might use it and see the base 10 we use as incorrect. It is all about perception and schema. Each culture uses its own form of counting to fulfill its needs. We may use base 10, but another culture might use base 4 because it is easier for them to count and communicate with each other.

      But what we don’t learn in school is whether mathematics is invented or discovered. As many historians say, the cave men invented math a while ago, as they used rocks and drew on the caves to count and communicate. But this is what our schema tells us, and what we perceive. To what extent can we rely on our schema and our perception? What if math was discovered, and we don’t notice it because our schema says it was invented? How can we know it after all? To what extent can we trust historians? All of these questions are really hard to answer, and this is what makes this question even harder. There is not enough information on either side for us to be 100% sure if math was really invented or was it already meant to be discovered.

To conclude, both arguments are correct, but I personally think that if I had to choose an answer, I would choose that mathematics is discovered. The example of the different bases proves to some extent that there are different ways to count and still reach the correct answer. Even though our schema tells us that the correct way is using base 10, if we use base 4, it is still correct according to its theories and rules. Each culture uses a different form of counting based on their needs. We use base 10 because we have 10 fingers (most of us), and this makes it easier to learn when little. But that doesn’t mean that it is the only correct way of counting. There is no such thing as the “only one”. And us, as human beings, have to respect each culture’s decisions. We shouldn’t see the other cultures as they are wrong, but as another way to count or solve a math problem.