Was Math Discovered or Invented?

What is math? A natural existing property on Earth that was dying to be discovered, or a human invention? Or does it fall somewhere in-between? To answer this complex philosophical question about mathematics, I turned to members of the Wheaton community. 

Out of the thirteen (13) respondents, the results were as follows: two (15%) said that math was discovered, eight (61%) said that math was invented, and three (23%) said that it was both discovered and invented. 

First, I will present the claim that math was discovered. The idea behind this claim is that mathematics was something that first existed in nature and humans stumbled upon it, like a scientific discovery. Interestingly, the two respondents that chose to argue that math was solely discovered did not provide me with an explanation, indicating that potentially the claim that math was discovered is the significantly weaker argument. Or perhaps, that it is just more challenging to argue. 

Next, I will present arguments in favor of math being invented. Ashley Valentine (‘22) said that math was “invented because everything in our world technically is invented by our mind and based on our perception, even if it is in consensus.” In all honesty, I love this point because everyone perceives the world in a slightly different way. Take colors, for instance, because a similar logic can be applied. It seems obvious that colors are something that simply existed in the world since the beginning of time, so if anything, they had to have been discovered. However, as humans we assigned made up names  (green, red, blue, etc.) for the limited amount of the electromagnetic spectrum that the human eye can see as “colors”. Once we invented names for colors, we remained in consensus about what ‘blue’ is, even though it is perceived differently for many individuals. Plus, Crayola “invents” new colors constantly, and artists “invent” colors like black 3.0, the “blackest black” paint in the world. I think math is similarly “invented” in the regard that new equations and terms are being made up by mathematicians over time and eventually they become globally in consensus (except for something like the metric system … thanks to the United States). Harry Topol  (‘22) brings up a similar claim that math is “…invented because it’s a human construct. It’s not naturally found in the world… like fossils are discovered, math is not”. This claim is also similarly echoed by  Stevent Cleto Garcia (‘22), who said that math was “invented as a means to an end” and “it’s a social construct”. 

Another common theme among “math was invented” arguments was that math was invented as a means to help discover, keep track, and make sense of things in this world. Emma Jarvis (‘21) made the claim that math was  “Invented to help discover things.” Katie Vidic (‘23) echoed a similar sentiment claiming that “math was invented as a tool to help keep track of things or make sense of them.” Lastly, Claire Richmond (‘23) also made a nearly identical claim saying that “math was invented as a way to make sense and understand the world.”

Next, I will present the claims that math was both invented and discovered. Katie Hubbard (‘24), claimed that math was “both (discovered and invented), some pieces of math that show up in nature like Fibonacci’s spiral were discovered but super complex algorithms and theories were invented. I think that Katie is right to say this. I have provided a picture of the Fibonacci’s spiral existing in nature. Sarah Simkevich (‘22) made a similar claim about math being both discovered and invented. She said that “The basics of math were unknowingly invented for everyday use and then they realized the math was useful in different ways and different contexts, so they created more rules and expanded on the basics they discovered.” 

Now, I had one more respondent say that math was both discovered and invented: math major, Eva Danielson (‘22). It is important that I dedicated this entire paragraph to her response. Eva first responded simply saying “It depends… mathematics was both discovered and invented… the whole universe is described by four operations?… something bigger is at play.”  She then absolutely went off explaining how math makes her feel spiritual and I have never heard math being described spiritually before but I love when people are really passionate about something, and she was, so I was very intrigued. Here is what she had to say:

I witness a lot of people thinking of math as rules that humans created, but it is actually just rules that humans observed. These rules can measure and explain pretty much all the processes of the universe, which is why many people think it was discovered, as it explains physical and natural sciences which were discovered. But what I find cool is that even in pure math, different concepts come together in the weirdest ways. Like the numbers i, e, pi, and -1, which are all very significant in multiple mathematical findings for different things (pi is discovered as the unit of measurement of a circle (used for cyclic things), i for the square root of a negative number?? E is for exponential growth?? How do they all magically come together to be -1? That’s some wild sh*t, and stuff like that falls together all the time. That’s proof to me that the universe isn’t pointless. I don’t know what the deal is with us existing, but I think there’s something pretty crazy going on there… Regardless of my spiritual beliefs, math being wild like that is really what makes me feel like there’s a balance in the world or the universe. I don’t know what the deal is but d*mn it’s something for sure.

Thank you so much for that explanation, Eva!

Of course, I had to do some research and thinking of my own, so here’s what I have come up with. In short, I believe that math is both discovered and invented. I believe that since there are elements in math that exist in nature, such as the Fibonacci Sequence, it wasn’t something that was completely made up. However, it was invented to help explain these sequences that naturally existed. Mathematical elements were discovered in nature. Math was invented to make sense of these elements.