Is math invented or discovered?

I had my students write their initial thoughts on the question: Is mathematics invented or discovered? Then they had to read a few people's opinions, discuss their ideas with the class, and then write down their final thoughts. Here are three student responses:


I believe that mathematics is a combination of both discovery and invention. As Dr.Mellendorf had stated, “What was discovered was how to mold the model to fit reality. What was invented was the model itself.” It was discovered how to use mathematics. Yet, the processes and whatnot were invented. As Einstein once questioned, “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” Even Einstein believed that there had to be some for of math on the earth before we invented the process of mathematics.
The use of mathematics has been there since the beginning of time. However, it took human thought to develop forms of mathematics. For centuries, our world was using math without knowing what exactly it was called. People have always used forms of addition and subtraction without knowing the technical terms. Math hadn’t come out of thin air, it was discovered. We had just invented the processes and technical terms for the different areas of math. All in all, math has been on the earth since the day it was created. It just took humans some time to pinpoint exactly what mathematics was.


People say that it is there to be discovered, that if it was only invented
anyone could come out and say that 2+2=4. They say that math is there for us to discover. But yet
there are people out there that say math is invented, made by us, that math was not there before
humans. I am somewhere in between the two viewpoints on this topic. I believe that math has
always been there, created by God along with everything else to make the universe go round. I
believe that Newton discovered gravity, he did not invent it. But, I believe that we invented the
system, or the language, that we use to interpret mathematics, but not the “math behind the
math”. Take Newton and Leibnitz for example. Both discovered calculus around the same time,
yet when you look at their theorems, they have many different notations and ways of expressing
the same thing. The calculus they both discovered is the same thing, but they invented different
ways of interpreting it. It would be next to impossible for men who have virtually no way of
communicating to both invent the same thing around the same time. Say the great mathematicians
of old had decided that 1 was really 2 and 2 was really three. Wouldn’t that mean 2+2 would equal
3 when there were really only 2 objects there? (If we were adding objects) Theoretically if the
mathematicians wanted everything to equal tree, then our notation would be different types of
trees, but it would mean the same thing as what we have today. After reading Eugene Vigner’s
quote that said mathematics is a gift, when you think about it, it really is. Mathematics, along with
everything, is a gift from God, therefore not invented, but discovered.



I think that it is both. I believe that the actual concept of math was invented, but I would say that the inner workings of it must be discovered. I’m assuming that people first started to use math in order to make building and other such tasks less difficult, so like discovering fire, it made our lives easier. It’s a tool. Although on the other hand, mathematicians today are still looking to divulge themselves into deeper knowledge of the subject. A prime example of how parts of math have been discovered is Calculus. Regardless of whether or not it was Leibnitz or Newton who discovered it, the fact remains the same; Calculus was discovered. It’s these new discoveries that expand our knowledge of mathematic world.

- Later on, we found that what made this so difficult to answer was the definition of “Math.” After a lot of discussing, we came to the conclusion that math can be defined as both the language of math, and how we use it / describe it, as well as the actual math itself. The actual math itself can be described as the truths and the fact that everything fits and how it works, which is discovered. The part that’s invented is the language of math.