Sometime ago I made this poll after reading Einstein’s remark “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”

I was happy to see that some of you voted. Thank you for your support. So, I wanted to tell you that so far the votes are 77% for discovered and 23% for invented.

This kind of problem/question is in fact extremely old and scientists thought about it and tried to give an exact answer. But, in fact an exact answer doesn’t exist. There are just believers. Some consider math to be an invention, and some consider math to be discovered. In the history, there were periods when people considered that every time they were doing mathematics, they were in fact discovering something that was already there; and periods when they believed that they were inventing more methods and tools to help them write what their mind was thinking.  Here is an interesting video that explains more :

Just this week I was talking with one of my teachers about this question and he gave me a nice statistics from his classes. It seems that the students that are doing pure mathematics (or just theory, as we call it) are more inclined to say that math is in fact discovered, they strongly believe that math is everywhere around us and we need to just open our eyes to see it. Also, the students that do applied math or study other subjects that imply math, such as computer science, engineering and physics, believe that mathematics is invented by humans to help them evolve; for them math is just the tool that helps them create/ invent/ evolve.

Doing pure mathematics at university, I am more in the ‘discovered’ category, but I also understand the reasons behind the ‘invented’ concept. My decision to consider mathematics to be discovered, and not invented, goes deep in my beliefs about the creation of the world and also involves my dreamy personality. I believe that around us are to many patterns, to many hidden numbers, equation for it to be invented by the human brain. It seems like all the chaos has a mathematical order in it, and it’s not just our brain that wants to do something special. Improving our understanding of the world around us is probably going to show us more math secrets. Also, other sciences are there to be discovered and understood better. Thus, when we will have the ability to create a whole new world from nothing, I believe that THEN and ONLY THEN we will have the power to say if all this was invented or discovered.

Before ending this post here are some interesting articles on the same topic: by Derek Abbott (physicist and electronic engineer) and by Mario Livio (theoretical astrophysicist).

Thank you for your support and cooperation so far! Any feedback is appreciated so use the like and share buttons! Also, the pool is still open, and you can still vote. Also let me know what is your opinion about this. Do you consider math to be an invention of the human mind?

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## 8 thoughts on “Math is Invented or Discovered?”

1. Yes you are right. Thanks for letting me know. I’ve just modified it.

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1. Andy says:

Sure.

And FWIW, I stand firmly in the “mathematics is invented” camp; sure, some things are discovered, but they are discoveries *about* mathematics, not the discovery of mathematics from some ether. To take a concrete example: we *invent* the notion of a circle as a set of points (which is itself an invention: nothing in the real world corresponds to a “point”, though you can model certain things in the real world as points with differing levels of accuracy), and then after having done that, we’ve discovered relationships between the length of the radius and the circumference or area of the circle, say.

As hinted it, the additional factor is that we then take these inventions of ours and we use them to model or to approximate reality. This is true for all of our mental inventions: mathematics, language, logic, etc. I think this follows fairly naturally from an understanding of both evolution via natural selection and computational theory, since together they tell us what the brain actually does (and why) and how it does it: it solves optimization problems by projecting a hard problem on to an easier space, solving the problem in that space, and then projecting the answer back to the original space. The “spaces” that our mind has in its toolbox includes things such as language, mathematics, logic, visual (e.g. if you’re trying to catch a thrown ball), and several others.

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1. Andy says:

Sorry: “we invent a circle as a set of points equidistant in two dimensions from a given point”. Missed the rest of the definition, though I realize you know it. 😉

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1. That’s fine, I believe you have strong points there, and I don’t want to convince you otherwise. It’s just that I feel that math must be more than our invention.
I agree with your example of a circle, it is right, but when we go to spheres it is not exactly the same thing, because we have sphere (or ellipsoids) in our world (in nature, universe) that are not something we invented. And the circle is just a way to construct these things. So, considering this I believe we are not on the invented pack.
Another things that take me away from the ‘invented’ part are the paradoxes and also the ones that are incredibly hard to imagine and comprehend. One of this is the concept of different types of infinity (Cantor’s theorems). And it just feels incredibly complicated and hard to digest to be invented by humans.

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1. Andy says:

“because we have sphere (or ellipsoids) in our world (in nature, universe)”

I think that’s my point: there are no such things. There are things in nature that we can reasonably *describe* or model as spheres, but they certainly don’t fit the mathematical definition exactly. They aren’t composed of points or lines or surfaces with zero thickness, they aren’t “perfect” sphere anyway, in fact if you’re talking about an “object”, if you drill down far enough it’s not really even clear where the boundaries of such an object are (because of atomic structure etc).

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2. I get your point, though I still consider some of the theorems to be hard to understand by humans in general, and this is one of the main point for me. But thank you for your extremely interesting comments. They made me think twice, but I am not still 100% convinced.

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