Is Math discovered or invented?

The conclusion I come to is BOTH!*

This is an oversimplification but I think it makes the point:

There is no such thing as 1 divided by 2. I can have 1/2 of 2 apples, that’s what we would call discovered math. I have 2 apples, I spilt them into 2 groups of one, and give you 1, and I have one left. We can do this easily. But if I cut a single apple into halves, then I have invented Math. I can’t grow a half of an apple, and I can’t cut an apple perfectly into halves.

Another way to look at this is that if I take 7 equal length 1-foot rulers and put them in a straight line, I have a 7 foot length that is made up of 7 single units. However, if I decide to make this length a single unit and I divide it into 7 parts, 1/7=0.142857 repeating.

There is math that we have discovered because it is discoverable in nature, and then there is math that is invented to make sense of ideas that we invent, like fractions of a whole. Using the 7 units of 1 divided by 7, versus 7 divided by one, is a clear example of this. A perfect 1/2 of an apple is another.

But it’s a bit more complicated and confusing than this simple explanation. This doesn’t mean that any irrational number is necessarily invented. π (pi) is discoverable and not invented. The golden ratio, Φ (phi), is also discoverable. The square root of 2 on the hypotenuse of a 1×1 square is an invention we sought to make sense of an imaginary line dissecting a square.

So, some Math is discoverable and some math is invented (capitalization is my own emphasis).

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*Note: I’ve come to this conclusion through discussions with Joe Truss on the nature of our universe and the premise that ‘We Live in a Tetraverse’.