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I think it just explains what is already in existence. So technically it was Developed by putting together the dots. So it is somewhere between Invention and Discovery.

We discovered a relationship between what exists and how to represent it on paper, or other medium. Zero and numbers exist in our physical world, but setting a number line was a representation so we can work with the numbers. Zero is the absence of numbers, but including in our number system made it more workable.

As an invention, math would be difficult to patent as rain water.Mathematics as counting was developed. The relationships between different values like the Pythagorean Theorem and geometry were discovered.

Is anything invented or discovered? It is a matter of semantics. One could say an invention is a discovery of how to do or make something. To begin with nothing can be invented without the existence of it's parts or processes so inventions have to be discoveries.

Plain and simple Mathematics, a process or way to study and understand the world could not be invented without already existing, so it is a discovery. If mathematics didn't exist it couldn't have been invented. There is nothing that man can create that hasn't existed in the mind of God who created the universe and everything in it, by default every conceivable and inconceivable invention.

And why?

Because if it didn't exist it couldn't be invented, be it creating a "new" object, idea or theory, it can't be created if it doesn't already exist, it can only be discovered.

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