What’s the difference between the two definition when in the end they do the same thing?
In: Mathematics
Well, discovery would likely be more of the first person to come across such a thing, and invention would be someone making something out of it. Not exactly a mathematical answer but your question can be answered easily.
The question is more “is mathematics something inherent in the universe, or is it something we humans invented.”
Like for example, say there’s an intelligent alien species out there. Would they understand our math and equations (sure with different symbols, but the baseline is the same) because that is the only way to do it inherently as a rule in the universe. Or would they have a brand new system of math that works differently than ours?
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If something in math is invented, then presumably it was not true before the invention. I don’t know anyone who holds this position
It’s kind of a philosophical distinction. Scientific facts are usually thought of as discovered and artistic or creative ideas are usually thought of as being invented. Math can be kind of seen as both. It’s an abstraction created by humans, but within that abstraction there are objective facts to be discovered.
Hot take, there’s no fundamental difference between discovery and invention. Just connotation.
Let’s say we ripped up all the books and did away with all knowledge, back to cave life with no written word, not even spoken language. We genuinely do this. The next generation grows up like cavemen. Eventually, life would civilize again, and eventually we get back to where we are now. The question is: what are we teaching in schools?
Languages would all be different, because they’re really just a matter of arbitrary convention. But one plus one would still equal two, and the ratio between a square and circle would still be that oddly specific value we know as pi, even if we used different words and symbols to express all of these concepts.
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