That’s philosophical.
Are our neurons, are waves etc. not just a system that directly ‘perform’ maths without ‘doing’ maths? Math can be seen as a language for us to describe, explore and predict stuff. But you could equivalently say that the math is already there and we just discover it and put it into words.
That relates to the question whether math is discovered or invented. The one is an act of uncovering universal and natural truths, the other a rather creative process of bringing something new into a universe where it isn’t naturally found.
But that’s the catch. We wouldn’t say that, for example, coffe machines are discovered, they are not found in nature. (If they would, that would be quite a headline to wake up to.) They are clearly invented. Math however builds upon a fundament of provable truths. Of stuff that is already there and can be found in nature. So while we might argue that at least some parts of math may be invented (just like the coffee machine that operates on physical principles that exist elsewhere in nature with respect to their components), isn’t the fundament of math itself rather discovered? We just put into words and symbols, what is already there and uncover the hidden mechanisms.
I am not a mathematician, but have heard somewhere that it is already quite an effort to prove why our numbers make sense or why 1+1 can equal 2. And while we certainly do not need to tie math to an observable physical reality, we derived fundamental working principles from it, don’t we?
That’s philosophical.
Are our neurons, are waves etc. not just a system that directly ‘perform’ maths without ‘doing’ maths? Math can be seen as a language for us to describe, explore and predict stuff. But you could equivalently say that the math is already there and we just discover it and put it into words.
That relates to the question whether math is discovered or invented. The one is an act of uncovering universal and natural truths, the other a rather creative process of bringing something new into a universe where it isn’t naturally found.
But that’s the catch. We wouldn’t say that, for example, coffe machines are discovered, they are not found in nature. (If they would, that would be quite a headline to wake up to.) They are clearly invented. Math however builds upon a fundament of provable truths. Of stuff that is already there and can be found in nature. So while we might argue that at least some parts of math may be invented (just like the coffee machine that operates on physical principles that exist elsewhere in nature with respect to their components), isn’t the fundament of math itself rather discovered? We just put into words and symbols, what is already there and uncover the hidden mechanisms.
I am not a mathematician, but have heard somewhere that it is already quite an effort to prove why our numbers make sense or why 1+1 can equal 2. And while we certainly do not need to tie math to an observable physical reality, we derived fundamental working principles from it, don’t we?