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Sure math itself may be profound. But asking whether math was "created" or "discovered" is a language thing. Put this way. Whether something was "created" of "

Sure math itself may be profound. But asking whether math was "created" or "discovered" is a language thing. Put this way. Whether something was "created" of "discovered" are human concepts materialized through language. To apply it to math is pointless.

tim333 6y ago
It seems to me some bits are clearly created and some discovered. Eg. pi is discovered but the symbols we use to represent it's value in decimal form, 1 2 3 . etc are human inventions. There may be some value in trying to figure what's what there? I think it can help to think what alien mathematicians would have the same and what would be different. No doubt they'd find pi and e if they were any good as those are the two most fundamental transcendental constants in math but our decimal representation is one amongst a very large set of possible representations.
- nendroid 6y ago
  I get what you're saying but my point still applies. Did we discover the decimal form of representation out of all possible forms of representing fractional quantities or did we create that form? Was the english language discovered out of the set of all possible languages or was it created? It's good to examine the intuitive differences though. Why does the choice of representation feel more "creative" than say the "choice" of what axioms to use in a certain field in mathematics? Many times you will discover that the intuition is just a biased flaw in the way we think, but many times you will discover that your intuition is demarcating an actual difference. I think our intuition is marking an actual difference here. The set of all symbols representing the number 3 is infinite not bounded by any rules. The set of all sets of axioms we can use to formulate a mathematical theory is infinite but it is actually a subset. We only choose axioms in math that are internally consistent. The number Inconsistent sets of axioms are a huge and many are discarded to find a consistent set. It is possibly this blurry demarcation of restriction and size of the domain that marks our intuitive feelings of what we label as "created" or "discovered." Who knows, I suspect the rules are much more complicated and if we dive in deeper you will find that our intuition is flawed. For example why does it feel extremely wrong to say that the Americas were created rather than discovered? But again, realize that we are discussing the intricacies of arbitrary words defined in language. Outside of the domain of language the concept is uninteresting.
  - tim333 6y ago
    Created implies a creator so it's obviously wrong to say the humans created the Americas though you could argue that forces of nature did. The case of mathematics seems more subtle though, beyond language issues. I find it quite interesting myself.

tim333 6y ago

It seems to me some bits are clearly created and some discovered. Eg. pi is discovered but the symbols we use to represent it's value in decimal form, 1 2 3 . etc are human inventions. There may be some value in trying to figure what's what there? I think it can help to think what alien mathematicians would have the same and what would be different. No doubt they'd find pi and e if they were any good as those are the two most fundamental transcendental constants in math but our decimal representation is one amongst a very large set of possible representations.

nendroid 6y ago
I get what you're saying but my point still applies. Did we discover the decimal form of representation out of all possible forms of representing fractional quantities or did we create that form? Was the english language discovered out of the set of all possible languages or was it created? It's good to examine the intuitive differences though. Why does the choice of representation feel more "creative" than say the "choice" of what axioms to use in a certain field in mathematics? Many times you will discover that the intuition is just a biased flaw in the way we think, but many times you will discover that your intuition is demarcating an actual difference. I think our intuition is marking an actual difference here. The set of all symbols representing the number 3 is infinite not bounded by any rules. The set of all sets of axioms we can use to formulate a mathematical theory is infinite but it is actually a subset. We only choose axioms in math that are internally consistent. The number Inconsistent sets of axioms are a huge and many are discarded to find a consistent set. It is possibly this blurry demarcation of restriction and size of the domain that marks our intuitive feelings of what we label as "created" or "discovered." Who knows, I suspect the rules are much more complicated and if we dive in deeper you will find that our intuition is flawed. For example why does it feel extremely wrong to say that the Americas were created rather than discovered? But again, realize that we are discussing the intricacies of arbitrary words defined in language. Outside of the domain of language the concept is uninteresting.
- tim333 6y ago
  Created implies a creator so it's obviously wrong to say the humans created the Americas though you could argue that forces of nature did. The case of mathematics seems more subtle though, beyond language issues. I find it quite interesting myself.