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Whether math is like an art or whether it is "discovered" is sort of a pointless question to me. To start off, math is simply the art of understanding the cons

Whether math is like an art or whether it is "discovered" is sort of a pointless question to me. To start off, math is simply the art of understanding the consequences and theorems from a set of axioms. Since there are an infinite amount of sets of axioms, there's an infinite amount of math. Whether a set of axioms or the theorems derived from a set of axioms is discovered or created is again a pointless philosophical debate that is not exclusive to mathematics. You can apply this question to any topic. Case in point: There is a finite set of paintings that can be painted on a fixed sized canvas using a fixed set of colored paint. When you create a painting... are you creating a painting or are you "discovering it" from the set of all paintings? Since the question does not pertain exclusively to math; if you think hard you can sort of realize that it's just philosophical speculation derived from intricacies in our language. Is anything truly created? Or is it just "discovered" from the set of all possible things? When we think about this stuff we're not actually thinking about anything profound, rather we are just examining intricacies of language and the definition of the word "discover" and "create." I mean if you think really hard and try to formalize the definition of "create" it can be said that to "create" something is to "discover" a single member from the set of all things. It can also be said to "discover" something is to "create" a new member from the set of all things. People are just getting excited over a language issue. The word "create" was never formalized and forms a sort of fuzzy overlap with "discover." Basically it's one and the same thing sort of like is the glass half full or half empty? The actual reality of this problem is uninteresting and pointless. This paradoxical-like phenomenon doesn't actually exist and arises exclusively because in our language, we have a word called "empty" and we have a word called "full." Consider the black wall. Is the wall "black" or does it lack color? Consider the flying bird. Is the bird flying or is it falling and missing the ground? Is the dark room full of darkness or is light just absent? It's all just language tricks I can "create" or "discover" an infinite amount of garbage here for you to think "profoundly" about without actually realizing it's just a language issue.

tim333 6y ago
Dunno - math seems to underlie the laws of physics and hence existence itself which is not just a language thing.
- nendroid 6y ago
  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

Dunno - math seems to underlie the laws of physics and hence existence itself which is not just a language thing.

nendroid 6y ago
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.