Mathematics is a word with many meanings, it can mean the product of mathematicians researches, what they supposedly refer to, or the human activity of thinking about those stuff.
Considering mathematics as the set of all possible axiomatic theories, I believe it's discovered, because of its very complex structure, which is what makes mathematics interesting. Each new detail of this intricate structure (proven proposition, theorem) is something no one knew (discovered), and was not under someone's control to make it true or false (invented).
Axiomatic theories can be developed mechanically, if there were physical systems that acted as theorem-proving computers on some random place in the universe, we could say that mathematics is really about the behavior of those computers (just like biology). There is no need of thinking beings or abstractions.
The real question is, where does the mathematics structure comes from? Does it depends on computational paradigms or notational systems? Is it specified by some more fundamental system?
If the answer is that it's somehow specified by aspects we invented or control, it might be considered an invention as well, otherwise, say, "it's a consequence of some physical law concerning information and computation", it might be considered a discovery, and a very special one.
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Mathematics is a word with many meanings, it can mean the product of mathematicians researches, what they supposedly refer to, or the human activity of thinking about those stuff.
Considering mathematics as the set of all possible axiomatic theories, I believe it's discovered, because of its very complex structure, which is what makes mathematics interesting. Each new detail of this intricate structure (proven proposition, theorem) is something no one knew (discovered), and was not under someone's control to make it true or false (invented).
Axiomatic theories can be developed mechanically, if there were physical systems that acted as theorem-proving computers on some random place in the universe, we could say that mathematics is really about the behavior of those computers (just like biology). There is no need of thinking beings or abstractions.
The real question is, where does the mathematics structure comes from? Does it depends on computational paradigms or notational systems? Is it specified by some more fundamental system?
If the answer is that it's somehow specified by aspects we invented or control, it might be considered an invention as well, otherwise, say, "it's a consequence of some physical law concerning information and computation", it might be considered a discovery, and a very special one.