I would argue that some maths is discovered and some is invented. A lot of ideas used in mathematics can be found in nature and hence were discovered, the sine and exponential functions are good examples of this. Other maths is simple created either for it's own sake or to help us solve a given problem, examples of this can be found by studying abstract algebraic structures which are often used as tools for solving complex problems.
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I would argue that some maths is discovered and some is invented. A lot of ideas used in mathematics can be found in nature and hence were discovered, the sine and exponential functions are good examples of this. Other maths is simple created either for it's own sake or to help us solve a given problem, examples of this can be found by studying abstract algebraic structures which are often used as tools for solving complex problems.