According to me, mathematics was neither discovered nor invented, but rather observed.
If you think of Mathematics as a formal documentation of formulae or proofs, then they are discovered. My definition of Mathematics includes not only documentation but also application, and application can be done without formal knowledge of mathematical theorems or proofs but by sheer observations in the surroundings.
I have seen people who can solve complex mathematical puzzles without building up equations or complex matrices, they do it just by relating problems to real-life scenarios. They can't even formulate mathematical equations but they still can get to the answer.
I am sure the Greeks "didn't" create Geometrical Algebra, they just "observed" it and documented it and started building up on their findings ("discover"ing new possibilites). And the same might have happened to Muhammad ibn Mūsā al-Khwārizmī when he wrote his famous book on Algebra.
This not only happens to mathematicians, the same theory can be extended to Physics (Sir Isaac Newton and his apple, you can't say that gravity was invented or discovered, it was and has always been there! You observe it and document your theories) and Chemistry ( John Dalton and theory of Atoms).
When you play ball, you don't calculate air resistance, the ball's rotational velocity or transitional velocity, mass, elevation, etc. You just watch it, and position yourself, intuitively based on your past and present observations.
That is the same what happened for mathematics :-)
P.S.: original answer on Quora here.