It is not the case that for every clear cut question there is a 'good' answer: was walking on two legs discovered or invented?
Just as the perception of straight lines, edges or corners, small numbers, say, up to 5, seem to be hardwired. Practical experience has given humans a 'feeling' what is to add/subtract, that is, for example, to get from 4 to 5 or to 3. Neither form nor content was first (just like in the chicken-or-egg problem).
Measuring is a refinement of counting and Pi is the name of the attempt to measure the circumference of a circle with its diameter; it can be expressed in infinitely many ways, just as any other number.
The alternative seems more meaningful when considering more advanced mathematics: many 'inventions' from one domain are 'discovered' elsewhere (eg the Gamma function).
Lee Smolin in his Singular Universe exposes a view according to which 'mathematics is evoked', so it is neither discovered nor invented and also it is not arbitrarily phantasized.
A more sociological-historical approach would propose that mathematical objects are a specific kind of 'collective representations'. Actual people live in a society which maintains a tradition. In early times observations and thoughts are anonymously 'sedimented'. Mythological figures fullfill the expection about heroic figures, a person who has been the first inventor or discoverer. Unstated contexts and rules offer for late-comers ready-to-use quasi-objects amenable to further perfecting.