<< Heron might have taken the square root of a negative number and thus DISCOVERED the imaginary numbers and soon the field of complex numbers. Were they entities that pre-existed so that they could be discovered by the one with the sharpest vision? Were they instead entities to be brought into being by someone who realized that they could be postulated without leading to contradiction? Or what? >>
It depends on what you believe the foundations of mathematics are like. Cf. Platonists vs formalists vs intuitionists vs empiricists vs ..... What if all of them are to some extent right, and to some extent wrong?
And, it appears that Goedel, to take an example, was a declared Platonist, but some logicians of note rejected Platonism of various kinds? Does belief or disbelief in some sort of Platonism in which one "discovers" what already somehow "existed" before discovery, and perhaps "exists eternally," somehow time-independently -- do differing beliefs in this matter affect what logicians, who take a stand on discovery versus invention, in some dichotomous way, do when they "do" logic? If so, how?