According to Tom Mueller the questions the fathers of Florence asked were, “Could a dome weighing tens of thousands of tons stay up without them? Was there enough timber in Tuscany for the scaffolding and templates that would be needed to shape the dome's masonry? And could a dome be built at all on the octagonal floor plan dictated by the existing walls -- eight pie-shaped wedges -- without collapsing inward as the masonry arced toward the apex?”
The significance of the discovery of his out of the box thinking is that Brunelleschi was
able to take what he knew from the past and incorporate into what he was trying to create in the present. He created two domes one inside the other. The outer dome was heavier and protected the church from the elements and the inside dome was made with lightweight materials. Inside both of the domes are oak timber ring and rib supports. Brunelleschi was able to take what he learned from the early architects in Rome and use techniques that had been forgotten.
The discovery relied on the work of others because without the history of Rome and the refugees that traveled from Greece to Rome there would be no interest in the Parthenon. I think Brunelleschi was influenced by the techniques the Greek used with their arches and support system.