hypotheses and Galileo

I'm incredibly baffled by the role of the hypothesis according to the Church during Galileo's time. What is it's purpose? At the beginning of the reading, one of the objections to Galileo is that "he treats the issue as undecided and as if one should await rather than presuppose the resolution" (221). Throughout the trial, there is tremendous emphasis on the (apparently vast) difference between hypothesis and what Galileo did, demonstration. If you're not supposed to ever treat something as undecided but rather already "know" how the problem ends, again, what is the purpose of a hypothesis? Is it merely for the purpose of "engaging in a disputation and exercising the mind" (265)? The section on mathematics is also very interesting in its pertinence to the question of hypotheses. In response to the trials, it is stated that "Galileo promises to proceed in the manner of a mathematical hypothesis, but a mathematical hypothesis is not established by physical and necessary conclusions" (266-7). Therefore, this would seem to support the idea that thinking about the world around us and the formation of hypotheses is merely for a stretching of the mind with no intention (or possibility) of concretely proving it, like math.