The Trial of Galileo

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         It would be quite a difficult task to convince the philosopher and mathematician to accept Galileo's findings. First of all, the philosopher and mathematician are both experts in their fields, and the knowledge of their fields directly competes with Galileo's findings. The philosopher believes full-heartedly in everything spoken by Aristotle, and as a species, we know how emotionally attached we are to something we believe in. But, if i had to convince the philosopher and mathematician to accept Galileo's findings for the sake of the benefit and growth of human society, I would first start by trying to convince the mathematician.
      If I were Galileo, I would find my own mathematician buddy to help me with my project. To convince the other mathematician, we would come up with mathematical formulas and reasons for the stars being where they are, and show the mathematician how the calculations match the real data. A mathematician is more likely to believe something if it involves a field that he is not only familiar with, but an expert in. Once I convinced the mathematician with my reason and proofs, the mathematician would help to convince the philosopher.
      The philosopher would be really hard to convince, even if I had the mathematician's help. Like I said before, he is an expert in his field, and his field directly contradicts what Galileo is saying. I would start by convincing him that the telescope isn't fake by first allowing him to look at the lens (which wouldn't have drawings on it) and then if that didn't work, by allowing him to take the telescope apart and put it back together on his own. Then, I would try to prove to him that all of Aristotle's findings are not 100% correct. Aristotle lived years and years ago in a time without as advanced technology. I would explain to the philosopher how far as a species we have come since then, and all of the new things we have learned (along with all of the old things we have proved wrong.) These things would not even have to be related to astronomy. Once I got the philosopher to see that 1) the mathematician was on my side 2) the telescope was not fake and 3) we have developed a lot since Aristotle, and Aristotle made predictions in a time without technology, I believe that that would be enough to let the philosopher explore outside his paradigm, and look into the telescope. Once he looked in the telescope, then the philosopher may choose to abandon his paradigm.
All of this of course would be quite a difficult task.