The Church, guided by the Holy Spirit, would never proclaim something to be true which is untrue.
So your example is a nonsensical one. It’s untrue that popcorn is made out of buttercups, so the Church would never proclaim that to be so.
However, if the Church proclaims something to be black that I once viewed as white, then I would conform to the Church’s view and work backwards, attempting to understand why it is indeed black.
And I would invoke Cardinal Newman’s quote here again: “Ten thousand difficulties do not make one doubt, for a man may be annoyed that he cannot work out a mathematical problem, without doubting that it admits an answer.”
It is as if the professor has said, here’s the answer to this problem:
f(θ)=100(A2B3−A3B2)2−(c1B3−c2B2)2−(c2A2−c1A3)2=0,
where:
A2=3cos(θ)−5
B2=3sin(θ)
A3=3(cos(θ)−sin(θ))
B3=3(cos(θ)+sin(θ))−6
c1=p22−25−A22−B22
c2=−16−A23−B23
The answer is: “23!”
and I believe the answer is “32!”
I need to change my computations.
That’s the Catholic way. The smart way. The way to become a good mathematician.