Obsessive thinking about an a problem has never fixed anything. Obsessive analysis = paralysis.
There are correct decisions both in mathematics and in life. You don't say 2+2=3 because you are afraid. You don't pronounce that a problem unsolvable just because it's difficult.
The basic reason of doing addition or multiplication correctly is not to get an end result. It is because it's the correct way to do it.
Similarly in life one doesn't do something correctly for a result, when everyone else is obviously abusing intelligence. One does something correctly because it is correct, in accordance with fact or truth.