I was in class the other day, and I was suddenly concerned with the idea that some methods don't work for solving certain problems. I'm working on integration right now, so some of the problem solving methods that I'm talking about involve integration by parts, u-substitution, trigonometric substitution, among others.
The fact that we hit road blocks if we tackle a certain problem with a certain method seems strange to me. If there is a solution to the problem, and granted your methods aren't so off track as though we were trying to integrate by differentiating or something, or in other words that you are using a method that fits the type of problem, why shouldn't all of them work? I can see that some of them will save time, but certainly all should be able to solve them eventually.
If the solution is there, shouldn't the mathematics be able to reveal it by any of its appropriate means?
Any advice on tagging is appreciated.