On problem solving ...

Professor Bob Palais has written an interesting article on problem solving. His arguments are not only motivating, but also enlightening. They make you believe that it is belief that you will be able to solve the problem that plays a major role in actually solving it.

You may wonder if you have the capability to solve it. But here is a simple trick that should help. It has helped me. Let us say you tried (for some time) to solve the problem and got nowhere. Then you read the solution or someone tells it to you. Now, ask yourself if you are able to understand the solution and how it solves the problem. If you really understood the solution, my argument is that you are (and were always) in a position to solve it all by yourself. It is not a silver bullet, but something that has worked for me. Of course, the concentration (that problem solving itself requires) is a must.

My argument can be supported (not proved) thus. If one is not able to understand the solution to a problem, we know that it can be concluded that he or she would not have been able to solve the problem. For example, I don't understand the Theory of Relativity yet and that is evident only because I don't understand the solutions to most of the problems in it.

I understand that converse is not true, but I am not proving anything anyway.