There are several important axiomatic properties about problems in mathematics.

• Unless you solved your problem, it is hard to know how difficult the problem is.
  • Without the correct tool, a problem can be impossible to solve.
  • Everyone is trying hard to use their favorite tools.
  • People are arrogant. People have a tendency to keep trying their favorite tool until it just fails miserably.

Then, we have several corollary

• Be humble. You should never naively think the tool you had just happens to be the solution to the problem.
• Understand your tool well!!! Given a tool, you should understand what kinds of obstacle for this kind of tool and what kinds of counterexamples you should keep in mind.

This is my current thought, subject to future addition.