The following guide takes after G. Polya's writings about how a mathematician thinks. Even though the topic is logic, the discovery and solution of mathematical problems involves induction and heuristic thinking.

    1 Understand the problem
    • What is the unknown?
    • What are the data?
    • What is the condition?
    • Can the problem be solved?
    2 Assumptions
    • What can you or need you assume?
    • What shouldn't you assume?
    • Have you made subconscious assumptions?
    3 Devising a plan of attack
    • Have you seen this or a related problem before?
    • Have you seen a similar unknown before?
    • Can you restate the problem?
    • If you can't solve this problem, can you solve a similar or simpler problem?
    4 Aftermath
    • Are you sure of the solution? Can you see it at a glance?
    • Did you use all the data? the whole condition?
    • Can you get the same solution another way?
    • Are there other valid solutions?
    • Can you apply the solution or method to another problem?
    • Was this a satisfying problem to solve?
    G. Polya's Plan of Attack