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