The Idea

From How to Solve It (1945). Four phases: understand the problem (what is the unknown, what are the data, what is the condition), devise a plan (have you seen a related problem, could you solve part of it), carry out the plan (check each step), and look back (can you check the result, can you derive it differently, where else does the method apply).

The phases are ordinary, and that is the point. Most wasted effort comes from skipping the first one and solving the wrong question, or from skipping the last one and learning nothing from the solution. Looking back is where a solved problem turns into a method.

Why I Keep It

It structures how I model (understand the phenomenon, plan the model, implement, reflect on fit) and how I read papers (what is their question, what is their method, what generalizes). It is the counterpart to the OODA loop: Pólya for well-defined problems, OODA for shifting ones.

Tensions

• Understanding and planning blur together in practice; real problems rarely have clean phases.
• The method says nothing about when to abandon an approach.

Key Sources

• Pólya, G. (1945). How to Solve It: A New Aspect of Mathematical Method
• Schoenfeld, A. (1985). Mathematical Problem Solving