Thinking books · Problem solving · George Pólya, 1945
How to Solve It — the big ideas
A mathematician’s general method for problems you do not immediately know how to solve.
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The big ideas
The four steps — understand, plan, carry out, look back — are simple enough to be dismissed and are skipped almost every time. Most failures happen at step one.
Understanding a problem means naming the unknown, the data, and the condition connecting them. Being unable to state those is itself the diagnosis.
Its heuristics are transferable: solve an easier version, solve a part, work backwards from the goal, find a related problem you have already solved, vary the problem.
Looking back is the step that produces transferable skill rather than a solved instance, and it is the step nobody has time for.
Practise it — no need to have read it
Take a problem you are stuck on. State the unknown, the data, and the condition connecting them — in that order, before planning anything.
A hint: If you cannot state the unknown precisely, that is the problem you are actually facing.
Where it shows up in real life
- Any technical problem
- Planning a project
- Getting unstuck on anything
Described in our own words with the source named — never quoted, and not a substitute for reading the book.
Thinking methods from this book
- The four steps — A general procedure for any problem you do not immediately know how to solve.
- Work backwards — Start from the outcome you want and ask what would have to be true immediately before it.
The thinking it builds
- Problem Solving — Break complex problems into manageable parts