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How to Solve It - G. Polya.

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The only thing I ever remember about that book is, paraphrased, if there’s a problem you can’t solve, there’s also a smaller problem you can’t solve. Find that smaller problem and solve it first.

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Sounds like a good summary, but for much broader meaning of the word “problem” that would seem from it. The book gives a list of questions designed to explore the space around your problem from many different perspectives, hopefully guiding you towards a different problem that’s easier to solve, and will contribute necessary insight or data into your main one.

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The idea is called divide and conquer.

1. 3

Divide and conquer is a specific instance of that tactic. It’s one where solving the smaller problem actually gives you part of the solution of the larger problem. But in mathematics you often solve a truly simpler version of a problem to discover a strategy to attack the larger problem. The solution to the simpler problem itself is not used any more.