The Idea

Pólya: “the more ambitious plan may have more chances of success.” When you are stuck on a specific problem, solving a more general version of it can be easier. Proving that √2 is irrational invites symbol-pushing; proving that √p is irrational for any prime forces you to see what actually makes the argument work. The specific case falls out as a corollary.

It works because generalizing forces you to separate what is essential from what is incidental, and because a general problem cannot be attacked with ad-hoc tricks, so you have to find the structure. It also breaks fixation: a specific problem can trap you in an unproductive framing.

Why I Keep It

When a model fails I try to ask “what class of models would handle this structure” instead of endlessly tweaking parameters. Same in debugging: build the general diagnostic rather than patch the specific bug. It pairs with the social science paradox, which runs the other way (go deep into specifics to earn general claims); one is for problem-solving, the other for inference.

Tensions

• More general can also mean more complex. The art is finding the right level of generality, and nothing in the principle tells you where that is.
• Generalizing can be an avoidance strategy: a way of not facing the hard specifics.

Key Sources

• Pólya, G. (1945). How to Solve It: A New Aspect of Mathematical Method
• Lakatos, I. (1976). Proofs and Refutations