Question

Why can more general problems — paradoxically — be easier to solve or prove? (from maths codidact)

Answer 1

Generality focuses on big picture attributes without getting bogged down in the noise of the particulars.

For example:  To prove that sqrt(x^6 + 5 sin^2 cos(x-3)) is continuous you are drawn to look at the properties of that particular function.  A lot to get bogged down in there.

 To prove that the composition of continuous functions is continuous, you focus on the relevant properties of continuity, without the noise.

Answer 2

It can be like being given a Where's Waldo where everyone's blurred out except for Waldo. (Such a picture generalizes all possible photos that disagree only in the blurred portion.)

Answer 3

3b1b’s recent cube shadow video is a fantastic look at general vs specific problem solving

Answer 4

Often the *wider* context happens to be the *natural* context of the problem.

Answer 5

Your link 404s

Answer 6

I do not think that this is true. To solve such a problem in that way you have to study how it can be generalized. And generalizations define what is important and incode implicit knowledge.
Some problems are easy because we know useful generalizations. Someone recogniced what is important to tackle certain problems, defined these properties and used them to study what these properties imply. I believe that many hard problems that we are unable to solve now are just hard, because we did not discover certain properties that lead to an useful generalization.