> Sometimes, amazingly, the more general problem is easier to solve, perhaps because fewer irrelevant details stand in the way. True, and that's why we like to

> Sometimes, amazingly, the more general problem is easier to solve, perhaps because fewer irrelevant details stand in the way. True, and that's why we like to generalize things. It's usually easier to prove a mathematical object belongs to another class of structure which has certain properties than to prove the object itself has all those properties. Of course as you've noted it's not always like that at all. It's significantly easier to prove many things about finite-dimensional vector spaces over fields versus infinite-dimensional modules over rings. Solving mathematical problems is a lot like working a sponge. It's often useful to alternate between expanding and contracting the scope of your problem.