Both are correct. Grammatically as well as in their meaning.
However, the two versions differ in their meaning.
The answer to big problems is always small solutions.
--> The answer to the (question of) big problems is always (the class of) small solutions, a generalization. (The precedent reference of is being the implied "the question of," or something of that sort.)
The answers to big problems are always small solutions.
--> Each big problem has its own small solution; applies uniformly across problems.
The first sentence structure may sound confusing to a reader not familiar with the usage.