> Synthesis is harder than analysis

Taking this statement at face value, it means something in computer science: computing an answer (synthesis) is currently believed to be harder than checking an answer (analysis).

The simplest example to illustrate the claim is that factoring a number is harder than multiplying the two factors to check that it equals the original number, or even to decide whether the original is prime or composite (but without yielding the factors).

This also cuts to the heart of what NP means - it means that the answer to a yes/no problem about binary strings can be checked in polynomial time. It doesn't give a recipe for how to generate the answer, but it is implied that finding an answer can take up to exponential time and no more.