'solve' vs. 'resolve'

HyeYoon wants to know the difference between 'solve' and 'resolve.'

There's a big difference between them.

Solve implies that there is a problem or a puzzle (or a puzzle-like problem) which you are trying to work out. When you solve the problem or puzzle, you have found its solution, which is the noun derived from the verb 'to solve.' 'Solve' and 'solution' both emphasize that the problem or puzzle has been completed, but also may suggest (to my mind, anyway) some ambiguity in either that it is only one way of solving the problem, or that the solution may not be permanent, or that the solution is hypothetical and has not yet been applied to the problem. Because puzzles usually have only one solution, we usually use 'solve' when talking about them; the ambiguities arise more with problems in real life or in more complex thinking.

To resolve, when used in relation to a problem, addresses the ambiguity of 'solve.' When something is 'resolved' or there is a 'resolution', it emphasizes that the problem has been permanently (or at least durably) solved. We often talk about a resolution to conflict, which means that an answer has been reached that all parties involved are happy with, and the conflict has ended. We usually talk about solutions to the Israel-Palestine conflict because it's a complex situation with no obvious solution, and because the solutions that have been proposed are often theoretical and/or have not been applied to the situation and/or have not been long-lasting solutions.