how they know the solution is right?

there is an unsolved problem, hundreds and thousands of ppl can not solve and they have to wait that one day someone comes and finds a solution for that problem.

and here is the part that i always try to understand as a non mathematician:

he finds the solution and everyone can say
"yes that's right" or "no, that's wrong".

how can they say it is right, when they weren't even able to solve it or how can they know it is wrong, when they couldn't even solve it themselves?

i mean obviously there is a problem noone can solve. if that's the case noone besides the problemsolver should be able to say anything about the solution.

am i missing something here?

Author: princepii