The fact that a problem has not been solved yet does not mean that it can't be. It implies only that it may take time and the problem is difficult. A very good example is Pascal's Last Theorem. This stated that you could not find three integer numbers, A, B and C, such that the sum of A raised to a power of N plus B raised to that power would equal C raised to N, for any N greater than 2.
Everybody knew you couldn't find them, but nobody could prove it. It took two centuries before this problem was solve. Before that happened, many people were saying that it couldn't be solved.
In conclusion, a problem may not be solved yet, it does not mean that it can't be solved - it just may take time.