There is a solution to every problem
George Bernard Dantzig was an American mathematician, known as the father of linear programming and the inventor of the "simplex method," an algorithm for solving linear programming problems. An event in Dantzig's life became the origin of a famous urban legend in 1939, while he was a graduate student at UC Berkeley. Near the beginning of a class for which Dantzig was late, his professor wrote two examples of famously unsolved statistics problems on the blackboard. When Dantzig arrived, he was unaware of the fact that these two problems were unsolvable and assumed that the problems were a homework assignment and wrote them down.
According to Dantzig, the problems "seemed to be a little harder than usual", but a few days later he handed in completed solutions for two, still believing that they were an assignment that was overdue.
Six weeks later, Dantzig received a visit from his excited professor, eager to tell him that the homework problems he had solved were two of the most famous unsolved problems in statistics. He had prepared one of Dantzig's solutions for publication in a mathematical journal! Years later another researcher was preparing to publish a paper which arrived at a conclusion for the second problem, and included Dantzig as its co-author when he learned of the earlier solution.
If we can keep our preconceived notions behind, every unsolvable problem can have a solution!