Problems are inevitable because the search for Good Explanations will create new problems and our Knowledge will always be incomplete.
Some problems are hard, but it is a mistake to confuse hard problems with problems that can't be solved.
All problems are soluble given the right knowledge, limited only by the laws of physics.
Edison famously said that genius is 1% inspiration and 99% perspiration. But once a problem has been solved and a Technology created, the perspiration aspect is automated.