>>13017467What do you mean by an "unsolvable problem"? Do you mean an undecidable statement, like the continuum hypothesis, or do you mean like an algebraic equation
with no solutions? Or do you just mean a statement that isn't true?
>>13017641That doesn't answer OP's question, that just shows there isn't an algorithm that can tell you whether a Diophantine equation has a solution: Hilbert's 10th problem forbids a systematic approach that will work on all equations, but any particular equation could still be proven insoluble by ad-hoc methods, though the equation that corresponds to the continuum hypothesis cannot be shown to have solutions, nor shown to be insoluble, starting from just ZFC, since CH is undecidable. That might be the sort of thing OP was after.
