Turing reports another unexpected discovery: that of unsolvable problems. These are problems that are well defined with unique answers that can be shown to exist, but that we can also prove can never be computed by any Turing machine—that is to say, by any machine, a reversal of what had been a nineteenth-century dogma that problems that could be defined would ultimately be solved. Turing showed that there are as many unsolvable problems as solvable ones.
