The two results are widely , but not universally , interpreted as showing that Hilbert 's program to find a complete and consistent set of axioms for all mathematics is impossible , giving a negative answer to Hilbert 's second problem .
Gödel said that every non-trivial formal system is either incomplete or inconsistent : Most people think this shows that Hilbert 's program to find a complete and consistent set of axioms for all of mathematics is impossible .