Kurt Gödel stunned the mathematical world in 1931 by proving that it is impossible to find a consistent mathematical system that will allow all possible truths to be decided. This is called the
incompleteness Theorem.
Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F.
The incompleteness theorem of
Kurt Gödel (Austrian logician, mathematician, philosopher) says that, for any formal proof system that includes arithmetic, there exist true statements that cannot be proven within the system. Part of Gödel's motivation was the belief that
there is no finite description of truth. That is, truth is infinite.