Someone left a nodeshell here. All right, I'll bite.
This was the title of Kurt Gödel
's famous paper where he proved that any finite formal system
of sufficient power to be meaningful necessarily contains "undecidable propositions", that is, well-formed
formulas for which a proof
of truth or falsity could not be generated using the system in question. See Also: Gödel's Incompleteness Theorem
This paper dashed the hopes of the formalists
, led by David Hilbert
, who thought all mathematics
could be brought under a program of formal systems. Principia Mathematica
was the mammoth attempt by Bertrand Russell
and Alfred North Whitehead
to do just that.