Mathematician-logician Kurt Godel (1906-1978) in 1931 proved that within a formal system questions exist that are neither provable nor disprovable on the basis of the axioms of that system.
This is known as "Godel's Undecidability Theorem" or "Incompleteness Theorem".
He showed that there are problems that cannot be solved by any set of rules or procedures because this would always require a higher set of rules.
Godel's theorem has direct relevance for information theory and mathematical reasoning and is of great importance in complex systems.