Kurt Gödel
Proved incompleteness theorems transforming mathematical logic
Most quoted
"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."
— from On Formally Undecidable Propositions of Principia Mathematica and Related Systems, 1931
"Either mathematics is incompletable in this sense, that its evident axioms can never be exhausted by a finite number of formal rules, or else there exist mathematical problems which are undecidable in principle."
— from On Formally Undecidable Propositions of Principia Mathematica and Related Systems I, 1931
"The incompleteness theorems are a profound statement about the limits of formal systems and the indispensable role of human intuition and insight in mathematics."
— from On Formally Undecidable Propositions of Principia Mathematica and Related Systems I, 1931
All quotes by Kurt Gödel (527)
The foundations of mathematics are not arbitrary fictions.
The concept of set is not a mere linguistic construct.
The world is not an illusion.
There is an absolute truth in mathematics.
The human mind can grasp the essence of things.
The incompleteness theorems are a profound statement about the nature of knowledge.
The concept of truth is not subjective.
The universe is not a meaningless void.
There is a spiritual dimension to reality.
The human mind is not a blank slate.
The foundations of mathematics are not arbitrary inventions.
The concept of number is not a cultural artifact.
The world is not a construct of our minds.
There is an objective reality to logic.
The human mind can reach for the divine.
The incompleteness theorems are a challenge to our understanding of the universe.
The concept of proof is not a mere formality.
The universe is not a closed box.
There is a transcendent reality.
The human mind is not limited by the physical world.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).