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 human creations.
The concept of set is not a mere human invention, but an objective reality.
The world is not a mere collection of sensory experiences.
There is an objective reality to the laws of logic.
The human mind can grasp the infinite and the eternal.
The incompleteness theorems are a profound statement about the relationship between mind and matter.
The concept of truth is not a mere social construct.
The universe is not a meaningless jumble of particles.
There is a divine plan.
The human mind is not a mere epiphenomenon.
The foundations of mathematics are not arbitrary human inventions, but reflect an objective reality.
The concept of number is not a mere human convention, but an objective reality.
The world is not a mere collection of random events.
There is an objective reality to the universe.
The human mind can grasp the ultimate nature of reality.
The incompleteness theorems are a profound statement about the limits of human knowledge.
The concept of proof is not a mere game of logic.
The universe is not a meaningless void, but a meaningful cosmos.
There is a higher purpose to existence.
The human mind is not a mere product of evolution.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).