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 constructions, but reflect an objective reality of abstract entities.
The concept of set is not a mere human invention, but an objective reality of abstract entities.
The world is not a mere collection of physical objects.
There is an objective reality to mathematical structures.
The human mind can grasp the essence of mathematical truth.
The incompleteness theorems are a profound statement about the nature of formal reasoning.
The concept of truth is not a mere human construct, but an objective reality.
The universe is not a meaningless void, but a cosmos with inherent meaning.
There is a higher reality beyond the physical world.
The human mind is not a mere biological computer.
The foundations of mathematics are not arbitrary human inventions, but reflect an objective reality of abstract mathematical objects.
The concept of number is not a mere human convention, but an objective reality of abstract mathematical objects.
The world is not a mere collection of physical phenomena.
There is an objective reality to the principles of logic.
The human mind can grasp the transcendental.
The incompleteness theorems are a profound statement about the limits of purely mechanical reasoning.
The concept of proof is not a mere formal manipulation, but a means to discover truth.
The universe is not a meaningless void, but a cosmos with inherent order and purpose.
There is a divine intelligence behind the universe.
The human mind is not a mere physical system.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).