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 inventions, but reflect an objective reality of abstract mathematical structures.
The concept of set is not a mere human invention, but an objective reality of abstract mathematical structures.
The world is not a mere collection of random data, but a coherent and meaningful whole.
There is an objective reality to the universe's laws.
The human mind can grasp the ultimate truths.
The incompleteness theorems are a profound statement about the limits of algorithmic thinking.
The concept of truth is not a mere human construct, but an objective reality that transcends human understanding.
The universe is not a meaningless void, but a cosmos with inherent order, purpose, and meaning.
There is a higher power that governs the universe.
The human mind is not a mere machine, but possesses a non-physical aspect.
The foundations of mathematics are not arbitrary human inventions, but reflect an objective reality of abstract mathematical structures and principles.
The concept of number is not a mere human convention, but an objective reality of abstract mathematical structures and principles.
The world is not a mere collection of random phenomena, but a coherent and meaningful whole governed by underlying laws.
There is an objective reality to the fundamental principles of the universe.
The human mind can grasp the ultimate meaning of existence and the universe.
The incompleteness theorems are a profound statement about the limits of formal systems and the power of human intuition.
The concept of proof is not a mere formal manipulation, but a means to discover and establish objective truths.
The universe is not a meaningless void, but a cosmos with inherent order, purpose, meaning, and a spiritual dimension.
There is a divine presence in the universe.
The human mind is not a mere biological machine, but possesses a non-physical, spiritual aspect.
Contemporaries of Kurt Gödel
Other Mathematicss born within 50 years of Kurt Gödel (1906–1978).